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scyther-proof 0.5.0.0 → 0.6.0.0

raw patch · 45 files changed

+20327/−18884 lines, 45 files

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@@ -1,3 +1,8 @@+* 0.6.0.0+    - ported to Isabelle-2013 by Andreas Lochbihler+    - removed buggy isabelle timout support+    - tested compilation on GHC 7.4.2+ * 0.5.0.0     - implemented proof generation for injective agreement     - fixed bug in unification of inverse-key constructors
README.md view
@@ -1,10 +1,9 @@ README: The scyther-proof security protocol verification tool ============================================================= -Author: Simon Meier <simon.meier@inf.ethz.ch>--Creation Date: 13/05/2011  --  Last Updated:  28/06/2012-+Authors: Simon Meier <iridcode@gmail.com>+Creation Date: 2011-05-13+Last Updated:  2013-02-27 by Andreas Lochbihler <andreas.lochbihler@inf.ethz.ch>  1. Introduction ===============@@ -56,42 +55,48 @@ 2.2 Installing the Isabelle/HOL theories ---------------------------------------- -Download and install full Isabelle2009-1 according to the installation+Download and install full Isabelle2013 according to the installation instructions at -    http://isabelle.in.tum.de/website-Isabelle2009-1/download_x86-linux.html+    http://isabelle.in.tum.de/website-Isabelle2013/download_x86-linux.html  The first time you call `scyther-proof` with the `--isabelle` flag it will build the logic image of the Isabelle/HOL theories formalizing the security protocol verification theory underlying `scyther-proof`. -For enabling interactive processing of theory files based using our-extensions to Isabelle's ISAR proof language use one of the following two-variants.+If you wish to use ProofGeneral to interactively process the theory files+using our extensions to Isabelle's ISAR proof language, use one of the+following two variants. This is needed in order to make the new ISAR keywords+`role`, `protocol`, `sources`, and `prefix_close` available in the Emacs+frontend. If you are using the Isabelle/jEdit Prover IDE, the keywords are+automatically registered. + Variant a: Brute Force ---------------------- -Overwrite the standard Emacs keywords file+Copy the Emacs keywords file provided with the ESPL distribution at -    $ISABELLE_HOME/etc/isar-keywords.el+    $SCYTHER_PROOF_HOME/data/isabelle/src/isar-keywords.el -with the Emacs keywords file provided with the ESPL distribution.+to your local Isabelle configuration in -    $SCYTHER_PROOF_HOME/isabelle/src/isar-keywords.el+    $ISABELLE_HOME_USER/etc -This is needed in order to make the new ISAR keywords `role`,-`protocol`, `sources`, and `prefix_close` available in the Emacs-frontend.+This will replace any custom keyword file that you have already+installed in that way. You can find out about $ISABELLE_HOME_USER+by running +    isabelle getenv ISABELLE_HOME_USER + Variant b: Elegance -------------------  A more elegant way is to copy the keywords file provided with our distribution to -    $ISABELLE_HOME/etc/isar-keywords-ESPL.el+    $ISABELLE_HOME_USER/etc/isar-keywords-ESPL.el  and start Isabelle using the -k switch as follows. @@ -104,7 +109,7 @@   3.1 scyther-proof-------------+-----------------     Usage Example@@ -120,15 +125,13 @@   all specified security properties together with the proof with the fewest   number of chain rule applications to stdout. -  In order to generate an Isabelle proof script two additional options need to-  be added+  To generate an Isabelle proof script, two additional options are required.      scyther-proof $EXAMPLE_DIR/classic/NS_Public.spthy --shortest --output=nsl_cert.thy --ASCII    The first one specifies the output file and the second one instructs   scyther-proof to use Isabelle's ASCII notation as the output format. -   To build the source code documentation you can use the call      cabal configure; cabal haddock@@ -141,25 +144,40 @@ 3.2 The Isabelle/HOL theories ----------------------------- +   Note that in many case the easiest way to start with constructing+   machine-checked proofs interactively is to use a proof script generated by+   scyther-proof.++   Using ProofGeneral+   ------------------+    In the directory output by scyther-proof, load the Tutorial on interactive    proof construction using the following commands          cd <theory-dir-output-by-scytherproof>/src         isabelle emacs Tutorial.thy -    or if you've chosen the elegant variant+    or if you've chosen the elegant variant for the keywords file          isabelle emacs -k ESPL Tutorial.thy -   Note that in many case the easiest way to start with constructing-   machine-checked proofs interactively is to use a proof script generated by-   scyther-proof. +   Using the Isabelle/jEdit Prover IDE+   ----------------------------------- +   In the directory output by scyther-proof, load the Tutorial on interactive+   proof construction using the following commands++        cd <theory-dir-output-by-scytherproof>/src+        isabelle jedit -d $SCYTHER_PROOF_HOME/data/isabelle -l ESPL Tutorial.thy++   where $SCYTHER_PROOF_HOME expands to the home directory of scyther-proof.++ ***  `Happy Proving :)` -In case of questions do not hesistate to contact me at+In case of questions do not hesistate to contact Simon Meier at iridcode@gmail.com.
data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-2-bdkey_cert_auto.thy view
@@ -1,3214 +1,3514 @@ theory "isoiec-9798-2-bdkey_cert_auto" imports-  "../ESPLogic"-begin--role isoiec_9798_2_1_bdkey_A-where "isoiec_9798_2_1_bdkey_A =-  [ Send ''leak_A'' ( sN ''TNA'' )-  , Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>-  , Send ''1'' <| sAV ''A'', sAV ''B'', sMV ''Text2'',-                  PEnc <| sC ''isoiec_9798_2_1_enc_1'', sN ''TNA'', sAV ''B'',-                          sMV ''Text1''-                       |>-                       ( sKbd (AVar ''A'') (AVar ''B'') )-               |>-  ]"--role isoiec_9798_2_1_bdkey_B-where "isoiec_9798_2_1_bdkey_B =-  [ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Text2'',-                  PEnc <| sC ''isoiec_9798_2_1_enc_1'', sMV ''TNA'', sAV ''B'',-                          sMV ''Text1''-                       |>-                       ( sKbd (MVar ''A'') (AVar ''B'') )-               |>-  ]"--role isoiec_9798_2_2_bdkey_A-where "isoiec_9798_2_2_bdkey_A =-  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''RB'', sMV ''Text1'' |>-  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>-  , Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'',-                  PEnc <| sC ''isoiec_9798_2_2_enc_2'', sMV ''RB'', sMV ''B'',-                          sMV ''Text2''-                       |>-                       ( sKbd (MVar ''B'') (AVar ''A'') )-               |>-  ]"--role isoiec_9798_2_2_bdkey_B-where "isoiec_9798_2_2_bdkey_B =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''RB'', sMV ''Text1'' |>-  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'',-                  PEnc <| sC ''isoiec_9798_2_2_enc_2'', sN ''RB'', sAV ''B'', sMV ''Text2''-                       |>-                       ( sKbd (AVar ''B'') (AVar ''A'') )-               |>-  ]"--role isoiec_9798_2_3_bdkey_A-where "isoiec_9798_2_3_bdkey_A =-  [ Send ''leak_A'' ( sN ''TNA'' )-  , Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>-  , Send ''1'' <| sAV ''A'', sAV ''B'', sMV ''Text2'',-                  PEnc <| sC ''isoiec_9798_2_3_enc_1'', sN ''TNA'', sAV ''B'',-                          sMV ''Text1''-                       |>-                       ( sKbd (AVar ''A'') (AVar ''B'') )-               |>-  , Recv ''2'' <| sAV ''B'', sAV ''A'', sMV ''Text4'',-                  PEnc <| sC ''isoiec_9798_2_3_enc_2'', sMV ''TNB'', sAV ''A'',-                          sMV ''Text3''-                       |>-                       ( sKbd (AVar ''B'') (AVar ''A'') )-               |>-  ]"--role isoiec_9798_2_3_bdkey_B-where "isoiec_9798_2_3_bdkey_B =-  [ Send ''leak_B'' ( sN ''TNB'' )-  , Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Text2'',-                  PEnc <| sC ''isoiec_9798_2_3_enc_1'', sMV ''TNA'', sAV ''B'',-                          sMV ''Text1''-                       |>-                       ( sKbd (MVar ''A'') (AVar ''B'') )-               |>-  , Recv ''text_2'' <| sMV ''Text3'', sMV ''Text4'' |>-  , Send ''2'' <| sAV ''B'', sMV ''A'', sMV ''Text4'',-                  PEnc <| sC ''isoiec_9798_2_3_enc_2'', sN ''TNB'', sMV ''A'',-                          sMV ''Text3''-                       |>-                       ( sKbd (AVar ''B'') (MVar ''A'') )-               |>-  ]"--role isoiec_9798_2_4_bdkey_A-where "isoiec_9798_2_4_bdkey_A =-  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''RB'', sMV ''Text1'' |>-  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>-  , Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'',-                  PEnc <| sC ''isoiec_9798_2_4_enc_1'', sN ''RA'', sMV ''RB'', sMV ''B'',-                          sMV ''Text2''-                       |>-                       ( sKbd (AVar ''A'') (MVar ''B'') )-               |>-  , Recv ''3'' <| sMV ''B'', sAV ''A'', sMV ''Text5'',-                  PEnc <| sC ''isoiec_9798_2_4_enc_2'', sMV ''RB'', sN ''RA'',-                          sMV ''Text4''-                       |>-                       ( sKbd (AVar ''A'') (MVar ''B'') )-               |>-  ]"--role isoiec_9798_2_4_bdkey_B-where "isoiec_9798_2_4_bdkey_B =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''RB'', sMV ''Text1'' |>-  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'',-                  PEnc <| sC ''isoiec_9798_2_4_enc_1'', sMV ''RA'', sN ''RB'', sAV ''B'',-                          sMV ''Text2''-                       |>-                       ( sKbd (AVar ''A'') (AVar ''B'') )-               |>-  , Recv ''text_3'' <| sMV ''Text4'', sMV ''Text5'' |>-  , Send ''3'' <| sAV ''B'', sAV ''A'', sMV ''Text5'',-                  PEnc <| sC ''isoiec_9798_2_4_enc_2'', sN ''RB'', sMV ''RA'',-                          sMV ''Text4''-                       |>-                       ( sKbd (AVar ''A'') (AVar ''B'') )-               |>-  ]"--role isoiec_9798_2_5_bdkey_A-where "isoiec_9798_2_5_bdkey_A =-  [ Send ''leak_A'' <| sN ''TVPa'', sN ''TNa'' |>-  , Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''A'', sAV ''P'', sN ''TVPa'', sAV ''B'',-                  sMV ''Text1''-               |>-  , Recv ''2'' <| sAV ''P'', sAV ''A'', sMV ''Text4'',-                  PEnc <| sC ''isoiec_9798_2_5_enc_2_1'', sN ''TVPa'', sMV ''Kab'',-                          sAV ''A'', sAV ''B'', sMV ''Text3''-                       |>-                       ( sKbd (AVar ''A'') (AVar ''P'') ),-                  sMV ''TokenPA_for_B''-               |>-  , Recv ''text_3'' <| sMV ''Text5'', sMV ''Text6'' |>-  , Send ''3'' <| sAV ''A'', sAV ''B'', sMV ''Text6'', sAV ''P'',-                  sMV ''TokenPA_for_B'',-                  PEnc <| sC ''isoiec_9798_2_5_enc_3'', sN ''TNa'', sAV ''B'',-                          sMV ''Text5''-                       |>-                       ( sMV ''Kab'' )-               |>-  , Recv ''4'' <| sAV ''B'', sAV ''A'', sMV ''Text8'',-                  PEnc <| sC ''isoiec_9798_2_5_enc_4'', sMV ''TNb'', sAV ''A'',-                          sMV ''Text7''-                       |>-                       ( sMV ''Kab'' )-               |>-  ]"--role isoiec_9798_2_5_bdkey_B-where "isoiec_9798_2_5_bdkey_B =-  [ Send ''leak_B'' ( sN ''TNb'' )-  , Recv ''3'' <| sMV ''A'', sAV ''B'', sMV ''Text6'', sMV ''P'',-                  PEnc <| sC ''isoiec_9798_2_5_enc_2_2'', sMV ''TNp'', sMV ''Kab'',-                          sMV ''A'', sAV ''B'', sMV ''Text2''-                       |>-                       ( sKbd (AVar ''B'') (MVar ''P'') ),-                  PEnc <| sC ''isoiec_9798_2_5_enc_3'', sMV ''TNa'', sAV ''B'',-                          sMV ''Text5''-                       |>-                       ( sMV ''Kab'' )-               |>-  , Recv ''text_4'' <| sMV ''Text7'', sMV ''Text8'' |>-  , Send ''4'' <| sAV ''B'', sMV ''A'', sMV ''Text8'',-                  PEnc <| sC ''isoiec_9798_2_5_enc_4'', sN ''TNb'', sMV ''A'',-                          sMV ''Text7''-                       |>-                       ( sMV ''Kab'' )-               |>-  ]"--role isoiec_9798_2_5_bdkey_P-where "isoiec_9798_2_5_bdkey_P =-  [ Send ''leak_P'' ( sN ''TNp'' )-  , Recv ''1'' <| sMV ''A'', sAV ''P'', sMV ''TVPa'', sMV ''B'',-                  sMV ''Text1''-               |>-  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'', sMV ''Text4'' |>-  , Send ''2'' <| sAV ''P'', sMV ''A'', sMV ''Text4'',-                  PEnc <| sC ''isoiec_9798_2_5_enc_2_1'', sMV ''TVPa'', sN ''Kab'',-                          sMV ''A'', sMV ''B'', sMV ''Text3''-                       |>-                       ( sKbd (MVar ''A'') (AVar ''P'') ),-                  PEnc <| sC ''isoiec_9798_2_5_enc_2_2'', sN ''TNp'', sN ''Kab'',-                          sMV ''A'', sMV ''B'', sMV ''Text2''-                       |>-                       ( sKbd (MVar ''B'') (AVar ''P'') )-               |>-  ]"--role isoiec_9798_2_6_bdkey_A-where "isoiec_9798_2_6_bdkey_A =-  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>-  , Recv ''text_2'' ( sMV ''Text2'' )-  , Send ''2'' <| sAV ''A'', sAV ''P'', sN ''Ra'', sMV ''Rb'', sMV ''B'',-                  sMV ''Text2''-               |>-  , Recv ''3'' <| sAV ''P'', sAV ''A'', sMV ''Text5'',-                  PEnc <| sC ''isoiec_9798_2_6_enc_3_1'', sN ''Ra'', sMV ''Kab'',-                          sAV ''A'', sMV ''B'', sMV ''Text4''-                       |>-                       ( sKbd (AVar ''A'') (AVar ''P'') ),-                  sMV ''TokenPA_for_B''-               |>-  , Recv ''text_4'' <| sMV ''Text6'', sMV ''Text7'' |>-  , Send ''4'' <| sAV ''A'', sMV ''B'', sMV ''Text7'', sAV ''P'',-                  sMV ''TokenPA_for_B'',-                  PEnc <| sC ''isoiec_9798_2_6_enc_4'', sN ''Rpa'', sMV ''Rb'',-                          sMV ''Text6''-                       |>-                       ( sMV ''Kab'' )-               |>-  , Recv ''5'' <| sMV ''B'', sAV ''A'', sMV ''Text9'',-                  PEnc <| sC ''isoiec_9798_2_6_enc_5'', sMV ''Rb'', sN ''Rpa'',-                          sMV ''Text8''-                       |>-                       ( sMV ''Kab'' )-               |>-  ]"--role isoiec_9798_2_6_bdkey_B-where "isoiec_9798_2_6_bdkey_B =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>-  , Recv ''4'' <| sAV ''A'', sAV ''B'', sMV ''Text7'', sMV ''P'',-                  PEnc <| sC ''isoiec_9798_2_6_enc_3_2'', sN ''Rb'', sMV ''Kab'',-                          sAV ''A'', sAV ''B'', sMV ''Text3''-                       |>-                       ( sKbd (AVar ''B'') (MVar ''P'') ),-                  PEnc <| sC ''isoiec_9798_2_6_enc_4'', sMV ''Rpa'', sN ''Rb'',-                          sMV ''Text6''-                       |>-                       ( sMV ''Kab'' )-               |>-  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>-  , Send ''5'' <| sAV ''B'', sAV ''A'', sMV ''Text9'',-                  PEnc <| sC ''isoiec_9798_2_6_enc_5'', sN ''Rb'', sMV ''Rpa'',-                          sMV ''Text8''-                       |>-                       ( sMV ''Kab'' )-               |>-  ]"--role isoiec_9798_2_6_bdkey_P-where "isoiec_9798_2_6_bdkey_P =-  [ Recv ''2'' <| sMV ''A'', sAV ''P'', sMV ''Ra'', sMV ''Rb'', sMV ''B'',-                  sMV ''Text2''-               |>-  , Recv ''text_3'' <| sMV ''Text3'', sMV ''Text4'', sMV ''Text5'' |>-  , Send ''3'' <| sAV ''P'', sMV ''A'', sMV ''Text5'',-                  PEnc <| sC ''isoiec_9798_2_6_enc_3_1'', sMV ''Ra'', sN ''Kab'',-                          sMV ''A'', sMV ''B'', sMV ''Text4''-                       |>-                       ( sKbd (MVar ''A'') (AVar ''P'') ),-                  PEnc <| sC ''isoiec_9798_2_6_enc_3_2'', sMV ''Rb'', sN ''Kab'',-                          sMV ''A'', sMV ''B'', sMV ''Text3''-                       |>-                       ( sKbd (MVar ''B'') (AVar ''P'') )-               |>-  ]"--role isoiec_9798_2_5_special_TTP_bdkey_A-where "isoiec_9798_2_5_special_TTP_bdkey_A =-  [ Send ''leak_A'' <| sN ''TVPa'', sN ''TNa'' |>-  , Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''A'', sAV ''P'', sN ''TVPa'', sAV ''B'',-                  sMV ''Text1''-               |>-  , Recv ''2'' <| sAV ''P'', sAV ''A'', sMV ''Text4'',-                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_2_1'', sN ''TVPa'',-                          sMV ''Kab'', sAV ''B'', sMV ''Text3''-                       |>-                       ( sKbd (AVar ''A'') (AVar ''P'') ),-                  sMV ''TokenPA_for_B''-               |>-  , Recv ''text_3'' <| sMV ''Text5'', sMV ''Text6'' |>-  , Send ''3'' <| sAV ''A'', sAV ''B'', sMV ''Text6'', sAV ''P'',-                  sMV ''TokenPA_for_B'',-                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_3'', sN ''TNa'', sAV ''B'',-                          sMV ''Text5''-                       |>-                       ( sMV ''Kab'' )-               |>-  , Recv ''4'' <| sAV ''B'', sAV ''A'', sMV ''Text8'',-                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_4'', sMV ''TNb'', sAV ''A'',-                          sMV ''Text7''-                       |>-                       ( sMV ''Kab'' )-               |>-  ]"--role isoiec_9798_2_5_special_TTP_bdkey_B-where "isoiec_9798_2_5_special_TTP_bdkey_B =-  [ Send ''leak_B'' ( sN ''TNb'' )-  , Recv ''3'' <| sMV ''A'', sAV ''B'', sMV ''Text6'', sMV ''P'',-                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_2_2'', sMV ''TNp'',-                          sMV ''Kab'', sMV ''A'', sMV ''Text2''-                       |>-                       ( sKbd (AVar ''B'') (MVar ''P'') ),-                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_3'', sMV ''TNa'', sAV ''B'',-                          sMV ''Text5''-                       |>-                       ( sMV ''Kab'' )-               |>-  , Recv ''text_4'' <| sMV ''Text7'', sMV ''Text8'' |>-  , Send ''4'' <| sAV ''B'', sMV ''A'', sMV ''Text8'',-                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_4'', sN ''TNb'', sMV ''A'',-                          sMV ''Text7''-                       |>-                       ( sMV ''Kab'' )-               |>-  ]"--role isoiec_9798_2_5_special_TTP_bdkey_P-where "isoiec_9798_2_5_special_TTP_bdkey_P =-  [ Send ''leak_P'' ( sN ''TNp'' )-  , Recv ''1'' <| sMV ''A'', sAV ''P'', sMV ''TVPa'', sMV ''B'',-                  sMV ''Text1''-               |>-  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'', sMV ''Text4'' |>-  , Send ''2'' <| sAV ''P'', sMV ''A'', sMV ''Text4'',-                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_2_1'', sMV ''TVPa'',-                          sN ''Kab'', sMV ''B'', sMV ''Text3''-                       |>-                       ( sKbd (MVar ''A'') (AVar ''P'') ),-                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_2_2'', sN ''TNp'',-                          sN ''Kab'', sMV ''A'', sMV ''Text2''-                       |>-                       ( sKbd (MVar ''B'') (AVar ''P'') )-               |>-  ]"--role isoiec_9798_2_6_special_TTP_bdkey_A-where "isoiec_9798_2_6_special_TTP_bdkey_A =-  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>-  , Recv ''text_2'' ( sMV ''Text2'' )-  , Send ''2'' <| sAV ''A'', sAV ''P'', sN ''Ra'', sMV ''Rb'', sMV ''B'',-                  sMV ''Text2''-               |>-  , Recv ''3'' <| sAV ''P'', sAV ''A'', sMV ''Text5'',-                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_3_1'', sN ''Ra'',-                          sMV ''Kab'', sMV ''B'', sMV ''Text4''-                       |>-                       ( sKbd (AVar ''A'') (AVar ''P'') ),-                  sMV ''TokenPA_for_B''-               |>-  , Recv ''text_4'' <| sMV ''Text6'', sMV ''Text7'' |>-  , Send ''4'' <| sAV ''A'', sMV ''B'', sMV ''Text7'', sAV ''P'',-                  sMV ''TokenPA_for_B'',-                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_4'', sN ''Rpa'', sMV ''Rb'',-                          sMV ''Text6''-                       |>-                       ( sMV ''Kab'' )-               |>-  , Recv ''5'' <| sMV ''B'', sAV ''A'', sMV ''Text9'',-                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_5'', sMV ''Rb'', sN ''Rpa'',-                          sMV ''Text8''-                       |>-                       ( sMV ''Kab'' )-               |>-  ]"--role isoiec_9798_2_6_special_TTP_bdkey_B-where "isoiec_9798_2_6_special_TTP_bdkey_B =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>-  , Recv ''4'' <| sAV ''A'', sAV ''B'', sMV ''Text7'', sMV ''P'',-                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_3_2'', sN ''Rb'',-                          sMV ''Kab'', sAV ''A'', sMV ''Text3''-                       |>-                       ( sKbd (AVar ''B'') (MVar ''P'') ),-                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_4'', sMV ''Rpa'', sN ''Rb'',-                          sMV ''Text6''-                       |>-                       ( sMV ''Kab'' )-               |>-  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>-  , Send ''5'' <| sAV ''B'', sAV ''A'', sMV ''Text9'',-                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_5'', sN ''Rb'', sMV ''Rpa'',-                          sMV ''Text8''-                       |>-                       ( sMV ''Kab'' )-               |>-  ]"--role isoiec_9798_2_6_special_TTP_bdkey_P-where "isoiec_9798_2_6_special_TTP_bdkey_P =-  [ Recv ''2'' <| sMV ''A'', sAV ''P'', sMV ''Ra'', sMV ''Rb'', sMV ''B'',-                  sMV ''Text2''-               |>-  , Recv ''text_3'' <| sMV ''Text3'', sMV ''Text4'', sMV ''Text5'' |>-  , Send ''3'' <| sAV ''P'', sMV ''A'', sMV ''Text5'',-                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_3_1'', sMV ''Ra'',-                          sN ''Kab'', sMV ''B'', sMV ''Text4''-                       |>-                       ( sKbd (MVar ''A'') (AVar ''P'') ),-                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_3_2'', sMV ''Rb'',-                          sN ''Kab'', sMV ''A'', sMV ''Text3''-                       |>-                       ( sKbd (MVar ''B'') (AVar ''P'') )-               |>-  ]"--protocol isoiec_9798_2_bdkey-where "isoiec_9798_2_bdkey =-{ isoiec_9798_2_1_bdkey_A, isoiec_9798_2_1_bdkey_B,-  isoiec_9798_2_2_bdkey_A, isoiec_9798_2_2_bdkey_B,-  isoiec_9798_2_3_bdkey_A, isoiec_9798_2_3_bdkey_B,-  isoiec_9798_2_4_bdkey_A, isoiec_9798_2_4_bdkey_B,-  isoiec_9798_2_5_bdkey_A, isoiec_9798_2_5_bdkey_B,-  isoiec_9798_2_5_bdkey_P, isoiec_9798_2_6_bdkey_A,-  isoiec_9798_2_6_bdkey_B, isoiec_9798_2_6_bdkey_P,-  isoiec_9798_2_5_special_TTP_bdkey_A, isoiec_9798_2_5_special_TTP_bdkey_B,-  isoiec_9798_2_5_special_TTP_bdkey_P, isoiec_9798_2_6_special_TTP_bdkey_A,-  isoiec_9798_2_6_special_TTP_bdkey_B, isoiec_9798_2_6_special_TTP_bdkey_P-}"--locale restricted_isoiec_9798_2_bdkey_state = isoiec_9798_2_bdkey_state +-  assumes isoiec_9798_2_5_special_TTP_bdkey_different_actors_A_P:-    "!! tid0 tid1.-       [| roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_A;-         roleMap r tid1 = Some isoiec_9798_2_5_special_TTP_bdkey_P;-         s(AV ''P'' tid1) = s(AV ''A'' tid0)-       |] ==> False"-  assumes isoiec_9798_2_6_special_TTP_bdkey_different_actors_A_P:-    "!! tid0 tid1.-       [| roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_A;-         roleMap r tid1 = Some isoiec_9798_2_6_special_TTP_bdkey_P;-         s(AV ''P'' tid1) = s(AV ''A'' tid0)-       |] ==> False"-  assumes isoiec_9798_2_6_special_TTP_bdkey_different_actors_B_P:-    "!! tid0 tid1.-       [| roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_B;-         roleMap r tid1 = Some isoiec_9798_2_6_special_TTP_bdkey_P;-         s(AV ''P'' tid1) = s(AV ''B'' tid0)-       |] ==> False"--type_invariant isoiec_9798_2_bdkey_composed_typing for isoiec_9798_2_bdkey-where "isoiec_9798_2_bdkey_composed_typing = mk_typing-  [ ((isoiec_9798_2_1_bdkey_B, ''A''), (KnownT isoiec_9798_2_1_bdkey_B_1))-  , ((isoiec_9798_2_3_bdkey_B, ''A''), (KnownT isoiec_9798_2_3_bdkey_B_1))-  , ((isoiec_9798_2_5_bdkey_B, ''A''), (KnownT isoiec_9798_2_5_bdkey_B_3))-  , ((isoiec_9798_2_5_bdkey_P, ''A''), (KnownT isoiec_9798_2_5_bdkey_P_1))-  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''A''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3))-  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''A''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_1))-  , ((isoiec_9798_2_6_bdkey_P, ''A''), (KnownT isoiec_9798_2_6_bdkey_P_2))-  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''A''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_2))-  , ((isoiec_9798_2_2_bdkey_A, ''B''), (KnownT isoiec_9798_2_2_bdkey_A_1))-  , ((isoiec_9798_2_4_bdkey_A, ''B''), (KnownT isoiec_9798_2_4_bdkey_A_1))-  , ((isoiec_9798_2_5_bdkey_P, ''B''), (KnownT isoiec_9798_2_5_bdkey_P_1))-  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''B''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_1))-  , ((isoiec_9798_2_6_bdkey_A, ''B''), (KnownT isoiec_9798_2_6_bdkey_A_1))-  , ((isoiec_9798_2_6_bdkey_P, ''B''), (KnownT isoiec_9798_2_6_bdkey_P_2))-  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''B''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_1))-  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''B''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_2))-  , ((isoiec_9798_2_5_bdkey_A, ''Kab''),-     (SumT (KnownT isoiec_9798_2_5_bdkey_A_2) (NonceT isoiec_9798_2_5_bdkey_P ''Kab'')))-  , ((isoiec_9798_2_5_bdkey_B, ''Kab''),-     (SumT (KnownT isoiec_9798_2_5_bdkey_B_3) (NonceT isoiec_9798_2_5_bdkey_P ''Kab'')))-  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Kab''),-     (SumT (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_2) (NonceT isoiec_9798_2_5_special_TTP_bdkey_P ''Kab'')))-  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''Kab''),-     (SumT (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3) (NonceT isoiec_9798_2_5_special_TTP_bdkey_P ''Kab'')))-  , ((isoiec_9798_2_6_bdkey_A, ''Kab''),-     (SumT (KnownT isoiec_9798_2_6_bdkey_A_3) (NonceT isoiec_9798_2_6_bdkey_P ''Kab'')))-  , ((isoiec_9798_2_6_bdkey_B, ''Kab''),-     (SumT (KnownT isoiec_9798_2_6_bdkey_B_4) (NonceT isoiec_9798_2_6_bdkey_P ''Kab'')))-  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Kab''),-     (SumT (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_3) (NonceT isoiec_9798_2_6_special_TTP_bdkey_P ''Kab'')))-  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Kab''),-     (SumT (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_4) (NonceT isoiec_9798_2_6_special_TTP_bdkey_P ''Kab'')))-  , ((isoiec_9798_2_5_bdkey_B, ''P''), (KnownT isoiec_9798_2_5_bdkey_B_3))-  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''P''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3))-  , ((isoiec_9798_2_6_bdkey_B, ''P''), (KnownT isoiec_9798_2_6_bdkey_B_4))-  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''P''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_4))-  , ((isoiec_9798_2_4_bdkey_B, ''RA''),-     (SumT (KnownT isoiec_9798_2_4_bdkey_B_2) (NonceT isoiec_9798_2_4_bdkey_A ''RA'')))-  , ((isoiec_9798_2_2_bdkey_A, ''RB''), (KnownT isoiec_9798_2_2_bdkey_A_1))-  , ((isoiec_9798_2_4_bdkey_A, ''RB''), (KnownT isoiec_9798_2_4_bdkey_A_1))-  , ((isoiec_9798_2_6_bdkey_P, ''Ra''), (KnownT isoiec_9798_2_6_bdkey_P_2))-  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''Ra''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_2))-  , ((isoiec_9798_2_6_bdkey_A, ''Rb''), (KnownT isoiec_9798_2_6_bdkey_A_1))-  , ((isoiec_9798_2_6_bdkey_P, ''Rb''), (KnownT isoiec_9798_2_6_bdkey_P_2))-  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Rb''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_1))-  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''Rb''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_2))-  , ((isoiec_9798_2_6_bdkey_B, ''Rpa''),-     (SumT (KnownT isoiec_9798_2_6_bdkey_B_4) (NonceT isoiec_9798_2_6_bdkey_A ''Rpa'')))-  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Rpa''),-     (SumT (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_4) (NonceT isoiec_9798_2_6_special_TTP_bdkey_A ''Rpa'')))-  , ((isoiec_9798_2_1_bdkey_B, ''TNA''),-     (SumT (KnownT isoiec_9798_2_1_bdkey_B_1) (NonceT isoiec_9798_2_1_bdkey_A ''TNA'')))-  , ((isoiec_9798_2_3_bdkey_B, ''TNA''),-     (SumT (KnownT isoiec_9798_2_3_bdkey_B_1) (NonceT isoiec_9798_2_3_bdkey_A ''TNA'')))-  , ((isoiec_9798_2_3_bdkey_A, ''TNB''),-     (SumT (KnownT isoiec_9798_2_3_bdkey_A_2) (NonceT isoiec_9798_2_3_bdkey_B ''TNB'')))-  , ((isoiec_9798_2_5_bdkey_B, ''TNa''),-     (SumT (KnownT isoiec_9798_2_5_bdkey_B_3) (NonceT isoiec_9798_2_5_bdkey_A ''TNa'')))-  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''TNa''),-     (SumT (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3) (NonceT isoiec_9798_2_5_special_TTP_bdkey_A ''TNa'')))-  , ((isoiec_9798_2_5_bdkey_A, ''TNb''),-     (SumT (KnownT isoiec_9798_2_5_bdkey_A_4) (NonceT isoiec_9798_2_5_bdkey_B ''TNb'')))-  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''TNb''),-     (SumT (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_4) (NonceT isoiec_9798_2_5_special_TTP_bdkey_B ''TNb'')))-  , ((isoiec_9798_2_5_bdkey_B, ''TNp''),-     (SumT (KnownT isoiec_9798_2_5_bdkey_B_3) (NonceT isoiec_9798_2_5_bdkey_P ''TNp'')))-  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''TNp''),-     (SumT (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3) (NonceT isoiec_9798_2_5_special_TTP_bdkey_P ''TNp'')))-  , ((isoiec_9798_2_5_bdkey_P, ''TVPa''),-     (KnownT isoiec_9798_2_5_bdkey_P_1))-  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''TVPa''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_1))-  , ((isoiec_9798_2_1_bdkey_A, ''Text1''),-     (KnownT isoiec_9798_2_1_bdkey_A_text_1))-  , ((isoiec_9798_2_1_bdkey_B, ''Text1''),-     (KnownT isoiec_9798_2_1_bdkey_B_1))-  , ((isoiec_9798_2_2_bdkey_A, ''Text1''),-     (KnownT isoiec_9798_2_2_bdkey_A_1))-  , ((isoiec_9798_2_2_bdkey_B, ''Text1''),-     (KnownT isoiec_9798_2_2_bdkey_B_text_1))-  , ((isoiec_9798_2_3_bdkey_A, ''Text1''),-     (KnownT isoiec_9798_2_3_bdkey_A_text_1))-  , ((isoiec_9798_2_3_bdkey_B, ''Text1''),-     (KnownT isoiec_9798_2_3_bdkey_B_1))-  , ((isoiec_9798_2_4_bdkey_A, ''Text1''),-     (KnownT isoiec_9798_2_4_bdkey_A_1))-  , ((isoiec_9798_2_4_bdkey_B, ''Text1''),-     (KnownT isoiec_9798_2_4_bdkey_B_text_1))-  , ((isoiec_9798_2_5_bdkey_A, ''Text1''),-     (KnownT isoiec_9798_2_5_bdkey_A_text_1))-  , ((isoiec_9798_2_5_bdkey_P, ''Text1''),-     (KnownT isoiec_9798_2_5_bdkey_P_1))-  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text1''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_text_1))-  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''Text1''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_1))-  , ((isoiec_9798_2_6_bdkey_A, ''Text1''),-     (KnownT isoiec_9798_2_6_bdkey_A_1))-  , ((isoiec_9798_2_6_bdkey_B, ''Text1''),-     (KnownT isoiec_9798_2_6_bdkey_B_text_1))-  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text1''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_1))-  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Text1''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_text_1))-  , ((isoiec_9798_2_1_bdkey_A, ''Text2''),-     (KnownT isoiec_9798_2_1_bdkey_A_text_1))-  , ((isoiec_9798_2_1_bdkey_B, ''Text2''),-     (KnownT isoiec_9798_2_1_bdkey_B_1))-  , ((isoiec_9798_2_2_bdkey_A, ''Text2''),-     (KnownT isoiec_9798_2_2_bdkey_A_text_2))-  , ((isoiec_9798_2_2_bdkey_B, ''Text2''),-     (KnownT isoiec_9798_2_2_bdkey_B_2))-  , ((isoiec_9798_2_3_bdkey_A, ''Text2''),-     (KnownT isoiec_9798_2_3_bdkey_A_text_1))-  , ((isoiec_9798_2_3_bdkey_B, ''Text2''),-     (KnownT isoiec_9798_2_3_bdkey_B_1))-  , ((isoiec_9798_2_4_bdkey_A, ''Text2''),-     (KnownT isoiec_9798_2_4_bdkey_A_text_2))-  , ((isoiec_9798_2_4_bdkey_B, ''Text2''),-     (KnownT isoiec_9798_2_4_bdkey_B_2))-  , ((isoiec_9798_2_5_bdkey_B, ''Text2''),-     (KnownT isoiec_9798_2_5_bdkey_B_3))-  , ((isoiec_9798_2_5_bdkey_P, ''Text2''),-     (KnownT isoiec_9798_2_5_bdkey_P_text_2))-  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''Text2''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3))-  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''Text2''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_text_2))-  , ((isoiec_9798_2_6_bdkey_A, ''Text2''),-     (KnownT isoiec_9798_2_6_bdkey_A_text_2))-  , ((isoiec_9798_2_6_bdkey_P, ''Text2''),-     (KnownT isoiec_9798_2_6_bdkey_P_2))-  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text2''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_text_2))-  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''Text2''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_2))-  , ((isoiec_9798_2_2_bdkey_A, ''Text3''),-     (KnownT isoiec_9798_2_2_bdkey_A_text_2))-  , ((isoiec_9798_2_2_bdkey_B, ''Text3''),-     (KnownT isoiec_9798_2_2_bdkey_B_2))-  , ((isoiec_9798_2_3_bdkey_A, ''Text3''),-     (KnownT isoiec_9798_2_3_bdkey_A_2))-  , ((isoiec_9798_2_3_bdkey_B, ''Text3''),-     (KnownT isoiec_9798_2_3_bdkey_B_text_2))-  , ((isoiec_9798_2_4_bdkey_A, ''Text3''),-     (KnownT isoiec_9798_2_4_bdkey_A_text_2))-  , ((isoiec_9798_2_4_bdkey_B, ''Text3''),-     (KnownT isoiec_9798_2_4_bdkey_B_2))-  , ((isoiec_9798_2_5_bdkey_A, ''Text3''),-     (KnownT isoiec_9798_2_5_bdkey_A_2))-  , ((isoiec_9798_2_5_bdkey_P, ''Text3''),-     (KnownT isoiec_9798_2_5_bdkey_P_text_2))-  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text3''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_2))-  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''Text3''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_text_2))-  , ((isoiec_9798_2_6_bdkey_B, ''Text3''),-     (KnownT isoiec_9798_2_6_bdkey_B_4))-  , ((isoiec_9798_2_6_bdkey_P, ''Text3''),-     (KnownT isoiec_9798_2_6_bdkey_P_text_3))-  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Text3''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_4))-  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''Text3''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_text_3))-  , ((isoiec_9798_2_3_bdkey_A, ''Text4''),-     (KnownT isoiec_9798_2_3_bdkey_A_2))-  , ((isoiec_9798_2_3_bdkey_B, ''Text4''),-     (KnownT isoiec_9798_2_3_bdkey_B_text_2))-  , ((isoiec_9798_2_4_bdkey_A, ''Text4''),-     (KnownT isoiec_9798_2_4_bdkey_A_3))-  , ((isoiec_9798_2_4_bdkey_B, ''Text4''),-     (KnownT isoiec_9798_2_4_bdkey_B_text_3))-  , ((isoiec_9798_2_5_bdkey_A, ''Text4''),-     (KnownT isoiec_9798_2_5_bdkey_A_2))-  , ((isoiec_9798_2_5_bdkey_P, ''Text4''),-     (KnownT isoiec_9798_2_5_bdkey_P_text_2))-  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text4''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_2))-  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''Text4''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_text_2))-  , ((isoiec_9798_2_6_bdkey_A, ''Text4''),-     (KnownT isoiec_9798_2_6_bdkey_A_3))-  , ((isoiec_9798_2_6_bdkey_P, ''Text4''),-     (KnownT isoiec_9798_2_6_bdkey_P_text_3))-  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text4''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_3))-  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''Text4''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_text_3))-  , ((isoiec_9798_2_4_bdkey_A, ''Text5''),-     (KnownT isoiec_9798_2_4_bdkey_A_3))-  , ((isoiec_9798_2_4_bdkey_B, ''Text5''),-     (KnownT isoiec_9798_2_4_bdkey_B_text_3))-  , ((isoiec_9798_2_5_bdkey_A, ''Text5''),-     (KnownT isoiec_9798_2_5_bdkey_A_text_3))-  , ((isoiec_9798_2_5_bdkey_B, ''Text5''),-     (KnownT isoiec_9798_2_5_bdkey_B_3))-  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text5''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_text_3))-  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''Text5''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3))-  , ((isoiec_9798_2_6_bdkey_A, ''Text5''),-     (KnownT isoiec_9798_2_6_bdkey_A_3))-  , ((isoiec_9798_2_6_bdkey_P, ''Text5''),-     (KnownT isoiec_9798_2_6_bdkey_P_text_3))-  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text5''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_3))-  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''Text5''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_text_3))-  , ((isoiec_9798_2_5_bdkey_A, ''Text6''),-     (KnownT isoiec_9798_2_5_bdkey_A_text_3))-  , ((isoiec_9798_2_5_bdkey_B, ''Text6''),-     (KnownT isoiec_9798_2_5_bdkey_B_3))-  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text6''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_text_3))-  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''Text6''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3))-  , ((isoiec_9798_2_6_bdkey_A, ''Text6''),-     (KnownT isoiec_9798_2_6_bdkey_A_text_4))-  , ((isoiec_9798_2_6_bdkey_B, ''Text6''),-     (KnownT isoiec_9798_2_6_bdkey_B_4))-  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text6''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_text_4))-  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Text6''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_4))-  , ((isoiec_9798_2_5_bdkey_A, ''Text7''),-     (KnownT isoiec_9798_2_5_bdkey_A_4))-  , ((isoiec_9798_2_5_bdkey_B, ''Text7''),-     (KnownT isoiec_9798_2_5_bdkey_B_text_4))-  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text7''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_4))-  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''Text7''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_text_4))-  , ((isoiec_9798_2_6_bdkey_A, ''Text7''),-     (KnownT isoiec_9798_2_6_bdkey_A_text_4))-  , ((isoiec_9798_2_6_bdkey_B, ''Text7''),-     (KnownT isoiec_9798_2_6_bdkey_B_4))-  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text7''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_text_4))-  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Text7''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_4))-  , ((isoiec_9798_2_5_bdkey_A, ''Text8''),-     (KnownT isoiec_9798_2_5_bdkey_A_4))-  , ((isoiec_9798_2_5_bdkey_B, ''Text8''),-     (KnownT isoiec_9798_2_5_bdkey_B_text_4))-  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text8''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_4))-  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''Text8''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_text_4))-  , ((isoiec_9798_2_6_bdkey_A, ''Text8''),-     (KnownT isoiec_9798_2_6_bdkey_A_5))-  , ((isoiec_9798_2_6_bdkey_B, ''Text8''),-     (KnownT isoiec_9798_2_6_bdkey_B_text_5))-  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text8''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_5))-  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Text8''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_text_5))-  , ((isoiec_9798_2_6_bdkey_A, ''Text9''),-     (KnownT isoiec_9798_2_6_bdkey_A_5))-  , ((isoiec_9798_2_6_bdkey_B, ''Text9''),-     (KnownT isoiec_9798_2_6_bdkey_B_text_5))-  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text9''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_5))-  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Text9''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_text_5))-  , ((isoiec_9798_2_5_bdkey_A, ''TokenPA_for_B''),-     (KnownT isoiec_9798_2_5_bdkey_A_2))-  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''TokenPA_for_B''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_2))-  , ((isoiec_9798_2_6_bdkey_A, ''TokenPA_for_B''),-     (KnownT isoiec_9798_2_6_bdkey_A_3))-  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''TokenPA_for_B''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_3))-  ]"--sublocale isoiec_9798_2_bdkey_state < isoiec_9798_2_bdkey_composed_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_2_bdkey_composed_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_2_bdkey_composed_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_2_1_bdkey_A_text_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_1_bdkey_A_text_1_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_1_bdkey_B_1_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_1_bdkey_B_1_TNA t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_1_enc_1'', s(MV ''TNA'' tid0),-               s(AV ''B'' tid0), s(MV ''Text1'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_1_bdkey_B_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_1_enc_1'', s(MV ''TNA'' tid0),-               s(AV ''B'' tid0), s(MV ''Text1'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_1_bdkey_B_1_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_2_bdkey_A_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_2_bdkey_A_1_RB t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_2_bdkey_A_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_2_bdkey_A_text_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_2_bdkey_A_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_2_bdkey_B_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_2_enc_2'', LN ''RB'' tid0, s(AV ''B'' tid0),-               s(MV ''Text2'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_2_bdkey_B_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_bdkey_A_text_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_bdkey_A_text_1_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_bdkey_A_2_TNB t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_3_enc_2'', s(MV ''TNB'' tid0),-               s(AV ''A'' tid0), s(MV ''Text3'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_3_bdkey_A_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_3_enc_2'', s(MV ''TNB'' tid0),-               s(AV ''A'' tid0), s(MV ''Text3'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_3_bdkey_A_2_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_bdkey_B_1_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_bdkey_B_1_TNA t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_3_enc_1'', s(MV ''TNA'' tid0),-               s(AV ''B'' tid0), s(MV ''Text1'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_3_bdkey_B_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_3_enc_1'', s(MV ''TNA'' tid0),-               s(AV ''B'' tid0), s(MV ''Text1'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_3_bdkey_B_1_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_bdkey_B_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_bdkey_B_text_2_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_bdkey_A_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_bdkey_A_1_RB t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_bdkey_A_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_bdkey_A_text_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_bdkey_A_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_bdkey_A_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_4_enc_2'', s(MV ''RB'' tid0), LN ''RA'' tid0,-               s(MV ''Text4'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_4_bdkey_A_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_bdkey_B_2_RA t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_4_enc_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,-               s(AV ''B'' tid0), s(MV ''Text2'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_4_bdkey_B_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_4_enc_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,-               s(AV ''B'' tid0), s(MV ''Text2'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_4_bdkey_B_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_bdkey_B_text_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_bdkey_B_text_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_A_2_Kab t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,-               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),-               s(MV ''Text3'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_bdkey_A_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,-               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),-               s(MV ''Text3'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_bdkey_A_2_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_A_2_TokenPA_for_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_A_text_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_A_text_3_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_A_4_TNb t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_4'', s(MV ''TNb'' tid0),-               s(AV ''A'' tid0), s(MV ''Text7'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_bdkey_A_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_4'', s(MV ''TNb'' tid0),-               s(AV ''A'' tid0), s(MV ''Text7'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_bdkey_A_4_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_B_3_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_B_3_Kab t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),-               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(AV ''B'' tid0),-               s(MV ''Text2'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_bdkey_B_3_P t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_B_3_TNa t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid0),-               s(AV ''B'' tid0), s(MV ''Text5'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_bdkey_B_3_TNp t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),-               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(AV ''B'' tid0),-               s(MV ''Text2'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_bdkey_B_3_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),-               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(AV ''B'' tid0),-               s(MV ''Text2'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_bdkey_B_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid0),-               s(AV ''B'' tid0), s(MV ''Text5'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_bdkey_B_3_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_B_text_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_B_text_4_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_P_1_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_P_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_P_1_TVPa t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_P_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_P_text_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_P_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_P_text_2_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_A_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_A_1_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_A_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_A_3_Kab t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,-               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),-               s(MV ''Text4'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_bdkey_A_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,-               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),-               s(MV ''Text4'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_bdkey_A_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_A_3_TokenPA_for_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_A_text_4_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_A_text_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_A_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_5'', s(MV ''Rb'' tid0), LN ''Rpa'' tid0,-               s(MV ''Text8'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_bdkey_A_5_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_B_4_Kab t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,-               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),-               s(MV ''Text3'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_bdkey_B_4_P t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_B_4_Rpa t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_4'', s(MV ''Rpa'' tid0), LN ''Rb'' tid0,-               s(MV ''Text6'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_bdkey_B_4_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,-               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),-               s(MV ''Text3'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_bdkey_B_4_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_4'', s(MV ''Rpa'' tid0), LN ''Rb'' tid0,-               s(MV ''Text6'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_bdkey_B_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_B_text_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_B_text_5_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_P_2_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_P_2_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_P_2_Ra t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_P_2_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_P_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_P_text_3_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_P_text_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_P_text_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_A_2_Kab t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid0,-               s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_A_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid0,-               s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_A_2_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_A_2_TokenPA_for_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_A_text_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_A_text_3_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_A_4_TNb t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_4'', s(MV ''TNb'' tid0),-               s(AV ''A'' tid0), s(MV ''Text7'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_A_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_4'', s(MV ''TNb'' tid0),-               s(AV ''A'' tid0), s(MV ''Text7'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_A_4_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_Kab t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid0),-               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_P t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_TNa t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_3'', s(MV ''TNa'' tid0),-               s(AV ''B'' tid0), s(MV ''Text5'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_TNp t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid0),-               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid0),-               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_3'', s(MV ''TNa'' tid0),-               s(AV ''B'' tid0), s(MV ''Text5'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_B_text_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_B_text_4_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_P_1_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_P_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_P_1_TVPa t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_P_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_P_text_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_P_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_P_text_2_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_A_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_A_1_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_A_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_A_3_Kab t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_1'', LN ''Ra'' tid0,-               s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_A_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_1'', LN ''Ra'' tid0,-               s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_A_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_A_3_TokenPA_for_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_A_text_4_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_A_text_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_A_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_5'', s(MV ''Rb'' tid0),-               LN ''Rpa'' tid0, s(MV ''Text8'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_A_5_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Kab t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_2'', LN ''Rb'' tid0,-               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_B_4_P t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Rpa t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_4'', s(MV ''Rpa'' tid0),-               LN ''Rb'' tid0, s(MV ''Text6'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_2'', LN ''Rb'' tid0,-               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_4'', s(MV ''Rpa'' tid0),-               LN ''Rb'' tid0, s(MV ''Text6'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_B_text_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_B_text_5_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_2_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_2_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_2_Ra t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_2_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_text_3_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_text_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_text_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_2_bdkey_composed_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_2_bdkey_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_1_bdkey_B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_1_bdkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_1_bdkey_B_1 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_1_bdkey_A &-        ( tid1, isoiec_9798_2_1_bdkey_A_1 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,-           s(MV ''Text1'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),-                s(MV ''Text1'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_1_enc_1'', s(MV ''TNA'' tid0),-                          s(AV ''B'' tid0), s(MV ''Text1'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_1_bdkey_A_1_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_2_bdkey_B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_2_bdkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_2_bdkey_B_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_2_bdkey_A &-        ( tid1, isoiec_9798_2_2_bdkey_A_2 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(MV ''RB'' tid1),-           s(MV ''Text2'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''RB'' tid0,-                s(MV ''Text2'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_2_enc_2'', LN ''RB'' tid0, s(AV ''B'' tid0),-                          s(MV ''Text2'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_2_bdkey_A_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_3_bdkey_A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_3_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_3_bdkey_A_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_3_bdkey_B &-        ( tid1, isoiec_9798_2_3_bdkey_B_2 ) : steps t &-        {| s(MV ''A'' tid1), s(AV ''B'' tid1), LN ''TNB'' tid1,-           s(MV ''Text3'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNB'' tid0),-                s(MV ''Text3'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_3_enc_2'', s(MV ''TNB'' tid0),-                          s(AV ''A'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_3_bdkey_B_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_3_bdkey_B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_3_bdkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_3_bdkey_B_1 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_3_bdkey_A &-        ( tid1, isoiec_9798_2_3_bdkey_A_1 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,-           s(MV ''Text1'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),-                s(MV ''Text1'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_3_enc_1'', s(MV ''TNA'' tid0),-                          s(AV ''B'' tid0), s(MV ''Text1'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_3_bdkey_A_1_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_4_bdkey_A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_4_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_4_bdkey_A_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_4_bdkey_B &-        ( tid1, isoiec_9798_2_4_bdkey_B_3 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''RA'' tid1), LN ''RB'' tid1,-           s(MV ''Text2'' tid1), s(MV ''Text4'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''RA'' tid0,-                s(MV ''RB'' tid0), s(MV ''Text2'' tid0), s(MV ''Text4'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_4_enc_2'', s(MV ''RB'' tid0), LN ''RA'' tid0,-                          s(MV ''Text4'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_4_bdkey_B_3_enc tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''A'' tid1) )-               ( s(AV ''B'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_4_enc_1'', LN ''RA'' tid0, LN ''RB'' tid1,-                              s(AV ''B'' tid1), s(MV ''Text2'' tid1)-                           |}-                           ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid1) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest!: ltk_secrecy)-      next-        case (isoiec_9798_2_4_bdkey_A_2_enc tid2) note_unified facts = this facts-        thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-      qed (insert facts, fastsimp+)?-    next-      case swapped note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_4_enc_1'', LN ''RA'' tid0, LN ''RB'' tid1,-                              s(AV ''A'' tid0), s(MV ''Text2'' tid1)-                           |}-                           ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''A'' tid1) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest!: ltk_secrecy)-      next-        case (isoiec_9798_2_4_bdkey_A_2_enc tid2) note_unified facts = this facts-        thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-      qed (insert facts, fastsimp+)?-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_4_bdkey_B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_4_bdkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_4_bdkey_B_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_4_bdkey_A &-        ( tid1, isoiec_9798_2_4_bdkey_A_2 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''RA'' tid1, s(MV ''RB'' tid1),-           s(MV ''Text2'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''RA'' tid0),-                LN ''RB'' tid0, s(MV ''Text2'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_4_enc_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,-                          s(AV ''B'' tid0), s(MV ''Text2'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_4_bdkey_A_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_bdkey_P_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_bdkey_P"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "LN ''Kab'' tid0 : knows t"-  shows "False"-using facts proof(sources! " LN ''Kab'' tid0 ")-  case isoiec_9798_2_5_bdkey_P_2_Kab note_unified facts = this facts-  thus ?thesis by (fastsimp dest!: ltk_secrecy)-next-  case isoiec_9798_2_5_bdkey_P_2_Kab_1 note_unified facts = this facts-  thus ?thesis by (fastsimp dest!: ltk_secrecy)-qed (insert facts, fastsimp+)?--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_bdkey_A_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_bdkey_A_2 ) : steps t"-    "s(MV ''Kab'' tid0) : knows t"-  shows "False"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),-                          s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_bdkey_P_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp dest: isoiec_9798_2_5_bdkey_P_secret_Kab intro: event_predOrdI)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_bdkey_B_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_bdkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_bdkey_B_3 ) : steps t"-    "s(MV ''Kab'' tid0) : knows t"-  shows "False"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),-                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(AV ''B'' tid0),-                          s(MV ''Text2'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_bdkey_P_2_enc_1 tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp dest: isoiec_9798_2_5_bdkey_P_secret_Kab intro: event_predOrdI)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_bdkey_A_non_injective_agreement_B:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_bdkey_A_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_5_bdkey_B &-        ( tid1, isoiec_9798_2_5_bdkey_B_4 ) : steps t &-        {| s(MV ''A'' tid1), s(AV ''B'' tid1), s(MV ''P'' tid1),-           s(MV ''Kab'' tid1), s(MV ''TNa'' tid1), s(MV ''Text5'' tid1),-           LN ''TNb'' tid1, s(MV ''Text7'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''P'' tid0),-                s(MV ''Kab'' tid0), LN ''TNa'' tid0, s(MV ''Text5'' tid0),-                s(MV ''TNb'' tid0), s(MV ''Text7'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),-                          s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_bdkey_P_2_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_2_5_enc_4'', s(MV ''TNb'' tid0),-                            s(AV ''A'' tid0), s(MV ''Text7'' tid0)-                         |}-                         ( LN ''Kab'' tid1 ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest: isoiec_9798_2_5_bdkey_P_secret_Kab intro: event_predOrdI)-    next-      case (isoiec_9798_2_5_bdkey_B_4_enc tid2) note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid2),-                              LN ''Kab'' tid1, s(AV ''A'' tid0), s(AV ''B'' tid2), s(MV ''Text2'' tid2)-                           |}-                           ( Kbd ( s(AV ''B'' tid2) ) ( s(MV ''P'' tid2) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest: isoiec_9798_2_5_bdkey_P_secret_Kab intro: event_predOrdI)-      next-        case (isoiec_9798_2_5_bdkey_P_2_enc_1 tid3) note_unified facts = this facts-        thus ?thesis proof(sources! "-                         Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid2),-                                s(AV ''B'' tid0), s(MV ''Text5'' tid2)-                             |}-                             ( LN ''Kab'' tid1 ) ")-          case fake note_unified facts = this facts-          thus ?thesis by (fastsimp dest: isoiec_9798_2_5_bdkey_P_secret_Kab intro: event_predOrdI)-        next-          case (isoiec_9798_2_5_bdkey_A_3_enc tid3) note_unified facts = this facts-          thus ?thesis proof(sources! "-                           Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid3, LN ''Kab'' tid1,-                                  s(AV ''A'' tid3), s(AV ''B'' tid0), s(MV ''Text3'' tid3)-                               |}-                               ( Kbd ( s(AV ''A'' tid3) ) ( s(AV ''P'' tid3) ) ) ")-            case fake note_unified facts = this facts-            thus ?thesis by (fastsimp dest: isoiec_9798_2_5_bdkey_P_secret_Kab intro: event_predOrdI)-          next-            case (isoiec_9798_2_5_bdkey_P_2_enc tid4) note_unified facts = this facts-            thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-          qed (insert facts, fastsimp+)?-        qed (insert facts, fastsimp+)?-      qed (insert facts, fastsimp+)?-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_bdkey_B_non_injective_agreement_A:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_bdkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_bdkey_B_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_5_bdkey_A &-        ( tid1, isoiec_9798_2_5_bdkey_A_3 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(AV ''P'' tid1),-           s(MV ''Kab'' tid1), LN ''TNa'' tid1, s(MV ''Text5'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),-                s(MV ''Kab'' tid0), s(MV ''TNa'' tid0), s(MV ''Text5'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),-                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(AV ''B'' tid0),-                          s(MV ''Text2'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_bdkey_P_2_enc_1 tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid0),-                            s(AV ''B'' tid0), s(MV ''Text5'' tid0)-                         |}-                         ( LN ''Kab'' tid1 ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest: isoiec_9798_2_5_bdkey_P_secret_Kab intro: event_predOrdI)-    next-      case (isoiec_9798_2_5_bdkey_A_3_enc tid2) note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid2, LN ''Kab'' tid1,-                              s(AV ''A'' tid2), s(AV ''B'' tid0), s(MV ''Text3'' tid2)-                           |}-                           ( Kbd ( s(AV ''A'' tid2) ) ( s(AV ''P'' tid2) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest: isoiec_9798_2_5_bdkey_P_secret_Kab intro: event_predOrdI)-      next-        case (isoiec_9798_2_5_bdkey_P_2_enc tid3) note_unified facts = this facts-        thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-      qed (insert facts, fastsimp+)?-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_bdkey_A_non_injective_agreement_P:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_bdkey_A_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_5_bdkey_P &-        ( tid1, isoiec_9798_2_5_bdkey_P_2 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1), LN ''Kab'' tid1,-           s(MV ''TVPa'' tid1), s(MV ''Text3'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''P'' tid0),-                s(MV ''Kab'' tid0), LN ''TVPa'' tid0, s(MV ''Text3'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),-                          s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_bdkey_P_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_bdkey_B_non_injective_agreement_P:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_bdkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_bdkey_B_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_5_bdkey_P &-        ( tid1, isoiec_9798_2_5_bdkey_P_2 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1), LN ''Kab'' tid1,-           LN ''TNp'' tid1, s(MV ''Text2'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),-                s(MV ''Kab'' tid0), s(MV ''TNp'' tid0), s(MV ''Text2'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),-                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(AV ''B'' tid0),-                          s(MV ''Text2'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_bdkey_P_2_enc_1 tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_bdkey_P_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_bdkey_P"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "LN ''Kab'' tid0 : knows t"-  shows "False"-using facts proof(sources! " LN ''Kab'' tid0 ")-  case isoiec_9798_2_6_bdkey_P_3_Kab note_unified facts = this facts-  thus ?thesis by (fastsimp dest!: ltk_secrecy)-next-  case isoiec_9798_2_6_bdkey_P_3_Kab_1 note_unified facts = this facts-  thus ?thesis by (fastsimp dest!: ltk_secrecy)-qed (insert facts, fastsimp+)?--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_bdkey_A_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_bdkey_A_3 ) : steps t"-    "s(MV ''Kab'' tid0) : knows t"-  shows "False"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),-                          s(MV ''Text4'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_bdkey_P_3_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp dest: isoiec_9798_2_6_bdkey_P_secret_Kab intro: event_predOrdI)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_bdkey_B_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_bdkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_bdkey_B_4 ) : steps t"-    "s(MV ''Kab'' tid0) : knows t"-  shows "False"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),-                          s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_bdkey_P_3_enc_1 tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp dest: isoiec_9798_2_6_bdkey_P_secret_Kab intro: event_predOrdI)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_bdkey_A_non_injective_agreement_B:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_bdkey_A_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_6_bdkey_B &-        ( tid1, isoiec_9798_2_6_bdkey_B_5 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''P'' tid1),-           s(MV ''Kab'' tid1), s(MV ''Rpa'' tid1), LN ''Rb'' tid1,-           s(MV ''Text6'' tid1), s(MV ''Text8'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''P'' tid0),-                s(MV ''Kab'' tid0), LN ''Rpa'' tid0, s(MV ''Rb'' tid0),-                s(MV ''Text6'' tid0), s(MV ''Text8'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),-                          s(MV ''Text4'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_bdkey_P_3_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_2_6_enc_5'', s(MV ''Rb'' tid0), LN ''Rpa'' tid0,-                            s(MV ''Text8'' tid0)-                         |}-                         ( LN ''Kab'' tid1 ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest: isoiec_9798_2_6_bdkey_P_secret_Kab intro: event_predOrdI)-    next-      case (isoiec_9798_2_6_bdkey_B_5_enc tid2) note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid2, LN ''Kab'' tid1,-                              s(AV ''A'' tid2), s(AV ''B'' tid2), s(MV ''Text3'' tid2)-                           |}-                           ( Kbd ( s(AV ''B'' tid2) ) ( s(MV ''P'' tid2) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest: isoiec_9798_2_6_bdkey_P_secret_Kab intro: event_predOrdI)-      next-        case (isoiec_9798_2_6_bdkey_P_3_enc_1 tid3) note_unified facts = this facts-        thus ?thesis proof(sources! "-                         Enc {| LC ''isoiec_9798_2_6_enc_4'', LN ''Rpa'' tid0, LN ''Rb'' tid2,-                                s(MV ''Text6'' tid2)-                             |}-                             ( LN ''Kab'' tid1 ) ")-          case fake note_unified facts = this facts-          thus ?thesis by (fastsimp dest: isoiec_9798_2_6_bdkey_P_secret_Kab intro: event_predOrdI)-        next-          case (isoiec_9798_2_6_bdkey_A_4_enc tid3) note_unified facts = this facts-          thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-        qed (insert facts, fastsimp+)?-      qed (insert facts, fastsimp+)?-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_bdkey_B_non_injective_agreement_A:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_bdkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_bdkey_B_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_6_bdkey_A &-        ( tid1, isoiec_9798_2_6_bdkey_A_4 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),-           s(MV ''Kab'' tid1), LN ''Rpa'' tid1, s(MV ''Rb'' tid1),-           s(MV ''Text6'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),-                s(MV ''Kab'' tid0), s(MV ''Rpa'' tid0), LN ''Rb'' tid0,-                s(MV ''Text6'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),-                          s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_bdkey_P_3_enc_1 tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_2_6_enc_4'', s(MV ''Rpa'' tid0), LN ''Rb'' tid0,-                            s(MV ''Text6'' tid0)-                         |}-                         ( LN ''Kab'' tid1 ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest: isoiec_9798_2_6_bdkey_P_secret_Kab intro: event_predOrdI)-    next-      case (isoiec_9798_2_6_bdkey_A_4_enc tid2) note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid2, LN ''Kab'' tid1,-                              s(AV ''A'' tid2), s(MV ''B'' tid2), s(MV ''Text4'' tid2)-                           |}-                           ( Kbd ( s(AV ''A'' tid2) ) ( s(AV ''P'' tid2) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest: isoiec_9798_2_6_bdkey_P_secret_Kab intro: event_predOrdI)-      next-        case (isoiec_9798_2_6_bdkey_P_3_enc tid3) note_unified facts = this facts-        thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-      qed (insert facts, fastsimp+)?-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_bdkey_A_non_injective_agreement_P:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_bdkey_A_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_6_bdkey_P &-        ( tid1, isoiec_9798_2_6_bdkey_P_3 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),-           s(MV ''Ra'' tid1), LN ''Kab'' tid1, s(MV ''Text4'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''P'' tid0),-                LN ''Ra'' tid0, s(MV ''Kab'' tid0), s(MV ''Text4'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),-                          s(MV ''Text4'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_bdkey_P_3_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_bdkey_B_non_injective_agreement_P:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_bdkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_bdkey_B_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_6_bdkey_P &-        ( tid1, isoiec_9798_2_6_bdkey_P_3 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),-           s(MV ''Rb'' tid1), LN ''Kab'' tid1, s(MV ''Text3'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),-                LN ''Rb'' tid0, s(MV ''Kab'' tid0), s(MV ''Text3'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),-                          s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_bdkey_P_3_enc_1 tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed---lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_special_TTP_bdkey_P_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_P"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "LN ''Kab'' tid0 : knows t"-  shows "False"-using facts proof(sources! " LN ''Kab'' tid0 ")-  case isoiec_9798_2_5_special_TTP_bdkey_P_2_Kab note_unified facts = this facts-  thus ?thesis by (fastsimp dest!: ltk_secrecy)-next-  case isoiec_9798_2_5_special_TTP_bdkey_P_2_Kab_1 note_unified facts = this facts-  thus ?thesis by (fastsimp dest!: ltk_secrecy)-qed (insert facts, fastsimp+)?--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_special_TTP_bdkey_A_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_special_TTP_bdkey_A_2 ) : steps t"-    "s(MV ''Kab'' tid0) : knows t"-  shows "False"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''P'' tid1) )-               ( s(MV ''A'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts-      thus ?thesis by (fastsimp dest: isoiec_9798_2_5_special_TTP_bdkey_different_actors_A_P intro: event_predOrdI)-    next-      case swapped note_unified facts = this facts-      thus ?thesis by (fastsimp dest: isoiec_9798_2_5_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_special_TTP_bdkey_B_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_special_TTP_bdkey_B_3 ) : steps t"-    "s(MV ''Kab'' tid0) : knows t"-  shows "False"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid0),-                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc_1 tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''P'' tid1) )-               ( s(MV ''B'' tid1) ) = Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts-      thus ?thesis by (fastsimp dest: isoiec_9798_2_5_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)-    next-      case swapped note_unified facts = this facts-      thus ?thesis by (fastsimp dest: isoiec_9798_2_5_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_special_TTP_bdkey_A_non_injective_agreement_B:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_special_TTP_bdkey_A_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_5_special_TTP_bdkey_B &-        ( tid1, isoiec_9798_2_5_special_TTP_bdkey_B_4 ) : steps t &-        {| s(MV ''A'' tid1), s(AV ''B'' tid1), s(MV ''P'' tid1),-           s(MV ''Kab'' tid1), s(MV ''TNa'' tid1), s(MV ''Text5'' tid1),-           LN ''TNb'' tid1, s(MV ''Text7'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''P'' tid0),-                s(MV ''Kab'' tid0), LN ''TNa'' tid0, s(MV ''Text5'' tid0),-                s(MV ''TNb'' tid0), s(MV ''Text7'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''P'' tid1) )-               ( s(MV ''A'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts-      thus ?thesis by (fastsimp dest: isoiec_9798_2_5_special_TTP_bdkey_different_actors_A_P intro: event_predOrdI)-    next-      case swapped note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_4'', s(MV ''TNb'' tid0),-                              s(AV ''A'' tid0), s(MV ''Text7'' tid0)-                           |}-                           ( LN ''Kab'' tid1 ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest: isoiec_9798_2_5_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)-      next-        case (isoiec_9798_2_5_special_TTP_bdkey_B_4_enc tid2) note_unified facts = this facts-        thus ?thesis proof(sources! "-                         Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_3'', s(MV ''TNa'' tid2),-                                s(AV ''B'' tid2), s(MV ''Text5'' tid2)-                             |}-                             ( LN ''Kab'' tid1 ) ")-          case fake note_unified facts = this facts-          thus ?thesis by (fastsimp dest: isoiec_9798_2_5_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)-        next-          case (isoiec_9798_2_5_special_TTP_bdkey_A_3_enc tid3) note_unified facts = this facts-          thus ?thesis proof(sources! "-                           Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid3,-                                  LN ''Kab'' tid1, s(AV ''B'' tid2), s(MV ''Text3'' tid3)-                               |}-                               ( Kbd ( s(AV ''A'' tid3) ) ( s(AV ''P'' tid3) ) ) ")-            case fake note_unified facts = this facts-            thus ?thesis by (fastsimp dest: isoiec_9798_2_5_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)-          next-            case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc tid4) note_unified facts = this facts-            thus ?thesis proof(sources! "-                             Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid2),-                                    LN ''Kab'' tid1, s(AV ''A'' tid0), s(MV ''Text2'' tid2)-                                 |}-                                 ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid2) ) ) ")-              case fake note_unified facts = this facts-              thus ?thesis by (fastsimp dest: isoiec_9798_2_5_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)-            next-              case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc_1 tid3) note_unified facts = this facts-              thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-            qed (insert facts, fastsimp+)?-          qed (insert facts, fastsimp+)?-        qed (insert facts, fastsimp+)?-      qed (insert facts, fastsimp+)?-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_special_TTP_bdkey_B_non_injective_agreement_A:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_special_TTP_bdkey_B_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_5_special_TTP_bdkey_A &-        ( tid1, isoiec_9798_2_5_special_TTP_bdkey_A_3 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(AV ''P'' tid1),-           s(MV ''Kab'' tid1), LN ''TNa'' tid1, s(MV ''Text5'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),-                s(MV ''Kab'' tid0), s(MV ''TNa'' tid0), s(MV ''Text5'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_3'', s(MV ''TNa'' tid0),-                          s(AV ''B'' tid0), s(MV ''Text5'' tid0)-                       |}-                       ( s(MV ''Kab'' tid0) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest: isoiec_9798_2_5_special_TTP_bdkey_B_secret_Kab intro: event_predOrdI)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_A_3_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid1,-                            s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid1)-                         |}-                         ( Kbd ( s(AV ''A'' tid1) ) ( s(AV ''P'' tid1) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest: isoiec_9798_2_5_special_TTP_bdkey_B_secret_Kab intro: event_predOrdI)-    next-      case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc tid2) note_unified facts = this facts-      hence "Kbd ( s(AV ''P'' tid2) )-                 ( s(MV ''A'' tid2) ) = Kbd ( s(AV ''A'' tid1) ) ( s(AV ''P'' tid1) )"-        by simp note facts = this facts-      thus ?thesis proof(cases rule: Kbd_cases)-        case noswap note_unified facts = this facts-        thus ?thesis by (fastsimp dest: isoiec_9798_2_5_special_TTP_bdkey_different_actors_A_P intro: event_predOrdI)-      next-        case swapped note_unified facts = this facts-        thus ?thesis proof(sources! "-                         Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid0),-                                LN ''Kab'' tid2, s(MV ''A'' tid0), s(MV ''Text2'' tid0)-                             |}-                             ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-          case fake note_unified facts = this facts-          thus ?thesis by (fastsimp dest!: ltk_secrecy)-        next-          case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc_1 tid3) note_unified facts = this facts-          thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-        qed (insert facts, fastsimp+)?-      qed (fastsimp+)?-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_special_TTP_bdkey_A_non_injective_agreement_P:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_special_TTP_bdkey_A_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_5_special_TTP_bdkey_P &-        ( tid1, isoiec_9798_2_5_special_TTP_bdkey_P_2 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1), LN ''Kab'' tid1,-           s(MV ''TVPa'' tid1), s(MV ''Text3'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''P'' tid0),-                s(MV ''Kab'' tid0), LN ''TVPa'' tid0, s(MV ''Text3'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''P'' tid1) )-               ( s(MV ''A'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts-      thus ?thesis by (fastsimp dest: isoiec_9798_2_5_special_TTP_bdkey_different_actors_A_P intro: event_predOrdI)-    next-      case swapped note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_special_TTP_bdkey_B_non_injective_agreement_P:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_special_TTP_bdkey_B_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_5_special_TTP_bdkey_P &-        ( tid1, isoiec_9798_2_5_special_TTP_bdkey_P_2 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1), LN ''Kab'' tid1,-           LN ''TNp'' tid1, s(MV ''Text2'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),-                s(MV ''Kab'' tid0), s(MV ''TNp'' tid0), s(MV ''Text2'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid0),-                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc_1 tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''P'' tid1) )-               ( s(MV ''B'' tid1) ) = Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_3'', s(MV ''TNa'' tid0),-                              s(AV ''B'' tid0), s(MV ''Text5'' tid0)-                           |}-                           ( LN ''Kab'' tid1 ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest: isoiec_9798_2_5_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)-      next-        case (isoiec_9798_2_5_special_TTP_bdkey_A_3_enc tid2) note_unified facts = this facts-        thus ?thesis proof(sources! "-                         Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid2,-                                LN ''Kab'' tid1, s(AV ''B'' tid0), s(MV ''Text3'' tid2)-                             |}-                             ( Kbd ( s(AV ''A'' tid2) ) ( s(AV ''P'' tid2) ) ) ")-          case fake note_unified facts = this facts-          thus ?thesis by (fastsimp dest: isoiec_9798_2_5_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)-        next-          case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc tid3) note_unified facts = this facts-          thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-        qed (insert facts, fastsimp+)?-      qed (insert facts, fastsimp+)?-    next-      case swapped note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?-qed----lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_special_TTP_bdkey_P_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_P"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "LN ''Kab'' tid0 : knows t"-  shows "False"-using facts proof(sources! " LN ''Kab'' tid0 ")-  case isoiec_9798_2_6_special_TTP_bdkey_P_3_Kab note_unified facts = this facts-  thus ?thesis by (fastsimp dest!: ltk_secrecy)-next-  case isoiec_9798_2_6_special_TTP_bdkey_P_3_Kab_1 note_unified facts = this facts-  thus ?thesis by (fastsimp dest!: ltk_secrecy)-qed (insert facts, fastsimp+)?--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_special_TTP_bdkey_A_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_special_TTP_bdkey_A_3 ) : steps t"-    "s(MV ''Kab'' tid0) : knows t"-  shows "False"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_1'', LN ''Ra'' tid0,-                          s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''P'' tid1) )-               ( s(MV ''A'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts-      thus ?thesis by (fastsimp dest: isoiec_9798_2_6_special_TTP_bdkey_different_actors_A_P intro: event_predOrdI)-    next-      case swapped note_unified facts = this facts-      thus ?thesis by (fastsimp dest: isoiec_9798_2_6_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_special_TTP_bdkey_B_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_special_TTP_bdkey_B_4 ) : steps t"-    "s(MV ''Kab'' tid0) : knows t"-  shows "False"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_2'', LN ''Rb'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc_1 tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''P'' tid1) )-               ( s(MV ''B'' tid1) ) = Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts-      thus ?thesis by (fastsimp dest: isoiec_9798_2_6_special_TTP_bdkey_different_actors_B_P intro: event_predOrdI)-    next-      case swapped note_unified facts = this facts-      thus ?thesis by (fastsimp dest: isoiec_9798_2_6_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_special_TTP_bdkey_A_non_injective_agreement_B:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_special_TTP_bdkey_A_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_6_special_TTP_bdkey_B &-        ( tid1, isoiec_9798_2_6_special_TTP_bdkey_B_5 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''P'' tid1),-           s(MV ''Kab'' tid1), s(MV ''Rpa'' tid1), LN ''Rb'' tid1,-           s(MV ''Text6'' tid1), s(MV ''Text8'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''P'' tid0),-                s(MV ''Kab'' tid0), LN ''Rpa'' tid0, s(MV ''Rb'' tid0),-                s(MV ''Text6'' tid0), s(MV ''Text8'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_1'', LN ''Ra'' tid0,-                          s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''P'' tid1) )-               ( s(MV ''A'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts-      thus ?thesis by (fastsimp dest: isoiec_9798_2_6_special_TTP_bdkey_different_actors_A_P intro: event_predOrdI)-    next-      case swapped note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_5'', s(MV ''Rb'' tid0),-                              LN ''Rpa'' tid0, s(MV ''Text8'' tid0)-                           |}-                           ( LN ''Kab'' tid1 ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest: isoiec_9798_2_6_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)-      next-        case (isoiec_9798_2_6_special_TTP_bdkey_B_5_enc tid2) note_unified facts = this facts-        thus ?thesis proof(sources! "-                         Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_2'', LN ''Rb'' tid2,-                                LN ''Kab'' tid1, s(AV ''A'' tid2), s(MV ''Text3'' tid2)-                             |}-                             ( Kbd ( s(AV ''B'' tid2) ) ( s(MV ''P'' tid2) ) ) ")-          case fake note_unified facts = this facts-          thus ?thesis by (fastsimp dest: isoiec_9798_2_6_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)-        next-          case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc_1 tid3) note_unified facts = this facts-          hence "Kbd ( s(AV ''P'' tid0) )-                     ( s(MV ''B'' tid0) ) = Kbd ( s(AV ''B'' tid2) ) ( s(MV ''P'' tid2) )"-            by simp note facts = this facts-          thus ?thesis proof(cases rule: Kbd_cases)-            case noswap note_unified facts = this facts-            thus ?thesis by (fastsimp dest: isoiec_9798_2_6_special_TTP_bdkey_different_actors_B_P intro: event_predOrdI)-          next-            case swapped note_unified facts = this facts-            thus ?thesis proof(sources! "-                             Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_4'', LN ''Rpa'' tid0,-                                    LN ''Rb'' tid2, s(MV ''Text6'' tid2)-                                 |}-                                 ( LN ''Kab'' tid1 ) ")-              case fake note_unified facts = this facts-              thus ?thesis by (fastsimp dest: isoiec_9798_2_6_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)-            next-              case (isoiec_9798_2_6_special_TTP_bdkey_A_4_enc tid3) note_unified facts = this facts-              thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-            qed (insert facts, fastsimp+)?-          qed (fastsimp+)?-        qed (insert facts, fastsimp+)?-      qed (insert facts, fastsimp+)?-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_special_TTP_bdkey_B_non_injective_agreement_A:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_special_TTP_bdkey_B_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_6_special_TTP_bdkey_A &-        ( tid1, isoiec_9798_2_6_special_TTP_bdkey_A_4 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),-           s(MV ''Kab'' tid1), LN ''Rpa'' tid1, s(MV ''Rb'' tid1),-           s(MV ''Text6'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),-                s(MV ''Kab'' tid0), s(MV ''Rpa'' tid0), LN ''Rb'' tid0,-                s(MV ''Text6'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_2'', LN ''Rb'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc_1 tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''P'' tid1) )-               ( s(MV ''B'' tid1) ) = Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts-      thus ?thesis by (fastsimp dest: isoiec_9798_2_6_special_TTP_bdkey_different_actors_B_P intro: event_predOrdI)-    next-      case swapped note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_4'', s(MV ''Rpa'' tid0),-                              LN ''Rb'' tid0, s(MV ''Text6'' tid0)-                           |}-                           ( LN ''Kab'' tid1 ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest: isoiec_9798_2_6_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)-      next-        case (isoiec_9798_2_6_special_TTP_bdkey_A_4_enc tid2) note_unified facts = this facts-        thus ?thesis proof(sources! "-                         Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_1'', LN ''Ra'' tid2,-                                LN ''Kab'' tid1, s(MV ''B'' tid2), s(MV ''Text4'' tid2)-                             |}-                             ( Kbd ( s(AV ''A'' tid2) ) ( s(AV ''P'' tid2) ) ) ")-          case fake note_unified facts = this facts-          thus ?thesis by (fastsimp dest: isoiec_9798_2_6_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)-        next-          case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc tid3) note_unified facts = this facts-          hence "Kbd ( s(AV ''A'' tid2) )-                     ( s(AV ''P'' tid2) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid1) )"-            by simp note facts = this facts-          thus ?thesis proof(cases rule: Kbd_cases)-            case noswap note_unified facts = this facts-            thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-          next-            case swapped note_unified facts = this facts-            thus ?thesis by (fastsimp dest: isoiec_9798_2_6_special_TTP_bdkey_different_actors_A_P intro: event_predOrdI)-          qed (fastsimp+)?-        qed (insert facts, fastsimp+)?-      qed (insert facts, fastsimp+)?-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_special_TTP_bdkey_A_non_injective_agreement_P:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_special_TTP_bdkey_A_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_6_special_TTP_bdkey_P &-        ( tid1, isoiec_9798_2_6_special_TTP_bdkey_P_3 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),-           s(MV ''Ra'' tid1), LN ''Kab'' tid1, s(MV ''Text4'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''P'' tid0),-                LN ''Ra'' tid0, s(MV ''Kab'' tid0), s(MV ''Text4'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_1'', LN ''Ra'' tid0,-                          s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''P'' tid1) )-               ( s(MV ''A'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts-      thus ?thesis by (fastsimp dest: isoiec_9798_2_6_special_TTP_bdkey_different_actors_A_P intro: event_predOrdI)-    next-      case swapped note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_special_TTP_bdkey_B_non_injective_agreement_P:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_special_TTP_bdkey_B_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_6_special_TTP_bdkey_P &-        ( tid1, isoiec_9798_2_6_special_TTP_bdkey_P_3 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),-           s(MV ''Rb'' tid1), LN ''Kab'' tid1, s(MV ''Text3'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),-                LN ''Rb'' tid0, s(MV ''Kab'' tid0), s(MV ''Text3'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_2'', LN ''Rb'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc_1 tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''P'' tid1) )-               ( s(MV ''B'' tid1) ) = Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts-      thus ?thesis by (fastsimp dest: isoiec_9798_2_6_special_TTP_bdkey_different_actors_B_P intro: event_predOrdI)-    next-      case swapped note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?+  "ESPLogic"+begin++role isoiec_9798_2_1_bdkey_A+where "isoiec_9798_2_1_bdkey_A =+  [ Send ''leak_A'' ( sN ''TNA'' )+  , Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>+  , Send ''1'' <| sAV ''A'', sAV ''B'', sMV ''Text2'',+                  PEnc <| sC ''isoiec_9798_2_1_enc_1'', sN ''TNA'', sAV ''B'',+                          sMV ''Text1''+                       |>+                       ( sKbd (AVar ''A'') (AVar ''B'') )+               |>+  ]"++role isoiec_9798_2_1_bdkey_B+where "isoiec_9798_2_1_bdkey_B =+  [ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Text2'',+                  PEnc <| sC ''isoiec_9798_2_1_enc_1'', sMV ''TNA'', sAV ''B'',+                          sMV ''Text1''+                       |>+                       ( sKbd (MVar ''A'') (AVar ''B'') )+               |>+  ]"++role isoiec_9798_2_2_bdkey_A+where "isoiec_9798_2_2_bdkey_A =+  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''RB'', sMV ''Text1'' |>+  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>+  , Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'',+                  PEnc <| sC ''isoiec_9798_2_2_enc_2'', sMV ''RB'', sMV ''B'',+                          sMV ''Text2''+                       |>+                       ( sKbd (MVar ''B'') (AVar ''A'') )+               |>+  ]"++role isoiec_9798_2_2_bdkey_B+where "isoiec_9798_2_2_bdkey_B =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''RB'', sMV ''Text1'' |>+  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'',+                  PEnc <| sC ''isoiec_9798_2_2_enc_2'', sN ''RB'', sAV ''B'', sMV ''Text2''+                       |>+                       ( sKbd (AVar ''B'') (AVar ''A'') )+               |>+  ]"++role isoiec_9798_2_3_bdkey_A+where "isoiec_9798_2_3_bdkey_A =+  [ Send ''leak_A'' ( sN ''TNA'' )+  , Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>+  , Send ''1'' <| sAV ''A'', sAV ''B'', sMV ''Text2'',+                  PEnc <| sC ''isoiec_9798_2_3_enc_1'', sN ''TNA'', sAV ''B'',+                          sMV ''Text1''+                       |>+                       ( sKbd (AVar ''A'') (AVar ''B'') )+               |>+  , Recv ''2'' <| sAV ''B'', sAV ''A'', sMV ''Text4'',+                  PEnc <| sC ''isoiec_9798_2_3_enc_2'', sMV ''TNB'', sAV ''A'',+                          sMV ''Text3''+                       |>+                       ( sKbd (AVar ''B'') (AVar ''A'') )+               |>+  ]"++role isoiec_9798_2_3_bdkey_B+where "isoiec_9798_2_3_bdkey_B =+  [ Send ''leak_B'' ( sN ''TNB'' )+  , Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Text2'',+                  PEnc <| sC ''isoiec_9798_2_3_enc_1'', sMV ''TNA'', sAV ''B'',+                          sMV ''Text1''+                       |>+                       ( sKbd (MVar ''A'') (AVar ''B'') )+               |>+  , Recv ''text_2'' <| sMV ''Text3'', sMV ''Text4'' |>+  , Send ''2'' <| sAV ''B'', sMV ''A'', sMV ''Text4'',+                  PEnc <| sC ''isoiec_9798_2_3_enc_2'', sN ''TNB'', sMV ''A'',+                          sMV ''Text3''+                       |>+                       ( sKbd (AVar ''B'') (MVar ''A'') )+               |>+  ]"++role isoiec_9798_2_4_bdkey_A+where "isoiec_9798_2_4_bdkey_A =+  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''RB'', sMV ''Text1'' |>+  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>+  , Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'',+                  PEnc <| sC ''isoiec_9798_2_4_enc_1'', sN ''RA'', sMV ''RB'', sMV ''B'',+                          sMV ''Text2''+                       |>+                       ( sKbd (AVar ''A'') (MVar ''B'') )+               |>+  , Recv ''3'' <| sMV ''B'', sAV ''A'', sMV ''Text5'',+                  PEnc <| sC ''isoiec_9798_2_4_enc_2'', sMV ''RB'', sN ''RA'',+                          sMV ''Text4''+                       |>+                       ( sKbd (AVar ''A'') (MVar ''B'') )+               |>+  ]"++role isoiec_9798_2_4_bdkey_B+where "isoiec_9798_2_4_bdkey_B =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''RB'', sMV ''Text1'' |>+  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'',+                  PEnc <| sC ''isoiec_9798_2_4_enc_1'', sMV ''RA'', sN ''RB'', sAV ''B'',+                          sMV ''Text2''+                       |>+                       ( sKbd (AVar ''A'') (AVar ''B'') )+               |>+  , Recv ''text_3'' <| sMV ''Text4'', sMV ''Text5'' |>+  , Send ''3'' <| sAV ''B'', sAV ''A'', sMV ''Text5'',+                  PEnc <| sC ''isoiec_9798_2_4_enc_2'', sN ''RB'', sMV ''RA'',+                          sMV ''Text4''+                       |>+                       ( sKbd (AVar ''A'') (AVar ''B'') )+               |>+  ]"++role isoiec_9798_2_5_bdkey_A+where "isoiec_9798_2_5_bdkey_A =+  [ Send ''leak_A'' <| sN ''TVPa'', sN ''TNa'' |>+  , Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''A'', sAV ''P'', sN ''TVPa'', sAV ''B'',+                  sMV ''Text1''+               |>+  , Recv ''2'' <| sAV ''P'', sAV ''A'', sMV ''Text4'',+                  PEnc <| sC ''isoiec_9798_2_5_enc_2_1'', sN ''TVPa'', sMV ''Kab'',+                          sAV ''A'', sAV ''B'', sMV ''Text3''+                       |>+                       ( sKbd (AVar ''A'') (AVar ''P'') ),+                  sMV ''TokenPA_for_B''+               |>+  , Recv ''text_3'' <| sMV ''Text5'', sMV ''Text6'' |>+  , Send ''3'' <| sAV ''A'', sAV ''B'', sMV ''Text6'', sAV ''P'',+                  sMV ''TokenPA_for_B'',+                  PEnc <| sC ''isoiec_9798_2_5_enc_3'', sN ''TNa'', sAV ''B'',+                          sMV ''Text5''+                       |>+                       ( sMV ''Kab'' )+               |>+  , Recv ''4'' <| sAV ''B'', sAV ''A'', sMV ''Text8'',+                  PEnc <| sC ''isoiec_9798_2_5_enc_4'', sMV ''TNb'', sAV ''A'',+                          sMV ''Text7''+                       |>+                       ( sMV ''Kab'' )+               |>+  ]"++role isoiec_9798_2_5_bdkey_B+where "isoiec_9798_2_5_bdkey_B =+  [ Send ''leak_B'' ( sN ''TNb'' )+  , Recv ''3'' <| sMV ''A'', sAV ''B'', sMV ''Text6'', sMV ''P'',+                  PEnc <| sC ''isoiec_9798_2_5_enc_2_2'', sMV ''TNp'', sMV ''Kab'',+                          sMV ''A'', sAV ''B'', sMV ''Text2''+                       |>+                       ( sKbd (AVar ''B'') (MVar ''P'') ),+                  PEnc <| sC ''isoiec_9798_2_5_enc_3'', sMV ''TNa'', sAV ''B'',+                          sMV ''Text5''+                       |>+                       ( sMV ''Kab'' )+               |>+  , Recv ''text_4'' <| sMV ''Text7'', sMV ''Text8'' |>+  , Send ''4'' <| sAV ''B'', sMV ''A'', sMV ''Text8'',+                  PEnc <| sC ''isoiec_9798_2_5_enc_4'', sN ''TNb'', sMV ''A'',+                          sMV ''Text7''+                       |>+                       ( sMV ''Kab'' )+               |>+  ]"++role isoiec_9798_2_5_bdkey_P+where "isoiec_9798_2_5_bdkey_P =+  [ Send ''leak_P'' ( sN ''TNp'' )+  , Recv ''1'' <| sMV ''A'', sAV ''P'', sMV ''TVPa'', sMV ''B'',+                  sMV ''Text1''+               |>+  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'', sMV ''Text4'' |>+  , Send ''2'' <| sAV ''P'', sMV ''A'', sMV ''Text4'',+                  PEnc <| sC ''isoiec_9798_2_5_enc_2_1'', sMV ''TVPa'', sN ''Kab'',+                          sMV ''A'', sMV ''B'', sMV ''Text3''+                       |>+                       ( sKbd (MVar ''A'') (AVar ''P'') ),+                  PEnc <| sC ''isoiec_9798_2_5_enc_2_2'', sN ''TNp'', sN ''Kab'',+                          sMV ''A'', sMV ''B'', sMV ''Text2''+                       |>+                       ( sKbd (MVar ''B'') (AVar ''P'') )+               |>+  ]"++role isoiec_9798_2_6_bdkey_A+where "isoiec_9798_2_6_bdkey_A =+  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>+  , Recv ''text_2'' ( sMV ''Text2'' )+  , Send ''2'' <| sAV ''A'', sAV ''P'', sN ''Ra'', sMV ''Rb'', sMV ''B'',+                  sMV ''Text2''+               |>+  , Recv ''3'' <| sAV ''P'', sAV ''A'', sMV ''Text5'',+                  PEnc <| sC ''isoiec_9798_2_6_enc_3_1'', sN ''Ra'', sMV ''Kab'',+                          sAV ''A'', sMV ''B'', sMV ''Text4''+                       |>+                       ( sKbd (AVar ''A'') (AVar ''P'') ),+                  sMV ''TokenPA_for_B''+               |>+  , Recv ''text_4'' <| sMV ''Text6'', sMV ''Text7'' |>+  , Send ''4'' <| sAV ''A'', sMV ''B'', sMV ''Text7'', sAV ''P'',+                  sMV ''TokenPA_for_B'',+                  PEnc <| sC ''isoiec_9798_2_6_enc_4'', sN ''Rpa'', sMV ''Rb'',+                          sMV ''Text6''+                       |>+                       ( sMV ''Kab'' )+               |>+  , Recv ''5'' <| sMV ''B'', sAV ''A'', sMV ''Text9'',+                  PEnc <| sC ''isoiec_9798_2_6_enc_5'', sMV ''Rb'', sN ''Rpa'',+                          sMV ''Text8''+                       |>+                       ( sMV ''Kab'' )+               |>+  ]"++role isoiec_9798_2_6_bdkey_B+where "isoiec_9798_2_6_bdkey_B =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>+  , Recv ''4'' <| sAV ''A'', sAV ''B'', sMV ''Text7'', sMV ''P'',+                  PEnc <| sC ''isoiec_9798_2_6_enc_3_2'', sN ''Rb'', sMV ''Kab'',+                          sAV ''A'', sAV ''B'', sMV ''Text3''+                       |>+                       ( sKbd (AVar ''B'') (MVar ''P'') ),+                  PEnc <| sC ''isoiec_9798_2_6_enc_4'', sMV ''Rpa'', sN ''Rb'',+                          sMV ''Text6''+                       |>+                       ( sMV ''Kab'' )+               |>+  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>+  , Send ''5'' <| sAV ''B'', sAV ''A'', sMV ''Text9'',+                  PEnc <| sC ''isoiec_9798_2_6_enc_5'', sN ''Rb'', sMV ''Rpa'',+                          sMV ''Text8''+                       |>+                       ( sMV ''Kab'' )+               |>+  ]"++role isoiec_9798_2_6_bdkey_P+where "isoiec_9798_2_6_bdkey_P =+  [ Recv ''2'' <| sMV ''A'', sAV ''P'', sMV ''Ra'', sMV ''Rb'', sMV ''B'',+                  sMV ''Text2''+               |>+  , Recv ''text_3'' <| sMV ''Text3'', sMV ''Text4'', sMV ''Text5'' |>+  , Send ''3'' <| sAV ''P'', sMV ''A'', sMV ''Text5'',+                  PEnc <| sC ''isoiec_9798_2_6_enc_3_1'', sMV ''Ra'', sN ''Kab'',+                          sMV ''A'', sMV ''B'', sMV ''Text4''+                       |>+                       ( sKbd (MVar ''A'') (AVar ''P'') ),+                  PEnc <| sC ''isoiec_9798_2_6_enc_3_2'', sMV ''Rb'', sN ''Kab'',+                          sMV ''A'', sMV ''B'', sMV ''Text3''+                       |>+                       ( sKbd (MVar ''B'') (AVar ''P'') )+               |>+  ]"++role isoiec_9798_2_5_special_TTP_bdkey_A+where "isoiec_9798_2_5_special_TTP_bdkey_A =+  [ Send ''leak_A'' <| sN ''TVPa'', sN ''TNa'' |>+  , Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''A'', sAV ''P'', sN ''TVPa'', sAV ''B'',+                  sMV ''Text1''+               |>+  , Recv ''2'' <| sAV ''P'', sAV ''A'', sMV ''Text4'',+                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_2_1'', sN ''TVPa'',+                          sMV ''Kab'', sAV ''B'', sMV ''Text3''+                       |>+                       ( sKbd (AVar ''A'') (AVar ''P'') ),+                  sMV ''TokenPA_for_B''+               |>+  , Recv ''text_3'' <| sMV ''Text5'', sMV ''Text6'' |>+  , Send ''3'' <| sAV ''A'', sAV ''B'', sMV ''Text6'', sAV ''P'',+                  sMV ''TokenPA_for_B'',+                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_3'', sN ''TNa'', sAV ''B'',+                          sMV ''Text5''+                       |>+                       ( sMV ''Kab'' )+               |>+  , Recv ''4'' <| sAV ''B'', sAV ''A'', sMV ''Text8'',+                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_4'', sMV ''TNb'', sAV ''A'',+                          sMV ''Text7''+                       |>+                       ( sMV ''Kab'' )+               |>+  ]"++role isoiec_9798_2_5_special_TTP_bdkey_B+where "isoiec_9798_2_5_special_TTP_bdkey_B =+  [ Send ''leak_B'' ( sN ''TNb'' )+  , Recv ''3'' <| sMV ''A'', sAV ''B'', sMV ''Text6'', sMV ''P'',+                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_2_2'', sMV ''TNp'',+                          sMV ''Kab'', sMV ''A'', sMV ''Text2''+                       |>+                       ( sKbd (AVar ''B'') (MVar ''P'') ),+                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_3'', sMV ''TNa'', sAV ''B'',+                          sMV ''Text5''+                       |>+                       ( sMV ''Kab'' )+               |>+  , Recv ''text_4'' <| sMV ''Text7'', sMV ''Text8'' |>+  , Send ''4'' <| sAV ''B'', sMV ''A'', sMV ''Text8'',+                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_4'', sN ''TNb'', sMV ''A'',+                          sMV ''Text7''+                       |>+                       ( sMV ''Kab'' )+               |>+  ]"++role isoiec_9798_2_5_special_TTP_bdkey_P+where "isoiec_9798_2_5_special_TTP_bdkey_P =+  [ Send ''leak_P'' ( sN ''TNp'' )+  , Recv ''1'' <| sMV ''A'', sAV ''P'', sMV ''TVPa'', sMV ''B'',+                  sMV ''Text1''+               |>+  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'', sMV ''Text4'' |>+  , Send ''2'' <| sAV ''P'', sMV ''A'', sMV ''Text4'',+                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_2_1'', sMV ''TVPa'',+                          sN ''Kab'', sMV ''B'', sMV ''Text3''+                       |>+                       ( sKbd (MVar ''A'') (AVar ''P'') ),+                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_2_2'', sN ''TNp'',+                          sN ''Kab'', sMV ''A'', sMV ''Text2''+                       |>+                       ( sKbd (MVar ''B'') (AVar ''P'') )+               |>+  ]"++role isoiec_9798_2_6_special_TTP_bdkey_A+where "isoiec_9798_2_6_special_TTP_bdkey_A =+  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>+  , Recv ''text_2'' ( sMV ''Text2'' )+  , Send ''2'' <| sAV ''A'', sAV ''P'', sN ''Ra'', sMV ''Rb'', sMV ''B'',+                  sMV ''Text2''+               |>+  , Recv ''3'' <| sAV ''P'', sAV ''A'', sMV ''Text5'',+                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_3_1'', sN ''Ra'',+                          sMV ''Kab'', sMV ''B'', sMV ''Text4''+                       |>+                       ( sKbd (AVar ''A'') (AVar ''P'') ),+                  sMV ''TokenPA_for_B''+               |>+  , Recv ''text_4'' <| sMV ''Text6'', sMV ''Text7'' |>+  , Send ''4'' <| sAV ''A'', sMV ''B'', sMV ''Text7'', sAV ''P'',+                  sMV ''TokenPA_for_B'',+                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_4'', sN ''Rpa'', sMV ''Rb'',+                          sMV ''Text6''+                       |>+                       ( sMV ''Kab'' )+               |>+  , Recv ''5'' <| sMV ''B'', sAV ''A'', sMV ''Text9'',+                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_5'', sMV ''Rb'', sN ''Rpa'',+                          sMV ''Text8''+                       |>+                       ( sMV ''Kab'' )+               |>+  ]"++role isoiec_9798_2_6_special_TTP_bdkey_B+where "isoiec_9798_2_6_special_TTP_bdkey_B =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>+  , Recv ''4'' <| sAV ''A'', sAV ''B'', sMV ''Text7'', sMV ''P'',+                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_3_2'', sN ''Rb'',+                          sMV ''Kab'', sAV ''A'', sMV ''Text3''+                       |>+                       ( sKbd (AVar ''B'') (MVar ''P'') ),+                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_4'', sMV ''Rpa'', sN ''Rb'',+                          sMV ''Text6''+                       |>+                       ( sMV ''Kab'' )+               |>+  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>+  , Send ''5'' <| sAV ''B'', sAV ''A'', sMV ''Text9'',+                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_5'', sN ''Rb'', sMV ''Rpa'',+                          sMV ''Text8''+                       |>+                       ( sMV ''Kab'' )+               |>+  ]"++role isoiec_9798_2_6_special_TTP_bdkey_P+where "isoiec_9798_2_6_special_TTP_bdkey_P =+  [ Recv ''2'' <| sMV ''A'', sAV ''P'', sMV ''Ra'', sMV ''Rb'', sMV ''B'',+                  sMV ''Text2''+               |>+  , Recv ''text_3'' <| sMV ''Text3'', sMV ''Text4'', sMV ''Text5'' |>+  , Send ''3'' <| sAV ''P'', sMV ''A'', sMV ''Text5'',+                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_3_1'', sMV ''Ra'',+                          sN ''Kab'', sMV ''B'', sMV ''Text4''+                       |>+                       ( sKbd (MVar ''A'') (AVar ''P'') ),+                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_3_2'', sMV ''Rb'',+                          sN ''Kab'', sMV ''A'', sMV ''Text3''+                       |>+                       ( sKbd (MVar ''B'') (AVar ''P'') )+               |>+  ]"++protocol isoiec_9798_2_bdkey+where "isoiec_9798_2_bdkey =+{ isoiec_9798_2_1_bdkey_A, isoiec_9798_2_1_bdkey_B,+  isoiec_9798_2_2_bdkey_A, isoiec_9798_2_2_bdkey_B,+  isoiec_9798_2_3_bdkey_A, isoiec_9798_2_3_bdkey_B,+  isoiec_9798_2_4_bdkey_A, isoiec_9798_2_4_bdkey_B,+  isoiec_9798_2_5_bdkey_A, isoiec_9798_2_5_bdkey_B,+  isoiec_9798_2_5_bdkey_P, isoiec_9798_2_6_bdkey_A,+  isoiec_9798_2_6_bdkey_B, isoiec_9798_2_6_bdkey_P,+  isoiec_9798_2_5_special_TTP_bdkey_A, isoiec_9798_2_5_special_TTP_bdkey_B,+  isoiec_9798_2_5_special_TTP_bdkey_P, isoiec_9798_2_6_special_TTP_bdkey_A,+  isoiec_9798_2_6_special_TTP_bdkey_B, isoiec_9798_2_6_special_TTP_bdkey_P+}"++locale restricted_isoiec_9798_2_bdkey_state = isoiec_9798_2_bdkey_state ++  assumes isoiec_9798_2_5_special_TTP_bdkey_different_actors_A_P:+    "!! tid0 tid1.+       [| roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_A;+         roleMap r tid1 = Some isoiec_9798_2_5_special_TTP_bdkey_P;+         s(AV ''P'' tid1) = s(AV ''A'' tid0)+       |] ==> False"+  assumes isoiec_9798_2_6_special_TTP_bdkey_different_actors_A_P:+    "!! tid0 tid1.+       [| roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_A;+         roleMap r tid1 = Some isoiec_9798_2_6_special_TTP_bdkey_P;+         s(AV ''P'' tid1) = s(AV ''A'' tid0)+       |] ==> False"+  assumes isoiec_9798_2_6_special_TTP_bdkey_different_actors_B_P:+    "!! tid0 tid1.+       [| roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_B;+         roleMap r tid1 = Some isoiec_9798_2_6_special_TTP_bdkey_P;+         s(AV ''P'' tid1) = s(AV ''B'' tid0)+       |] ==> False"++type_invariant isoiec_9798_2_bdkey_composed_typing for isoiec_9798_2_bdkey+where "isoiec_9798_2_bdkey_composed_typing = mk_typing+  [ ((isoiec_9798_2_1_bdkey_B, ''A''), (KnownT isoiec_9798_2_1_bdkey_B_1))+  , ((isoiec_9798_2_3_bdkey_B, ''A''), (KnownT isoiec_9798_2_3_bdkey_B_1))+  , ((isoiec_9798_2_5_bdkey_B, ''A''), (KnownT isoiec_9798_2_5_bdkey_B_3))+  , ((isoiec_9798_2_5_bdkey_P, ''A''), (KnownT isoiec_9798_2_5_bdkey_P_1))+  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''A''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3))+  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''A''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_1))+  , ((isoiec_9798_2_6_bdkey_P, ''A''), (KnownT isoiec_9798_2_6_bdkey_P_2))+  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''A''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_2))+  , ((isoiec_9798_2_2_bdkey_A, ''B''), (KnownT isoiec_9798_2_2_bdkey_A_1))+  , ((isoiec_9798_2_4_bdkey_A, ''B''), (KnownT isoiec_9798_2_4_bdkey_A_1))+  , ((isoiec_9798_2_5_bdkey_P, ''B''), (KnownT isoiec_9798_2_5_bdkey_P_1))+  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''B''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_1))+  , ((isoiec_9798_2_6_bdkey_A, ''B''), (KnownT isoiec_9798_2_6_bdkey_A_1))+  , ((isoiec_9798_2_6_bdkey_P, ''B''), (KnownT isoiec_9798_2_6_bdkey_P_2))+  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''B''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_1))+  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''B''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_2))+  , ((isoiec_9798_2_5_bdkey_A, ''Kab''),+     (SumT (KnownT isoiec_9798_2_5_bdkey_A_2) (NonceT isoiec_9798_2_5_bdkey_P ''Kab'')))+  , ((isoiec_9798_2_5_bdkey_B, ''Kab''),+     (SumT (KnownT isoiec_9798_2_5_bdkey_B_3) (NonceT isoiec_9798_2_5_bdkey_P ''Kab'')))+  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Kab''),+     (SumT (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_2) (NonceT isoiec_9798_2_5_special_TTP_bdkey_P ''Kab'')))+  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''Kab''),+     (SumT (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3) (NonceT isoiec_9798_2_5_special_TTP_bdkey_P ''Kab'')))+  , ((isoiec_9798_2_6_bdkey_A, ''Kab''),+     (SumT (KnownT isoiec_9798_2_6_bdkey_A_3) (NonceT isoiec_9798_2_6_bdkey_P ''Kab'')))+  , ((isoiec_9798_2_6_bdkey_B, ''Kab''),+     (SumT (KnownT isoiec_9798_2_6_bdkey_B_4) (NonceT isoiec_9798_2_6_bdkey_P ''Kab'')))+  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Kab''),+     (SumT (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_3) (NonceT isoiec_9798_2_6_special_TTP_bdkey_P ''Kab'')))+  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Kab''),+     (SumT (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_4) (NonceT isoiec_9798_2_6_special_TTP_bdkey_P ''Kab'')))+  , ((isoiec_9798_2_5_bdkey_B, ''P''), (KnownT isoiec_9798_2_5_bdkey_B_3))+  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''P''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3))+  , ((isoiec_9798_2_6_bdkey_B, ''P''), (KnownT isoiec_9798_2_6_bdkey_B_4))+  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''P''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_4))+  , ((isoiec_9798_2_4_bdkey_B, ''RA''),+     (SumT (KnownT isoiec_9798_2_4_bdkey_B_2) (NonceT isoiec_9798_2_4_bdkey_A ''RA'')))+  , ((isoiec_9798_2_2_bdkey_A, ''RB''), (KnownT isoiec_9798_2_2_bdkey_A_1))+  , ((isoiec_9798_2_4_bdkey_A, ''RB''), (KnownT isoiec_9798_2_4_bdkey_A_1))+  , ((isoiec_9798_2_6_bdkey_P, ''Ra''), (KnownT isoiec_9798_2_6_bdkey_P_2))+  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''Ra''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_2))+  , ((isoiec_9798_2_6_bdkey_A, ''Rb''), (KnownT isoiec_9798_2_6_bdkey_A_1))+  , ((isoiec_9798_2_6_bdkey_P, ''Rb''), (KnownT isoiec_9798_2_6_bdkey_P_2))+  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Rb''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_1))+  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''Rb''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_2))+  , ((isoiec_9798_2_6_bdkey_B, ''Rpa''),+     (SumT (KnownT isoiec_9798_2_6_bdkey_B_4) (NonceT isoiec_9798_2_6_bdkey_A ''Rpa'')))+  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Rpa''),+     (SumT (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_4) (NonceT isoiec_9798_2_6_special_TTP_bdkey_A ''Rpa'')))+  , ((isoiec_9798_2_1_bdkey_B, ''TNA''),+     (SumT (KnownT isoiec_9798_2_1_bdkey_B_1) (NonceT isoiec_9798_2_1_bdkey_A ''TNA'')))+  , ((isoiec_9798_2_3_bdkey_B, ''TNA''),+     (SumT (KnownT isoiec_9798_2_3_bdkey_B_1) (NonceT isoiec_9798_2_3_bdkey_A ''TNA'')))+  , ((isoiec_9798_2_3_bdkey_A, ''TNB''),+     (SumT (KnownT isoiec_9798_2_3_bdkey_A_2) (NonceT isoiec_9798_2_3_bdkey_B ''TNB'')))+  , ((isoiec_9798_2_5_bdkey_B, ''TNa''),+     (SumT (KnownT isoiec_9798_2_5_bdkey_B_3) (NonceT isoiec_9798_2_5_bdkey_A ''TNa'')))+  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''TNa''),+     (SumT (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3) (NonceT isoiec_9798_2_5_special_TTP_bdkey_A ''TNa'')))+  , ((isoiec_9798_2_5_bdkey_A, ''TNb''),+     (SumT (KnownT isoiec_9798_2_5_bdkey_A_4) (NonceT isoiec_9798_2_5_bdkey_B ''TNb'')))+  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''TNb''),+     (SumT (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_4) (NonceT isoiec_9798_2_5_special_TTP_bdkey_B ''TNb'')))+  , ((isoiec_9798_2_5_bdkey_B, ''TNp''),+     (SumT (KnownT isoiec_9798_2_5_bdkey_B_3) (NonceT isoiec_9798_2_5_bdkey_P ''TNp'')))+  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''TNp''),+     (SumT (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3) (NonceT isoiec_9798_2_5_special_TTP_bdkey_P ''TNp'')))+  , ((isoiec_9798_2_5_bdkey_P, ''TVPa''),+     (KnownT isoiec_9798_2_5_bdkey_P_1))+  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''TVPa''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_1))+  , ((isoiec_9798_2_1_bdkey_A, ''Text1''),+     (KnownT isoiec_9798_2_1_bdkey_A_text_1))+  , ((isoiec_9798_2_1_bdkey_B, ''Text1''),+     (KnownT isoiec_9798_2_1_bdkey_B_1))+  , ((isoiec_9798_2_2_bdkey_A, ''Text1''),+     (KnownT isoiec_9798_2_2_bdkey_A_1))+  , ((isoiec_9798_2_2_bdkey_B, ''Text1''),+     (KnownT isoiec_9798_2_2_bdkey_B_text_1))+  , ((isoiec_9798_2_3_bdkey_A, ''Text1''),+     (KnownT isoiec_9798_2_3_bdkey_A_text_1))+  , ((isoiec_9798_2_3_bdkey_B, ''Text1''),+     (KnownT isoiec_9798_2_3_bdkey_B_1))+  , ((isoiec_9798_2_4_bdkey_A, ''Text1''),+     (KnownT isoiec_9798_2_4_bdkey_A_1))+  , ((isoiec_9798_2_4_bdkey_B, ''Text1''),+     (KnownT isoiec_9798_2_4_bdkey_B_text_1))+  , ((isoiec_9798_2_5_bdkey_A, ''Text1''),+     (KnownT isoiec_9798_2_5_bdkey_A_text_1))+  , ((isoiec_9798_2_5_bdkey_P, ''Text1''),+     (KnownT isoiec_9798_2_5_bdkey_P_1))+  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text1''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_text_1))+  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''Text1''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_1))+  , ((isoiec_9798_2_6_bdkey_A, ''Text1''),+     (KnownT isoiec_9798_2_6_bdkey_A_1))+  , ((isoiec_9798_2_6_bdkey_B, ''Text1''),+     (KnownT isoiec_9798_2_6_bdkey_B_text_1))+  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text1''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_1))+  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Text1''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_text_1))+  , ((isoiec_9798_2_1_bdkey_A, ''Text2''),+     (KnownT isoiec_9798_2_1_bdkey_A_text_1))+  , ((isoiec_9798_2_1_bdkey_B, ''Text2''),+     (KnownT isoiec_9798_2_1_bdkey_B_1))+  , ((isoiec_9798_2_2_bdkey_A, ''Text2''),+     (KnownT isoiec_9798_2_2_bdkey_A_text_2))+  , ((isoiec_9798_2_2_bdkey_B, ''Text2''),+     (KnownT isoiec_9798_2_2_bdkey_B_2))+  , ((isoiec_9798_2_3_bdkey_A, ''Text2''),+     (KnownT isoiec_9798_2_3_bdkey_A_text_1))+  , ((isoiec_9798_2_3_bdkey_B, ''Text2''),+     (KnownT isoiec_9798_2_3_bdkey_B_1))+  , ((isoiec_9798_2_4_bdkey_A, ''Text2''),+     (KnownT isoiec_9798_2_4_bdkey_A_text_2))+  , ((isoiec_9798_2_4_bdkey_B, ''Text2''),+     (KnownT isoiec_9798_2_4_bdkey_B_2))+  , ((isoiec_9798_2_5_bdkey_B, ''Text2''),+     (KnownT isoiec_9798_2_5_bdkey_B_3))+  , ((isoiec_9798_2_5_bdkey_P, ''Text2''),+     (KnownT isoiec_9798_2_5_bdkey_P_text_2))+  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''Text2''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3))+  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''Text2''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_text_2))+  , ((isoiec_9798_2_6_bdkey_A, ''Text2''),+     (KnownT isoiec_9798_2_6_bdkey_A_text_2))+  , ((isoiec_9798_2_6_bdkey_P, ''Text2''),+     (KnownT isoiec_9798_2_6_bdkey_P_2))+  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text2''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_text_2))+  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''Text2''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_2))+  , ((isoiec_9798_2_2_bdkey_A, ''Text3''),+     (KnownT isoiec_9798_2_2_bdkey_A_text_2))+  , ((isoiec_9798_2_2_bdkey_B, ''Text3''),+     (KnownT isoiec_9798_2_2_bdkey_B_2))+  , ((isoiec_9798_2_3_bdkey_A, ''Text3''),+     (KnownT isoiec_9798_2_3_bdkey_A_2))+  , ((isoiec_9798_2_3_bdkey_B, ''Text3''),+     (KnownT isoiec_9798_2_3_bdkey_B_text_2))+  , ((isoiec_9798_2_4_bdkey_A, ''Text3''),+     (KnownT isoiec_9798_2_4_bdkey_A_text_2))+  , ((isoiec_9798_2_4_bdkey_B, ''Text3''),+     (KnownT isoiec_9798_2_4_bdkey_B_2))+  , ((isoiec_9798_2_5_bdkey_A, ''Text3''),+     (KnownT isoiec_9798_2_5_bdkey_A_2))+  , ((isoiec_9798_2_5_bdkey_P, ''Text3''),+     (KnownT isoiec_9798_2_5_bdkey_P_text_2))+  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text3''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_2))+  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''Text3''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_text_2))+  , ((isoiec_9798_2_6_bdkey_B, ''Text3''),+     (KnownT isoiec_9798_2_6_bdkey_B_4))+  , ((isoiec_9798_2_6_bdkey_P, ''Text3''),+     (KnownT isoiec_9798_2_6_bdkey_P_text_3))+  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Text3''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_4))+  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''Text3''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_text_3))+  , ((isoiec_9798_2_3_bdkey_A, ''Text4''),+     (KnownT isoiec_9798_2_3_bdkey_A_2))+  , ((isoiec_9798_2_3_bdkey_B, ''Text4''),+     (KnownT isoiec_9798_2_3_bdkey_B_text_2))+  , ((isoiec_9798_2_4_bdkey_A, ''Text4''),+     (KnownT isoiec_9798_2_4_bdkey_A_3))+  , ((isoiec_9798_2_4_bdkey_B, ''Text4''),+     (KnownT isoiec_9798_2_4_bdkey_B_text_3))+  , ((isoiec_9798_2_5_bdkey_A, ''Text4''),+     (KnownT isoiec_9798_2_5_bdkey_A_2))+  , ((isoiec_9798_2_5_bdkey_P, ''Text4''),+     (KnownT isoiec_9798_2_5_bdkey_P_text_2))+  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text4''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_2))+  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''Text4''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_text_2))+  , ((isoiec_9798_2_6_bdkey_A, ''Text4''),+     (KnownT isoiec_9798_2_6_bdkey_A_3))+  , ((isoiec_9798_2_6_bdkey_P, ''Text4''),+     (KnownT isoiec_9798_2_6_bdkey_P_text_3))+  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text4''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_3))+  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''Text4''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_text_3))+  , ((isoiec_9798_2_4_bdkey_A, ''Text5''),+     (KnownT isoiec_9798_2_4_bdkey_A_3))+  , ((isoiec_9798_2_4_bdkey_B, ''Text5''),+     (KnownT isoiec_9798_2_4_bdkey_B_text_3))+  , ((isoiec_9798_2_5_bdkey_A, ''Text5''),+     (KnownT isoiec_9798_2_5_bdkey_A_text_3))+  , ((isoiec_9798_2_5_bdkey_B, ''Text5''),+     (KnownT isoiec_9798_2_5_bdkey_B_3))+  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text5''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_text_3))+  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''Text5''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3))+  , ((isoiec_9798_2_6_bdkey_A, ''Text5''),+     (KnownT isoiec_9798_2_6_bdkey_A_3))+  , ((isoiec_9798_2_6_bdkey_P, ''Text5''),+     (KnownT isoiec_9798_2_6_bdkey_P_text_3))+  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text5''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_3))+  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''Text5''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_text_3))+  , ((isoiec_9798_2_5_bdkey_A, ''Text6''),+     (KnownT isoiec_9798_2_5_bdkey_A_text_3))+  , ((isoiec_9798_2_5_bdkey_B, ''Text6''),+     (KnownT isoiec_9798_2_5_bdkey_B_3))+  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text6''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_text_3))+  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''Text6''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3))+  , ((isoiec_9798_2_6_bdkey_A, ''Text6''),+     (KnownT isoiec_9798_2_6_bdkey_A_text_4))+  , ((isoiec_9798_2_6_bdkey_B, ''Text6''),+     (KnownT isoiec_9798_2_6_bdkey_B_4))+  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text6''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_text_4))+  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Text6''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_4))+  , ((isoiec_9798_2_5_bdkey_A, ''Text7''),+     (KnownT isoiec_9798_2_5_bdkey_A_4))+  , ((isoiec_9798_2_5_bdkey_B, ''Text7''),+     (KnownT isoiec_9798_2_5_bdkey_B_text_4))+  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text7''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_4))+  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''Text7''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_text_4))+  , ((isoiec_9798_2_6_bdkey_A, ''Text7''),+     (KnownT isoiec_9798_2_6_bdkey_A_text_4))+  , ((isoiec_9798_2_6_bdkey_B, ''Text7''),+     (KnownT isoiec_9798_2_6_bdkey_B_4))+  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text7''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_text_4))+  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Text7''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_4))+  , ((isoiec_9798_2_5_bdkey_A, ''Text8''),+     (KnownT isoiec_9798_2_5_bdkey_A_4))+  , ((isoiec_9798_2_5_bdkey_B, ''Text8''),+     (KnownT isoiec_9798_2_5_bdkey_B_text_4))+  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text8''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_4))+  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''Text8''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_text_4))+  , ((isoiec_9798_2_6_bdkey_A, ''Text8''),+     (KnownT isoiec_9798_2_6_bdkey_A_5))+  , ((isoiec_9798_2_6_bdkey_B, ''Text8''),+     (KnownT isoiec_9798_2_6_bdkey_B_text_5))+  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text8''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_5))+  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Text8''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_text_5))+  , ((isoiec_9798_2_6_bdkey_A, ''Text9''),+     (KnownT isoiec_9798_2_6_bdkey_A_5))+  , ((isoiec_9798_2_6_bdkey_B, ''Text9''),+     (KnownT isoiec_9798_2_6_bdkey_B_text_5))+  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text9''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_5))+  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Text9''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_text_5))+  , ((isoiec_9798_2_5_bdkey_A, ''TokenPA_for_B''),+     (KnownT isoiec_9798_2_5_bdkey_A_2))+  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''TokenPA_for_B''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_2))+  , ((isoiec_9798_2_6_bdkey_A, ''TokenPA_for_B''),+     (KnownT isoiec_9798_2_6_bdkey_A_3))+  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''TokenPA_for_B''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_3))+  ]"++sublocale isoiec_9798_2_bdkey_state < isoiec_9798_2_bdkey_composed_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_2_bdkey_composed_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_2_bdkey_composed_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_2_1_bdkey_A_text_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_1_bdkey_A_text_1_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_1_bdkey_B_1_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_1_bdkey_B_1_TNA t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_1_enc_1'', s(MV ''TNA'' tid0),+               s(AV ''B'' tid0), s(MV ''Text1'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_1_bdkey_B_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_1_enc_1'', s(MV ''TNA'' tid0),+               s(AV ''B'' tid0), s(MV ''Text1'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_1_bdkey_B_1_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_2_bdkey_A_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_2_bdkey_A_1_RB t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_2_bdkey_A_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_2_bdkey_A_text_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_2_bdkey_A_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_2_bdkey_B_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_2_enc_2'', LN ''RB'' tid0, s(AV ''B'' tid0),+               s(MV ''Text2'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_2_bdkey_B_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_bdkey_A_text_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_bdkey_A_text_1_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_bdkey_A_2_TNB t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_3_enc_2'', s(MV ''TNB'' tid0),+               s(AV ''A'' tid0), s(MV ''Text3'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_3_bdkey_A_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_3_enc_2'', s(MV ''TNB'' tid0),+               s(AV ''A'' tid0), s(MV ''Text3'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_3_bdkey_A_2_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_bdkey_B_1_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_bdkey_B_1_TNA t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_3_enc_1'', s(MV ''TNA'' tid0),+               s(AV ''B'' tid0), s(MV ''Text1'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_3_bdkey_B_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_3_enc_1'', s(MV ''TNA'' tid0),+               s(AV ''B'' tid0), s(MV ''Text1'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_3_bdkey_B_1_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_bdkey_B_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_bdkey_B_text_2_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_bdkey_A_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_bdkey_A_1_RB t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_bdkey_A_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_bdkey_A_text_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_bdkey_A_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_bdkey_A_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_4_enc_2'', s(MV ''RB'' tid0), LN ''RA'' tid0,+               s(MV ''Text4'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_4_bdkey_A_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_bdkey_B_2_RA t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_4_enc_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,+               s(AV ''B'' tid0), s(MV ''Text2'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_4_bdkey_B_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_4_enc_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,+               s(AV ''B'' tid0), s(MV ''Text2'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_4_bdkey_B_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_bdkey_B_text_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_bdkey_B_text_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_A_2_Kab t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,+               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),+               s(MV ''Text3'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_bdkey_A_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,+               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),+               s(MV ''Text3'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_bdkey_A_2_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_A_2_TokenPA_for_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_A_text_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_A_text_3_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_A_4_TNb t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_4'', s(MV ''TNb'' tid0),+               s(AV ''A'' tid0), s(MV ''Text7'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_bdkey_A_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_4'', s(MV ''TNb'' tid0),+               s(AV ''A'' tid0), s(MV ''Text7'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_bdkey_A_4_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_B_3_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_B_3_Kab t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),+               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(AV ''B'' tid0),+               s(MV ''Text2'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_bdkey_B_3_P t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_B_3_TNa t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid0),+               s(AV ''B'' tid0), s(MV ''Text5'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_bdkey_B_3_TNp t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),+               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(AV ''B'' tid0),+               s(MV ''Text2'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_bdkey_B_3_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),+               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(AV ''B'' tid0),+               s(MV ''Text2'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_bdkey_B_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid0),+               s(AV ''B'' tid0), s(MV ''Text5'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_bdkey_B_3_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_B_text_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_B_text_4_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_P_1_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_P_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_P_1_TVPa t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_P_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_P_text_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_P_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_P_text_2_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_A_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_A_1_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_A_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_A_3_Kab t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,+               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),+               s(MV ''Text4'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_bdkey_A_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,+               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),+               s(MV ''Text4'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_bdkey_A_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_A_3_TokenPA_for_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_A_text_4_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_A_text_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_A_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_5'', s(MV ''Rb'' tid0), LN ''Rpa'' tid0,+               s(MV ''Text8'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_bdkey_A_5_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_B_4_Kab t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,+               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),+               s(MV ''Text3'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_bdkey_B_4_P t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_B_4_Rpa t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_4'', s(MV ''Rpa'' tid0), LN ''Rb'' tid0,+               s(MV ''Text6'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_bdkey_B_4_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,+               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),+               s(MV ''Text3'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_bdkey_B_4_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_4'', s(MV ''Rpa'' tid0), LN ''Rb'' tid0,+               s(MV ''Text6'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_bdkey_B_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_B_text_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_B_text_5_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_P_2_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_P_2_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_P_2_Ra t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_P_2_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_P_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_P_text_3_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_P_text_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_P_text_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_A_2_Kab t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid0,+               s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_A_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid0,+               s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_A_2_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_A_2_TokenPA_for_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_A_text_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_A_text_3_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_A_4_TNb t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_4'', s(MV ''TNb'' tid0),+               s(AV ''A'' tid0), s(MV ''Text7'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_A_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_4'', s(MV ''TNb'' tid0),+               s(AV ''A'' tid0), s(MV ''Text7'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_A_4_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_Kab t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid0),+               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_P t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_TNa t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_3'', s(MV ''TNa'' tid0),+               s(AV ''B'' tid0), s(MV ''Text5'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_TNp t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid0),+               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid0),+               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_3'', s(MV ''TNa'' tid0),+               s(AV ''B'' tid0), s(MV ''Text5'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_B_text_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_B_text_4_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_P_1_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_P_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_P_1_TVPa t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_P_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_P_text_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_P_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_P_text_2_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_A_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_A_1_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_A_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_A_3_Kab t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_1'', LN ''Ra'' tid0,+               s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_A_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_1'', LN ''Ra'' tid0,+               s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_A_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_A_3_TokenPA_for_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_A_text_4_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_A_text_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_A_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_5'', s(MV ''Rb'' tid0),+               LN ''Rpa'' tid0, s(MV ''Text8'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_A_5_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Kab t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_2'', LN ''Rb'' tid0,+               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_B_4_P t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Rpa t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_4'', s(MV ''Rpa'' tid0),+               LN ''Rb'' tid0, s(MV ''Text6'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_2'', LN ''Rb'' tid0,+               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_4'', s(MV ''Rpa'' tid0),+               LN ''Rb'' tid0, s(MV ''Text6'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_B_text_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_B_text_5_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_P_2_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_P_2_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_P_2_Ra t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_P_2_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_P_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_P_text_3_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_P_text_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_P_text_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_2_bdkey_composed_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_2_bdkey_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_1_bdkey_B_non_injective_agreement:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_1_bdkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_1_bdkey_B_1 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_2_1_bdkey_A &+        ( tid1, isoiec_9798_2_1_bdkey_A_1 ) : steps t &+        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,+           s(MV ''Text1'' tid1)+        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),+                s(MV ''Text1'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_1_enc_1'', s(MV ''TNA'' tid0),+                          s(AV ''B'' tid0), s(MV ''Text1'' tid0)+                       |}+                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_1_bdkey_A_1_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_2_bdkey_B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_2_bdkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_2_bdkey_B_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_2_bdkey_A &+          ( tid1, isoiec_9798_2_2_bdkey_A_2 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(MV ''RB'' tid1),+             s(MV ''Text2'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''RB'' tid0,+                  s(MV ''Text2'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_2_enc_2'', LN ''RB'' tid0, s(AV ''B'' tid0),+                              s(MV ''Text2'' tid0)+                           |}+                           ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_2_bdkey_A_2_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_3_bdkey_A_non_injective_agreement:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_3_bdkey_A"+    "RLKR(s(AV ''A'' tid0)) ~: reveals t"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_3_bdkey_A_2 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_2_3_bdkey_B &+        ( tid1, isoiec_9798_2_3_bdkey_B_2 ) : steps t &+        {| s(MV ''A'' tid1), s(AV ''B'' tid1), LN ''TNB'' tid1,+           s(MV ''Text3'' tid1)+        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNB'' tid0),+                s(MV ''Text3'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_3_enc_2'', s(MV ''TNB'' tid0),+                          s(AV ''A'' tid0), s(MV ''Text3'' tid0)+                       |}+                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_3_bdkey_B_2_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_3_bdkey_B_non_injective_agreement:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_3_bdkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_3_bdkey_B_1 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_2_3_bdkey_A &+        ( tid1, isoiec_9798_2_3_bdkey_A_1 ) : steps t &+        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,+           s(MV ''Text1'' tid1)+        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),+                s(MV ''Text1'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_3_enc_1'', s(MV ''TNA'' tid0),+                          s(AV ''B'' tid0), s(MV ''Text1'' tid0)+                       |}+                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_3_bdkey_A_1_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_4_bdkey_A_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_4_bdkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_4_bdkey_A_3 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_4_bdkey_B &+          ( tid1, isoiec_9798_2_4_bdkey_B_3 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''RA'' tid1), LN ''RB'' tid1,+             s(MV ''Text2'' tid1), s(MV ''Text4'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''RA'' tid0,+                  s(MV ''RB'' tid0), s(MV ''Text2'' tid0), s(MV ''Text4'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_4_enc_2'', s(MV ''RB'' tid0), LN ''RA'' tid0,+                              s(MV ''Text4'' tid0)+                           |}+                           ( Kbd ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_4_bdkey_B_3_enc tid1) note_unified facts = this facts+        hence "Kbd ( s(AV ''A'' tid1) )+                   ( s(AV ''B'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) )"+          by simp note facts = this facts+        thus ?thesis proof(cases rule: Kbd_cases)+          case noswap note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_2_4_enc_1'', LN ''RA'' tid0, LN ''RB'' tid1,+                                  s(AV ''B'' tid1), s(MV ''Text2'' tid1)+                               |}+                               ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid1) ) ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest!: ltk_secrecy)+          next+            case (isoiec_9798_2_4_bdkey_A_2_enc tid2) note_unified facts = this facts+            thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+          qed (insert facts, fastforce+)?+        next+          case swapped note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_2_4_enc_1'', LN ''RA'' tid0, LN ''RB'' tid1,+                                  s(AV ''A'' tid0), s(MV ''Text2'' tid1)+                               |}+                               ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''A'' tid1) ) ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest!: ltk_secrecy)+          next+            case (isoiec_9798_2_4_bdkey_A_2_enc tid2) note_unified facts = this facts+            thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+          qed (insert facts, fastforce+)?+        qed (fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_4_bdkey_B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_4_bdkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_4_bdkey_B_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_4_bdkey_A &+          ( tid1, isoiec_9798_2_4_bdkey_A_2 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''RA'' tid1, s(MV ''RB'' tid1),+             s(MV ''Text2'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''RA'' tid0),+                  LN ''RB'' tid0, s(MV ''Text2'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_4_enc_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,+                              s(AV ''B'' tid0), s(MV ''Text2'' tid0)+                           |}+                           ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_4_bdkey_A_2_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_bdkey_P_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_bdkey_P"+    "RLKR(s(AV ''P'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''B'' tid0)) ~: reveals t"+    "LN ''Kab'' tid0 : knows t"+  shows "False"+using facts proof(sources! " LN ''Kab'' tid0 ")+  case isoiec_9798_2_5_bdkey_P_2_Kab note_unified facts = this facts+  thus ?thesis by (fastforce dest!: ltk_secrecy)+next+  case isoiec_9798_2_5_bdkey_P_2_Kab_1 note_unified facts = this facts+  thus ?thesis by (fastforce dest!: ltk_secrecy)+qed (insert facts, fastforce+)?++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_bdkey_A_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_bdkey_A"+    "RLKR(s(AV ''A'' tid0)) ~: reveals t"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(AV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_5_bdkey_A_2 ) : steps t"+    "s(MV ''Kab'' tid0) : knows t"+  shows "False"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,+                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),+                          s(MV ''Text3'' tid0)+                       |}+                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_5_bdkey_P_2_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce dest: isoiec_9798_2_5_bdkey_P_secret_Kab intro: event_predOrdI)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_bdkey_B_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_bdkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_5_bdkey_B_3 ) : steps t"+    "s(MV ''Kab'' tid0) : knows t"+  shows "False"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),+                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(AV ''B'' tid0),+                          s(MV ''Text2'' tid0)+                       |}+                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_5_bdkey_P_2_enc_1 tid1) note_unified facts = this facts+    thus ?thesis by (fastforce dest: isoiec_9798_2_5_bdkey_P_secret_Kab intro: event_predOrdI)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_bdkey_A_injective_agreement_B:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_5_bdkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(AV ''P'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_5_bdkey_A_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_5_bdkey_B &+          ( tid1, isoiec_9798_2_5_bdkey_B_4 ) : steps t &+          {| s(MV ''A'' tid1), s(AV ''B'' tid1), s(MV ''P'' tid1),+             s(MV ''Kab'' tid1), s(MV ''TNa'' tid1), s(MV ''Text5'' tid1),+             LN ''TNb'' tid1, s(MV ''Text7'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''P'' tid0),+                  s(MV ''Kab'' tid0), LN ''TNa'' tid0, s(MV ''Text5'' tid0),+                  s(MV ''TNb'' tid0), s(MV ''Text7'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),+                              s(MV ''Text3'' tid0)+                           |}+                           ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_5_bdkey_P_2_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_2_5_enc_4'', s(MV ''TNb'' tid0),+                                s(AV ''A'' tid0), s(MV ''Text7'' tid0)+                             |}+                             ( LN ''Kab'' tid1 ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest: isoiec_9798_2_5_bdkey_P_secret_Kab intro: event_predOrdI)+        next+          case (isoiec_9798_2_5_bdkey_B_4_enc tid2) note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid2),+                                  LN ''Kab'' tid1, s(AV ''A'' tid0), s(AV ''B'' tid2), s(MV ''Text2'' tid2)+                               |}+                               ( Kbd ( s(AV ''B'' tid2) ) ( s(MV ''P'' tid2) ) ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest: isoiec_9798_2_5_bdkey_P_secret_Kab intro: event_predOrdI)+          next+            case (isoiec_9798_2_5_bdkey_P_2_enc_1 tid3) note_unified facts = this facts+            thus ?thesis proof(sources! "+                             Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid2),+                                    s(AV ''B'' tid0), s(MV ''Text5'' tid2)+                                 |}+                                 ( LN ''Kab'' tid1 ) ")+              case fake note_unified facts = this facts+              thus ?thesis by (fastforce dest: isoiec_9798_2_5_bdkey_P_secret_Kab intro: event_predOrdI)+            next+              case (isoiec_9798_2_5_bdkey_A_3_enc tid3) note_unified facts = this facts+              thus ?thesis proof(sources! "+                               Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid3, LN ''Kab'' tid1,+                                      s(AV ''A'' tid3), s(AV ''B'' tid0), s(MV ''Text3'' tid3)+                                   |}+                                   ( Kbd ( s(AV ''A'' tid3) ) ( s(AV ''P'' tid3) ) ) ")+                case fake note_unified facts = this facts+                thus ?thesis by (fastforce dest: isoiec_9798_2_5_bdkey_P_secret_Kab intro: event_predOrdI)+              next+                case (isoiec_9798_2_5_bdkey_P_2_enc tid4) note_unified facts = this facts+                thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+              qed (insert facts, fastforce+)?+            qed (insert facts, fastforce+)?+          qed (insert facts, fastforce+)?+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_bdkey_B_non_injective_agreement_A:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_bdkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_5_bdkey_B_3 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_2_5_bdkey_A &+        ( tid1, isoiec_9798_2_5_bdkey_A_3 ) : steps t &+        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(AV ''P'' tid1),+           s(MV ''Kab'' tid1), LN ''TNa'' tid1, s(MV ''Text5'' tid1)+        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),+                s(MV ''Kab'' tid0), s(MV ''TNa'' tid0), s(MV ''Text5'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),+                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(AV ''B'' tid0),+                          s(MV ''Text2'' tid0)+                       |}+                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_5_bdkey_P_2_enc_1 tid1) note_unified facts = this facts+    thus ?thesis proof(sources! "+                     Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid0),+                            s(AV ''B'' tid0), s(MV ''Text5'' tid0)+                         |}+                         ( LN ''Kab'' tid1 ) ")+      case fake note_unified facts = this facts+      thus ?thesis by (fastforce dest: isoiec_9798_2_5_bdkey_P_secret_Kab intro: event_predOrdI)+    next+      case (isoiec_9798_2_5_bdkey_A_3_enc tid2) note_unified facts = this facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid2, LN ''Kab'' tid1,+                              s(AV ''A'' tid2), s(AV ''B'' tid0), s(MV ''Text3'' tid2)+                           |}+                           ( Kbd ( s(AV ''A'' tid2) ) ( s(AV ''P'' tid2) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest: isoiec_9798_2_5_bdkey_P_secret_Kab intro: event_predOrdI)+      next+        case (isoiec_9798_2_5_bdkey_P_2_enc tid3) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed (insert facts, fastforce+)?+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_bdkey_A_injective_agreement_P:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_5_bdkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(AV ''P'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_5_bdkey_A_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_5_bdkey_P &+          ( tid1, isoiec_9798_2_5_bdkey_P_2 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1), LN ''Kab'' tid1,+             s(MV ''TVPa'' tid1), s(MV ''Text3'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''P'' tid0),+                  s(MV ''Kab'' tid0), LN ''TVPa'' tid0, s(MV ''Text3'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),+                              s(MV ''Text3'' tid0)+                           |}+                           ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_5_bdkey_P_2_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_bdkey_B_non_injective_agreement_P:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_bdkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_5_bdkey_B_3 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_2_5_bdkey_P &+        ( tid1, isoiec_9798_2_5_bdkey_P_2 ) : steps t &+        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1), LN ''Kab'' tid1,+           LN ''TNp'' tid1, s(MV ''Text2'' tid1)+        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),+                s(MV ''Kab'' tid0), s(MV ''TNp'' tid0), s(MV ''Text2'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),+                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(AV ''B'' tid0),+                          s(MV ''Text2'' tid0)+                       |}+                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_5_bdkey_P_2_enc_1 tid1) note_unified facts = this facts+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_bdkey_P_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_6_bdkey_P"+    "RLKR(s(AV ''P'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''B'' tid0)) ~: reveals t"+    "LN ''Kab'' tid0 : knows t"+  shows "False"+using facts proof(sources! " LN ''Kab'' tid0 ")+  case isoiec_9798_2_6_bdkey_P_3_Kab note_unified facts = this facts+  thus ?thesis by (fastforce dest!: ltk_secrecy)+next+  case isoiec_9798_2_6_bdkey_P_3_Kab_1 note_unified facts = this facts+  thus ?thesis by (fastforce dest!: ltk_secrecy)+qed (insert facts, fastforce+)?++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_bdkey_A_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_6_bdkey_A"+    "RLKR(s(AV ''A'' tid0)) ~: reveals t"+    "RLKR(s(AV ''P'' tid0)) ~: reveals t"+    "RLKR(s(MV ''B'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_6_bdkey_A_3 ) : steps t"+    "s(MV ''Kab'' tid0) : knows t"+  shows "False"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,+                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),+                          s(MV ''Text4'' tid0)+                       |}+                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_6_bdkey_P_3_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce dest: isoiec_9798_2_6_bdkey_P_secret_Kab intro: event_predOrdI)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_bdkey_B_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_6_bdkey_B"+    "RLKR(s(AV ''A'' tid0)) ~: reveals t"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_6_bdkey_B_4 ) : steps t"+    "s(MV ''Kab'' tid0) : knows t"+  shows "False"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,+                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),+                          s(MV ''Text3'' tid0)+                       |}+                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_6_bdkey_P_3_enc_1 tid1) note_unified facts = this facts+    thus ?thesis by (fastforce dest: isoiec_9798_2_6_bdkey_P_secret_Kab intro: event_predOrdI)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_bdkey_A_injective_agreement_B:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_6_bdkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''P'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_6_bdkey_A_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_6_bdkey_B &+          ( tid1, isoiec_9798_2_6_bdkey_B_5 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''P'' tid1),+             s(MV ''Kab'' tid1), s(MV ''Rpa'' tid1), LN ''Rb'' tid1,+             s(MV ''Text6'' tid1), s(MV ''Text8'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''P'' tid0),+                  s(MV ''Kab'' tid0), LN ''Rpa'' tid0, s(MV ''Rb'' tid0),+                  s(MV ''Text6'' tid0), s(MV ''Text8'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),+                              s(MV ''Text4'' tid0)+                           |}+                           ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_6_bdkey_P_3_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_2_6_enc_5'', s(MV ''Rb'' tid0), LN ''Rpa'' tid0,+                                s(MV ''Text8'' tid0)+                             |}+                             ( LN ''Kab'' tid1 ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest: isoiec_9798_2_6_bdkey_P_secret_Kab intro: event_predOrdI)+        next+          case (isoiec_9798_2_6_bdkey_B_5_enc tid2) note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid2, LN ''Kab'' tid1,+                                  s(AV ''A'' tid2), s(AV ''B'' tid2), s(MV ''Text3'' tid2)+                               |}+                               ( Kbd ( s(AV ''B'' tid2) ) ( s(MV ''P'' tid2) ) ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest: isoiec_9798_2_6_bdkey_P_secret_Kab intro: event_predOrdI)+          next+            case (isoiec_9798_2_6_bdkey_P_3_enc_1 tid3) note_unified facts = this facts+            thus ?thesis proof(sources! "+                             Enc {| LC ''isoiec_9798_2_6_enc_4'', LN ''Rpa'' tid0, LN ''Rb'' tid2,+                                    s(MV ''Text6'' tid2)+                                 |}+                                 ( LN ''Kab'' tid1 ) ")+              case fake note_unified facts = this facts+              thus ?thesis by (fastforce dest: isoiec_9798_2_6_bdkey_P_secret_Kab intro: event_predOrdI)+            next+              case (isoiec_9798_2_6_bdkey_A_4_enc tid3) note_unified facts = this facts+              thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+            qed (insert facts, fastforce+)?+          qed (insert facts, fastforce+)?+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_bdkey_B_injective_agreement_A:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_6_bdkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(MV ''P'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_6_bdkey_B_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_6_bdkey_A &+          ( tid1, isoiec_9798_2_6_bdkey_A_4 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),+             s(MV ''Kab'' tid1), LN ''Rpa'' tid1, s(MV ''Rb'' tid1),+             s(MV ''Text6'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),+                  s(MV ''Kab'' tid0), s(MV ''Rpa'' tid0), LN ''Rb'' tid0,+                  s(MV ''Text6'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),+                              s(MV ''Text3'' tid0)+                           |}+                           ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_6_bdkey_P_3_enc_1 tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_2_6_enc_4'', s(MV ''Rpa'' tid0), LN ''Rb'' tid0,+                                s(MV ''Text6'' tid0)+                             |}+                             ( LN ''Kab'' tid1 ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest: isoiec_9798_2_6_bdkey_P_secret_Kab intro: event_predOrdI)+        next+          case (isoiec_9798_2_6_bdkey_A_4_enc tid2) note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid2, LN ''Kab'' tid1,+                                  s(AV ''A'' tid2), s(MV ''B'' tid2), s(MV ''Text4'' tid2)+                               |}+                               ( Kbd ( s(AV ''A'' tid2) ) ( s(AV ''P'' tid2) ) ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest: isoiec_9798_2_6_bdkey_P_secret_Kab intro: event_predOrdI)+          next+            case (isoiec_9798_2_6_bdkey_P_3_enc tid3) note_unified facts = this facts+            thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+          qed (insert facts, fastforce+)?+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_bdkey_A_injective_agreement_P:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_6_bdkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''P'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_6_bdkey_A_3 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_6_bdkey_P &+          ( tid1, isoiec_9798_2_6_bdkey_P_3 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),+             s(MV ''Ra'' tid1), LN ''Kab'' tid1, s(MV ''Text4'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''P'' tid0),+                  LN ''Ra'' tid0, s(MV ''Kab'' tid0), s(MV ''Text4'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),+                              s(MV ''Text4'' tid0)+                           |}+                           ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_6_bdkey_P_3_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_bdkey_B_injective_agreement_P:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_6_bdkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(MV ''P'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_6_bdkey_B_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_6_bdkey_P &+          ( tid1, isoiec_9798_2_6_bdkey_P_3 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),+             s(MV ''Rb'' tid1), LN ''Kab'' tid1, s(MV ''Text3'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),+                  LN ''Rb'' tid0, s(MV ''Kab'' tid0), s(MV ''Text3'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),+                              s(MV ''Text3'' tid0)+                           |}+                           ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_6_bdkey_P_3_enc_1 tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed+++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_special_TTP_bdkey_P_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_P"+    "RLKR(s(AV ''P'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''B'' tid0)) ~: reveals t"+    "LN ''Kab'' tid0 : knows t"+  shows "False"+using facts proof(sources! " LN ''Kab'' tid0 ")+  case isoiec_9798_2_5_special_TTP_bdkey_P_2_Kab note_unified facts = this facts+  thus ?thesis by (fastforce dest!: ltk_secrecy)+next+  case isoiec_9798_2_5_special_TTP_bdkey_P_2_Kab_1 note_unified facts = this facts+  thus ?thesis by (fastforce dest!: ltk_secrecy)+qed (insert facts, fastforce+)?++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_special_TTP_bdkey_A_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_A"+    "RLKR(s(AV ''A'' tid0)) ~: reveals t"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(AV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_5_special_TTP_bdkey_A_2 ) : steps t"+    "s(MV ''Kab'' tid0) : knows t"+  shows "False"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid0,+                          s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)+                       |}+                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc tid1) note_unified facts = this facts+    hence "Kbd ( s(AV ''P'' tid1) )+               ( s(MV ''A'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) )"+      by simp note facts = this facts+    thus ?thesis proof(cases rule: Kbd_cases)+      case noswap note_unified facts = this facts+      thus ?thesis by (fastforce dest: isoiec_9798_2_5_special_TTP_bdkey_different_actors_A_P intro: event_predOrdI)+    next+      case swapped note_unified facts = this facts+      thus ?thesis by (fastforce dest: isoiec_9798_2_5_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)+    qed (fastforce+)?+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_special_TTP_bdkey_B_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_5_special_TTP_bdkey_B_3 ) : steps t"+    "s(MV ''Kab'' tid0) : knows t"+  shows "False"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid0),+                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)+                       |}+                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc_1 tid1) note_unified facts = this facts+    hence "Kbd ( s(AV ''P'' tid1) )+               ( s(MV ''B'' tid1) ) = Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) )"+      by simp note facts = this facts+    thus ?thesis proof(cases rule: Kbd_cases)+      case noswap note_unified facts = this facts+      thus ?thesis by (fastforce dest: isoiec_9798_2_5_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)+    next+      case swapped note_unified facts = this facts+      thus ?thesis by (fastforce dest: isoiec_9798_2_5_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)+    qed (fastforce+)?+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_special_TTP_bdkey_A_injective_agreement_B:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(AV ''P'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_5_special_TTP_bdkey_A_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_5_special_TTP_bdkey_B &+          ( tid1, isoiec_9798_2_5_special_TTP_bdkey_B_4 ) : steps t &+          {| s(MV ''A'' tid1), s(AV ''B'' tid1), s(MV ''P'' tid1),+             s(MV ''Kab'' tid1), s(MV ''TNa'' tid1), s(MV ''Text5'' tid1),+             LN ''TNb'' tid1, s(MV ''Text7'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''P'' tid0),+                  s(MV ''Kab'' tid0), LN ''TNa'' tid0, s(MV ''Text5'' tid0),+                  s(MV ''TNb'' tid0), s(MV ''Text7'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc tid1) note_unified facts = this facts+        hence "Kbd ( s(AV ''P'' tid1) )+                   ( s(MV ''A'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) )"+          by simp note facts = this facts+        thus ?thesis proof(cases rule: Kbd_cases)+          case noswap note_unified facts = this facts+          thus ?thesis by (fastforce dest: isoiec_9798_2_5_special_TTP_bdkey_different_actors_A_P intro: event_predOrdI)+        next+          case swapped note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_4'', s(MV ''TNb'' tid0),+                                  s(AV ''A'' tid0), s(MV ''Text7'' tid0)+                               |}+                               ( LN ''Kab'' tid1 ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest: isoiec_9798_2_5_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)+          next+            case (isoiec_9798_2_5_special_TTP_bdkey_B_4_enc tid2) note_unified facts = this facts+            thus ?thesis proof(sources! "+                             Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_3'', s(MV ''TNa'' tid2),+                                    s(AV ''B'' tid2), s(MV ''Text5'' tid2)+                                 |}+                                 ( LN ''Kab'' tid1 ) ")+              case fake note_unified facts = this facts+              thus ?thesis by (fastforce dest: isoiec_9798_2_5_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)+            next+              case (isoiec_9798_2_5_special_TTP_bdkey_A_3_enc tid3) note_unified facts = this facts+              thus ?thesis proof(sources! "+                               Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid3,+                                      LN ''Kab'' tid1, s(AV ''B'' tid2), s(MV ''Text3'' tid3)+                                   |}+                                   ( Kbd ( s(AV ''A'' tid3) ) ( s(AV ''P'' tid3) ) ) ")+                case fake note_unified facts = this facts+                thus ?thesis by (fastforce dest: isoiec_9798_2_5_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)+              next+                case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc tid4) note_unified facts = this facts+                thus ?thesis proof(sources! "+                                 Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid2),+                                        LN ''Kab'' tid1, s(AV ''A'' tid0), s(MV ''Text2'' tid2)+                                     |}+                                     ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid2) ) ) ")+                  case fake note_unified facts = this facts+                  thus ?thesis by (fastforce dest: isoiec_9798_2_5_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)+                next+                  case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc_1 tid3) note_unified facts = this facts+                  thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+                qed (insert facts, fastforce+)?+              qed (insert facts, fastforce+)?+            qed (insert facts, fastforce+)?+          qed (insert facts, fastforce+)?+        qed (fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_special_TTP_bdkey_B_non_injective_agreement_A:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_5_special_TTP_bdkey_B_3 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_2_5_special_TTP_bdkey_A &+        ( tid1, isoiec_9798_2_5_special_TTP_bdkey_A_3 ) : steps t &+        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(AV ''P'' tid1),+           s(MV ''Kab'' tid1), LN ''TNa'' tid1, s(MV ''Text5'' tid1)+        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),+                s(MV ''Kab'' tid0), s(MV ''TNa'' tid0), s(MV ''Text5'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_3'', s(MV ''TNa'' tid0),+                          s(AV ''B'' tid0), s(MV ''Text5'' tid0)+                       |}+                       ( s(MV ''Kab'' tid0) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest: isoiec_9798_2_5_special_TTP_bdkey_B_secret_Kab intro: event_predOrdI)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_A_3_enc tid1) note_unified facts = this facts+    thus ?thesis proof(sources! "+                     Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid1,+                            s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid1)+                         |}+                         ( Kbd ( s(AV ''A'' tid1) ) ( s(AV ''P'' tid1) ) ) ")+      case fake note_unified facts = this facts+      thus ?thesis by (fastforce dest: isoiec_9798_2_5_special_TTP_bdkey_B_secret_Kab intro: event_predOrdI)+    next+      case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc tid2) note_unified facts = this facts+      hence "Kbd ( s(AV ''P'' tid2) )+                 ( s(MV ''A'' tid2) ) = Kbd ( s(AV ''A'' tid1) ) ( s(AV ''P'' tid1) )"+        by simp note facts = this facts+      thus ?thesis proof(cases rule: Kbd_cases)+        case noswap note_unified facts = this facts+        thus ?thesis by (fastforce dest: isoiec_9798_2_5_special_TTP_bdkey_different_actors_A_P intro: event_predOrdI)+      next+        case swapped note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid0),+                                LN ''Kab'' tid2, s(MV ''A'' tid0), s(MV ''Text2'' tid0)+                             |}+                             ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc_1 tid3) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (fastforce+)?+    qed (insert facts, fastforce+)?+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_special_TTP_bdkey_A_injective_agreement_P:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(AV ''P'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_5_special_TTP_bdkey_A_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_5_special_TTP_bdkey_P &+          ( tid1, isoiec_9798_2_5_special_TTP_bdkey_P_2 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1), LN ''Kab'' tid1,+             s(MV ''TVPa'' tid1), s(MV ''Text3'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''P'' tid0),+                  s(MV ''Kab'' tid0), LN ''TVPa'' tid0, s(MV ''Text3'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc tid1) note_unified facts = this facts+        hence "Kbd ( s(AV ''P'' tid1) )+                   ( s(MV ''A'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) )"+          by simp note facts = this facts+        thus ?thesis proof(cases rule: Kbd_cases)+          case noswap note_unified facts = this facts+          thus ?thesis by (fastforce dest: isoiec_9798_2_5_special_TTP_bdkey_different_actors_A_P intro: event_predOrdI)+        next+          case swapped note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_special_TTP_bdkey_B_non_injective_agreement_P:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_5_special_TTP_bdkey_B_3 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_2_5_special_TTP_bdkey_P &+        ( tid1, isoiec_9798_2_5_special_TTP_bdkey_P_2 ) : steps t &+        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1), LN ''Kab'' tid1,+           LN ''TNp'' tid1, s(MV ''Text2'' tid1)+        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),+                s(MV ''Kab'' tid0), s(MV ''TNp'' tid0), s(MV ''Text2'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid0),+                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)+                       |}+                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc_1 tid1) note_unified facts = this facts+    hence "Kbd ( s(AV ''P'' tid1) )+               ( s(MV ''B'' tid1) ) = Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) )"+      by simp note facts = this facts+    thus ?thesis proof(cases rule: Kbd_cases)+      case noswap note_unified facts = this facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_3'', s(MV ''TNa'' tid0),+                              s(AV ''B'' tid0), s(MV ''Text5'' tid0)+                           |}+                           ( LN ''Kab'' tid1 ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest: isoiec_9798_2_5_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)+      next+        case (isoiec_9798_2_5_special_TTP_bdkey_A_3_enc tid2) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid2,+                                LN ''Kab'' tid1, s(AV ''B'' tid0), s(MV ''Text3'' tid2)+                             |}+                             ( Kbd ( s(AV ''A'' tid2) ) ( s(AV ''P'' tid2) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest: isoiec_9798_2_5_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)+        next+          case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc tid3) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    next+      case swapped note_unified facts = this facts+      thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+    qed (fastforce+)?+  qed (insert facts, fastforce+)?+qed++++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_special_TTP_bdkey_P_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_P"+    "RLKR(s(AV ''P'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''B'' tid0)) ~: reveals t"+    "LN ''Kab'' tid0 : knows t"+  shows "False"+using facts proof(sources! " LN ''Kab'' tid0 ")+  case isoiec_9798_2_6_special_TTP_bdkey_P_3_Kab note_unified facts = this facts+  thus ?thesis by (fastforce dest!: ltk_secrecy)+next+  case isoiec_9798_2_6_special_TTP_bdkey_P_3_Kab_1 note_unified facts = this facts+  thus ?thesis by (fastforce dest!: ltk_secrecy)+qed (insert facts, fastforce+)?++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_special_TTP_bdkey_A_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_A"+    "RLKR(s(AV ''A'' tid0)) ~: reveals t"+    "RLKR(s(AV ''P'' tid0)) ~: reveals t"+    "RLKR(s(MV ''B'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_6_special_TTP_bdkey_A_3 ) : steps t"+    "s(MV ''Kab'' tid0) : knows t"+  shows "False"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_1'', LN ''Ra'' tid0,+                          s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)+                       |}+                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc tid1) note_unified facts = this facts+    hence "Kbd ( s(AV ''P'' tid1) )+               ( s(MV ''A'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) )"+      by simp note facts = this facts+    thus ?thesis proof(cases rule: Kbd_cases)+      case noswap note_unified facts = this facts+      thus ?thesis by (fastforce dest: isoiec_9798_2_6_special_TTP_bdkey_different_actors_A_P intro: event_predOrdI)+    next+      case swapped note_unified facts = this facts+      thus ?thesis by (fastforce dest: isoiec_9798_2_6_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)+    qed (fastforce+)?+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_special_TTP_bdkey_B_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_B"+    "RLKR(s(AV ''A'' tid0)) ~: reveals t"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_6_special_TTP_bdkey_B_4 ) : steps t"+    "s(MV ''Kab'' tid0) : knows t"+  shows "False"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_2'', LN ''Rb'' tid0,+                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)+                       |}+                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc_1 tid1) note_unified facts = this facts+    hence "Kbd ( s(AV ''P'' tid1) )+               ( s(MV ''B'' tid1) ) = Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) )"+      by simp note facts = this facts+    thus ?thesis proof(cases rule: Kbd_cases)+      case noswap note_unified facts = this facts+      thus ?thesis by (fastforce dest: isoiec_9798_2_6_special_TTP_bdkey_different_actors_B_P intro: event_predOrdI)+    next+      case swapped note_unified facts = this facts+      thus ?thesis by (fastforce dest: isoiec_9798_2_6_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)+    qed (fastforce+)?+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_special_TTP_bdkey_A_injective_agreement_B:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''P'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_6_special_TTP_bdkey_A_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_6_special_TTP_bdkey_B &+          ( tid1, isoiec_9798_2_6_special_TTP_bdkey_B_5 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''P'' tid1),+             s(MV ''Kab'' tid1), s(MV ''Rpa'' tid1), LN ''Rb'' tid1,+             s(MV ''Text6'' tid1), s(MV ''Text8'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''P'' tid0),+                  s(MV ''Kab'' tid0), LN ''Rpa'' tid0, s(MV ''Rb'' tid0),+                  s(MV ''Text6'' tid0), s(MV ''Text8'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_1'', LN ''Ra'' tid0,+                              s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)+                           |}+                           ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc tid1) note_unified facts = this facts+        hence "Kbd ( s(AV ''P'' tid1) )+                   ( s(MV ''A'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) )"+          by simp note facts = this facts+        thus ?thesis proof(cases rule: Kbd_cases)+          case noswap note_unified facts = this facts+          thus ?thesis by (fastforce dest: isoiec_9798_2_6_special_TTP_bdkey_different_actors_A_P intro: event_predOrdI)+        next+          case swapped note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_5'', s(MV ''Rb'' tid0),+                                  LN ''Rpa'' tid0, s(MV ''Text8'' tid0)+                               |}+                               ( LN ''Kab'' tid1 ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest: isoiec_9798_2_6_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)+          next+            case (isoiec_9798_2_6_special_TTP_bdkey_B_5_enc tid2) note_unified facts = this facts+            thus ?thesis proof(sources! "+                             Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_2'', LN ''Rb'' tid2,+                                    LN ''Kab'' tid1, s(AV ''A'' tid2), s(MV ''Text3'' tid2)+                                 |}+                                 ( Kbd ( s(AV ''B'' tid2) ) ( s(MV ''P'' tid2) ) ) ")+              case fake note_unified facts = this facts+              thus ?thesis by (fastforce dest: isoiec_9798_2_6_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)+            next+              case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc_1 tid3) note_unified facts = this facts+              hence "Kbd ( s(AV ''P'' tid0) )+                         ( s(MV ''B'' tid0) ) = Kbd ( s(AV ''B'' tid2) ) ( s(MV ''P'' tid2) )"+                by simp note facts = this facts+              thus ?thesis proof(cases rule: Kbd_cases)+                case noswap note_unified facts = this facts+                thus ?thesis by (fastforce dest: isoiec_9798_2_6_special_TTP_bdkey_different_actors_B_P intro: event_predOrdI)+              next+                case swapped note_unified facts = this facts+                thus ?thesis proof(sources! "+                                 Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_4'', LN ''Rpa'' tid0,+                                        LN ''Rb'' tid2, s(MV ''Text6'' tid2)+                                     |}+                                     ( LN ''Kab'' tid1 ) ")+                  case fake note_unified facts = this facts+                  thus ?thesis by (fastforce dest: isoiec_9798_2_6_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)+                next+                  case (isoiec_9798_2_6_special_TTP_bdkey_A_4_enc tid3) note_unified facts = this facts+                  thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+                qed (insert facts, fastforce+)?+              qed (fastforce+)?+            qed (insert facts, fastforce+)?+          qed (insert facts, fastforce+)?+        qed (fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_special_TTP_bdkey_B_injective_agreement_A:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(MV ''P'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_6_special_TTP_bdkey_B_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_6_special_TTP_bdkey_A &+          ( tid1, isoiec_9798_2_6_special_TTP_bdkey_A_4 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),+             s(MV ''Kab'' tid1), LN ''Rpa'' tid1, s(MV ''Rb'' tid1),+             s(MV ''Text6'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),+                  s(MV ''Kab'' tid0), s(MV ''Rpa'' tid0), LN ''Rb'' tid0,+                  s(MV ''Text6'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_2'', LN ''Rb'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc_1 tid1) note_unified facts = this facts+        hence "Kbd ( s(AV ''P'' tid1) )+                   ( s(MV ''B'' tid1) ) = Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) )"+          by simp note facts = this facts+        thus ?thesis proof(cases rule: Kbd_cases)+          case noswap note_unified facts = this facts+          thus ?thesis by (fastforce dest: isoiec_9798_2_6_special_TTP_bdkey_different_actors_B_P intro: event_predOrdI)+        next+          case swapped note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_4'', s(MV ''Rpa'' tid0),+                                  LN ''Rb'' tid0, s(MV ''Text6'' tid0)+                               |}+                               ( LN ''Kab'' tid1 ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest: isoiec_9798_2_6_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)+          next+            case (isoiec_9798_2_6_special_TTP_bdkey_A_4_enc tid2) note_unified facts = this facts+            thus ?thesis proof(sources! "+                             Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_1'', LN ''Ra'' tid2,+                                    LN ''Kab'' tid1, s(MV ''B'' tid2), s(MV ''Text4'' tid2)+                                 |}+                                 ( Kbd ( s(AV ''A'' tid2) ) ( s(AV ''P'' tid2) ) ) ")+              case fake note_unified facts = this facts+              thus ?thesis by (fastforce dest: isoiec_9798_2_6_special_TTP_bdkey_P_secret_Kab intro: event_predOrdI)+            next+              case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc tid3) note_unified facts = this facts+              hence "Kbd ( s(AV ''A'' tid2) )+                         ( s(AV ''P'' tid2) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid1) )"+                by simp note facts = this facts+              thus ?thesis proof(cases rule: Kbd_cases)+                case noswap note_unified facts = this facts+                thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+              next+                case swapped note_unified facts = this facts+                thus ?thesis by (fastforce dest: isoiec_9798_2_6_special_TTP_bdkey_different_actors_A_P intro: event_predOrdI)+              qed (fastforce+)?+            qed (insert facts, fastforce+)?+          qed (insert facts, fastforce+)?+        qed (fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_special_TTP_bdkey_A_injective_agreement_P:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''P'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_6_special_TTP_bdkey_A_3 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_6_special_TTP_bdkey_P &+          ( tid1, isoiec_9798_2_6_special_TTP_bdkey_P_3 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),+             s(MV ''Ra'' tid1), LN ''Kab'' tid1, s(MV ''Text4'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''P'' tid0),+                  LN ''Ra'' tid0, s(MV ''Kab'' tid0), s(MV ''Text4'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_1'', LN ''Ra'' tid0,+                              s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)+                           |}+                           ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc tid1) note_unified facts = this facts+        hence "Kbd ( s(AV ''P'' tid1) )+                   ( s(MV ''A'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) )"+          by simp note facts = this facts+        thus ?thesis proof(cases rule: Kbd_cases)+          case noswap note_unified facts = this facts+          thus ?thesis by (fastforce dest: isoiec_9798_2_6_special_TTP_bdkey_different_actors_A_P intro: event_predOrdI)+        next+          case swapped note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_special_TTP_bdkey_B_injective_agreement_P:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(MV ''P'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_6_special_TTP_bdkey_B_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_6_special_TTP_bdkey_P &+          ( tid1, isoiec_9798_2_6_special_TTP_bdkey_P_3 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),+             s(MV ''Rb'' tid1), LN ''Kab'' tid1, s(MV ''Text3'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),+                  LN ''Rb'' tid0, s(MV ''Kab'' tid0), s(MV ''Text3'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_2'', LN ''Rb'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc_1 tid1) note_unified facts = this facts+        hence "Kbd ( s(AV ''P'' tid1) )+                   ( s(MV ''B'' tid1) ) = Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) )"+          by simp note facts = this facts+        thus ?thesis proof(cases rule: Kbd_cases)+          case noswap note_unified facts = this facts+          thus ?thesis by (fastforce dest: isoiec_9798_2_6_special_TTP_bdkey_different_actors_B_P intro: event_predOrdI)+        next+          case swapped note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj) qed  end
data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-2-udkey_cert_auto.thy view
@@ -1,1843 +1,2023 @@ theory "isoiec-9798-2-udkey_cert_auto" imports-  "../ESPLogic"-begin--role isoiec_9798_2_1_udkey_A-where "isoiec_9798_2_1_udkey_A =-  [ Send ''leak_A'' ( sN ''TNA'' )-  , Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>-  , Send ''1'' <| sAV ''A'', sAV ''B'', sMV ''Text2'',-                  PEnc <| sC ''isoiec_9798_2_1_enc_1'', sN ''TNA'', sMV ''Text1'' |>-                       ( sK ''A'' ''B'' )-               |>-  ]"--role isoiec_9798_2_1_udkey_B-where "isoiec_9798_2_1_udkey_B =-  [ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Text2'',-                  PEnc <| sC ''isoiec_9798_2_1_enc_1'', sMV ''TNA'', sMV ''Text1'' |>-                       ( PSymK ( sMV ''A'' ) ( sAV ''B'' ) )-               |>-  ]"--role isoiec_9798_2_2_udkey_A-where "isoiec_9798_2_2_udkey_A =-  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''RB'', sMV ''Text1'' |>-  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>-  , Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'',-                  PEnc <| sC ''isoiec_9798_2_2_enc_2'', sMV ''RB'', sMV ''Text2'' |>-                       ( PSymK ( sAV ''A'' ) ( sMV ''B'' ) )-               |>-  ]"--role isoiec_9798_2_2_udkey_B-where "isoiec_9798_2_2_udkey_B =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''RB'', sMV ''Text1'' |>-  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'',-                  PEnc <| sC ''isoiec_9798_2_2_enc_2'', sN ''RB'', sMV ''Text2'' |>-                       ( sK ''A'' ''B'' )-               |>-  ]"--role isoiec_9798_2_3_udkey_A-where "isoiec_9798_2_3_udkey_A =-  [ Send ''leak_A'' ( sN ''TNA'' )-  , Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>-  , Send ''1'' <| sAV ''A'', sAV ''B'', sMV ''Text2'',-                  PEnc <| sC ''isoiec_9798_2_3_enc_1'', sN ''TNA'', sMV ''Text1'' |>-                       ( sK ''A'' ''B'' )-               |>-  , Recv ''2'' <| sAV ''B'', sAV ''A'', sMV ''Text4'',-                  PEnc <| sC ''isoiec_9798_2_3_enc_2'', sMV ''TNB'', sMV ''Text3'' |>-                       ( sK ''B'' ''A'' )-               |>-  ]"--role isoiec_9798_2_3_udkey_B-where "isoiec_9798_2_3_udkey_B =-  [ Send ''leak_B'' ( sN ''TNB'' )-  , Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Text2'',-                  PEnc <| sC ''isoiec_9798_2_3_enc_1'', sMV ''TNA'', sMV ''Text1'' |>-                       ( PSymK ( sMV ''A'' ) ( sAV ''B'' ) )-               |>-  , Recv ''text_2'' <| sMV ''Text3'', sMV ''Text4'' |>-  , Send ''2'' <| sAV ''B'', sMV ''A'', sMV ''Text4'',-                  PEnc <| sC ''isoiec_9798_2_3_enc_2'', sN ''TNB'', sMV ''Text3'' |>-                       ( PSymK ( sAV ''B'' ) ( sMV ''A'' ) )-               |>-  ]"--role isoiec_9798_2_4_udkey_A-where "isoiec_9798_2_4_udkey_A =-  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''RB'', sMV ''Text1'' |>-  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>-  , Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'',-                  PEnc <| sC ''isoiec_9798_2_4_enc_1'', sN ''RA'', sMV ''RB'',-                          sMV ''Text2''-                       |>-                       ( PSymK ( sAV ''A'' ) ( sMV ''B'' ) )-               |>-  , Recv ''3'' <| sMV ''B'', sAV ''A'', sMV ''Text5'',-                  PEnc <| sC ''isoiec_9798_2_4_enc_2'', sMV ''RB'', sN ''RA'',-                          sMV ''Text4''-                       |>-                       ( PSymK ( sMV ''B'' ) ( sAV ''A'' ) )-               |>-  ]"--role isoiec_9798_2_4_udkey_B-where "isoiec_9798_2_4_udkey_B =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''RB'', sMV ''Text1'' |>-  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'',-                  PEnc <| sC ''isoiec_9798_2_4_enc_1'', sMV ''RA'', sN ''RB'',-                          sMV ''Text2''-                       |>-                       ( sK ''A'' ''B'' )-               |>-  , Recv ''text_3'' <| sMV ''Text4'', sMV ''Text5'' |>-  , Send ''3'' <| sAV ''B'', sAV ''A'', sMV ''Text5'',-                  PEnc <| sC ''isoiec_9798_2_4_enc_2'', sN ''RB'', sMV ''RA'',-                          sMV ''Text4''-                       |>-                       ( sK ''B'' ''A'' )-               |>-  ]"--role isoiec_9798_2_5_udkey_A-where "isoiec_9798_2_5_udkey_A =-  [ Send ''leak_A'' <| sN ''TVPa'', sN ''TNa'' |>-  , Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''A'', sAV ''P'', sN ''TVPa'', sAV ''B'',-                  sMV ''Text1''-               |>-  , Recv ''2'' <| sAV ''P'', sAV ''A'', sMV ''Text4'',-                  PEnc <| sC ''isoiec_9798_2_5_enc_2_1'', sN ''TVPa'', sMV ''Kab'',-                          sAV ''B'', sMV ''Text3''-                       |>-                       ( sK ''A'' ''P'' ),-                  sMV ''TokenPA_for_B''-               |>-  , Recv ''text_3'' <| sMV ''Text5'', sMV ''Text6'' |>-  , Send ''3'' <| sAV ''A'', sAV ''B'', sMV ''Text6'', sAV ''P'',-                  sMV ''TokenPA_for_B'',-                  PEnc <| sC ''isoiec_9798_2_5_enc_3'', sN ''TNa'', sAV ''B'',-                          sMV ''Text5''-                       |>-                       ( sMV ''Kab'' )-               |>-  , Recv ''4'' <| sAV ''B'', sAV ''A'', sMV ''Text8'',-                  PEnc <| sC ''isoiec_9798_2_5_enc_4'', sMV ''TNb'', sAV ''A'',-                          sMV ''Text7''-                       |>-                       ( sMV ''Kab'' )-               |>-  ]"--role isoiec_9798_2_5_udkey_B-where "isoiec_9798_2_5_udkey_B =-  [ Send ''leak_B'' ( sN ''TNb'' )-  , Recv ''3'' <| sMV ''A'', sAV ''B'', sMV ''Text6'', sMV ''P'',-                  PEnc <| sC ''isoiec_9798_2_5_enc_2_2'', sMV ''TNp'', sMV ''Kab'',-                          sMV ''A'', sMV ''Text2''-                       |>-                       ( PSymK ( sAV ''B'' ) ( sMV ''P'' ) ),-                  PEnc <| sC ''isoiec_9798_2_5_enc_3'', sMV ''TNa'', sAV ''B'',-                          sMV ''Text5''-                       |>-                       ( sMV ''Kab'' )-               |>-  , Recv ''text_4'' <| sMV ''Text7'', sMV ''Text8'' |>-  , Send ''4'' <| sAV ''B'', sMV ''A'', sMV ''Text8'',-                  PEnc <| sC ''isoiec_9798_2_5_enc_4'', sN ''TNb'', sMV ''A'',-                          sMV ''Text7''-                       |>-                       ( sMV ''Kab'' )-               |>-  ]"--role isoiec_9798_2_5_udkey_P-where "isoiec_9798_2_5_udkey_P =-  [ Send ''leak_P'' ( sN ''TNp'' )-  , Recv ''1'' <| sMV ''A'', sAV ''P'', sMV ''TVPa'', sMV ''B'',-                  sMV ''Text1''-               |>-  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'', sMV ''Text4'' |>-  , Send ''2'' <| sAV ''P'', sMV ''A'', sMV ''Text4'',-                  PEnc <| sC ''isoiec_9798_2_5_enc_2_1'', sMV ''TVPa'', sN ''Kab'',-                          sMV ''B'', sMV ''Text3''-                       |>-                       ( PSymK ( sMV ''A'' ) ( sAV ''P'' ) ),-                  PEnc <| sC ''isoiec_9798_2_5_enc_2_2'', sN ''TNp'', sN ''Kab'',-                          sMV ''A'', sMV ''Text2''-                       |>-                       ( PSymK ( sMV ''B'' ) ( sAV ''P'' ) )-               |>-  ]"--role isoiec_9798_2_6_udkey_A-where "isoiec_9798_2_6_udkey_A =-  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>-  , Recv ''text_2'' ( sMV ''Text2'' )-  , Send ''2'' <| sAV ''A'', sAV ''P'', sN ''Ra'', sMV ''Rb'', sMV ''B'',-                  sMV ''Text2''-               |>-  , Recv ''3'' <| sAV ''P'', sAV ''A'', sMV ''Text5'',-                  PEnc <| sC ''isoiec_9798_2_6_enc_3_1'', sN ''Ra'', sMV ''Kab'',-                          sMV ''B'', sMV ''Text4''-                       |>-                       ( sK ''A'' ''P'' ),-                  sMV ''TokenPA_for_B''-               |>-  , Recv ''text_4'' <| sMV ''Text6'', sMV ''Text7'' |>-  , Send ''4'' <| sAV ''A'', sMV ''B'', sMV ''Text7'', sAV ''P'',-                  sMV ''TokenPA_for_B'',-                  PEnc <| sC ''isoiec_9798_2_6_enc_4'', sN ''Rpa'', sMV ''Rb'',-                          sMV ''Text6''-                       |>-                       ( sMV ''Kab'' )-               |>-  , Recv ''5'' <| sMV ''B'', sAV ''A'', sMV ''Text9'',-                  PEnc <| sC ''isoiec_9798_2_6_enc_5'', sMV ''Rb'', sN ''Rpa'',-                          sMV ''Text8''-                       |>-                       ( sMV ''Kab'' )-               |>-  ]"--role isoiec_9798_2_6_udkey_B-where "isoiec_9798_2_6_udkey_B =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>-  , Recv ''4'' <| sAV ''A'', sAV ''B'', sMV ''Text7'', sMV ''P'',-                  PEnc <| sC ''isoiec_9798_2_6_enc_3_2'', sN ''Rb'', sMV ''Kab'',-                          sAV ''A'', sMV ''Text3''-                       |>-                       ( PSymK ( sAV ''B'' ) ( sMV ''P'' ) ),-                  PEnc <| sC ''isoiec_9798_2_6_enc_4'', sMV ''Rpa'', sN ''Rb'',-                          sMV ''Text6''-                       |>-                       ( sMV ''Kab'' )-               |>-  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>-  , Send ''5'' <| sAV ''B'', sAV ''A'', sMV ''Text9'',-                  PEnc <| sC ''isoiec_9798_2_6_enc_5'', sN ''Rb'', sMV ''Rpa'',-                          sMV ''Text8''-                       |>-                       ( sMV ''Kab'' )-               |>-  ]"--role isoiec_9798_2_6_udkey_P-where "isoiec_9798_2_6_udkey_P =-  [ Recv ''2'' <| sMV ''A'', sAV ''P'', sMV ''Ra'', sMV ''Rb'', sMV ''B'',-                  sMV ''Text2''-               |>-  , Recv ''text_3'' <| sMV ''Text3'', sMV ''Text4'', sMV ''Text5'' |>-  , Send ''3'' <| sAV ''P'', sMV ''A'', sMV ''Text5'',-                  PEnc <| sC ''isoiec_9798_2_6_enc_3_1'', sMV ''Ra'', sN ''Kab'',-                          sMV ''B'', sMV ''Text4''-                       |>-                       ( PSymK ( sMV ''A'' ) ( sAV ''P'' ) ),-                  PEnc <| sC ''isoiec_9798_2_6_enc_3_2'', sMV ''Rb'', sN ''Kab'',-                          sMV ''A'', sMV ''Text3''-                       |>-                       ( PSymK ( sMV ''B'' ) ( sAV ''P'' ) )-               |>-  ]"--protocol isoiec_9798_2_bdkey-where "isoiec_9798_2_bdkey =-{ isoiec_9798_2_1_udkey_A, isoiec_9798_2_1_udkey_B,-  isoiec_9798_2_2_udkey_A, isoiec_9798_2_2_udkey_B,-  isoiec_9798_2_3_udkey_A, isoiec_9798_2_3_udkey_B,-  isoiec_9798_2_4_udkey_A, isoiec_9798_2_4_udkey_B,-  isoiec_9798_2_5_udkey_A, isoiec_9798_2_5_udkey_B,-  isoiec_9798_2_5_udkey_P, isoiec_9798_2_6_udkey_A,-  isoiec_9798_2_6_udkey_B, isoiec_9798_2_6_udkey_P-}"--locale restricted_isoiec_9798_2_bdkey_state = isoiec_9798_2_bdkey_state--type_invariant isoiec_9798_2_bdkey_composed_typing for isoiec_9798_2_bdkey-where "isoiec_9798_2_bdkey_composed_typing = mk_typing-  [ ((isoiec_9798_2_1_udkey_B, ''A''), (KnownT isoiec_9798_2_1_udkey_B_1))-  , ((isoiec_9798_2_3_udkey_B, ''A''), (KnownT isoiec_9798_2_3_udkey_B_1))-  , ((isoiec_9798_2_5_udkey_B, ''A''), (KnownT isoiec_9798_2_5_udkey_B_3))-  , ((isoiec_9798_2_5_udkey_P, ''A''), (KnownT isoiec_9798_2_5_udkey_P_1))-  , ((isoiec_9798_2_6_udkey_P, ''A''), (KnownT isoiec_9798_2_6_udkey_P_2))-  , ((isoiec_9798_2_2_udkey_A, ''B''), (KnownT isoiec_9798_2_2_udkey_A_1))-  , ((isoiec_9798_2_4_udkey_A, ''B''), (KnownT isoiec_9798_2_4_udkey_A_1))-  , ((isoiec_9798_2_5_udkey_P, ''B''), (KnownT isoiec_9798_2_5_udkey_P_1))-  , ((isoiec_9798_2_6_udkey_A, ''B''), (KnownT isoiec_9798_2_6_udkey_A_1))-  , ((isoiec_9798_2_6_udkey_P, ''B''), (KnownT isoiec_9798_2_6_udkey_P_2))-  , ((isoiec_9798_2_5_udkey_A, ''Kab''),-     (SumT (KnownT isoiec_9798_2_5_udkey_A_2) (NonceT isoiec_9798_2_5_udkey_P ''Kab'')))-  , ((isoiec_9798_2_5_udkey_B, ''Kab''),-     (SumT (KnownT isoiec_9798_2_5_udkey_B_3) (NonceT isoiec_9798_2_5_udkey_P ''Kab'')))-  , ((isoiec_9798_2_6_udkey_A, ''Kab''),-     (SumT (KnownT isoiec_9798_2_6_udkey_A_3) (NonceT isoiec_9798_2_6_udkey_P ''Kab'')))-  , ((isoiec_9798_2_6_udkey_B, ''Kab''),-     (SumT (KnownT isoiec_9798_2_6_udkey_B_4) (NonceT isoiec_9798_2_6_udkey_P ''Kab'')))-  , ((isoiec_9798_2_5_udkey_B, ''P''), (KnownT isoiec_9798_2_5_udkey_B_3))-  , ((isoiec_9798_2_6_udkey_B, ''P''), (KnownT isoiec_9798_2_6_udkey_B_4))-  , ((isoiec_9798_2_4_udkey_B, ''RA''),-     (SumT (KnownT isoiec_9798_2_4_udkey_B_2) (NonceT isoiec_9798_2_4_udkey_A ''RA'')))-  , ((isoiec_9798_2_2_udkey_A, ''RB''), (KnownT isoiec_9798_2_2_udkey_A_1))-  , ((isoiec_9798_2_4_udkey_A, ''RB''), (KnownT isoiec_9798_2_4_udkey_A_1))-  , ((isoiec_9798_2_6_udkey_P, ''Ra''), (KnownT isoiec_9798_2_6_udkey_P_2))-  , ((isoiec_9798_2_6_udkey_A, ''Rb''), (KnownT isoiec_9798_2_6_udkey_A_1))-  , ((isoiec_9798_2_6_udkey_P, ''Rb''), (KnownT isoiec_9798_2_6_udkey_P_2))-  , ((isoiec_9798_2_6_udkey_B, ''Rpa''),-     (SumT (KnownT isoiec_9798_2_6_udkey_B_4) (NonceT isoiec_9798_2_6_udkey_A ''Rpa'')))-  , ((isoiec_9798_2_1_udkey_B, ''TNA''),-     (SumT (KnownT isoiec_9798_2_1_udkey_B_1) (NonceT isoiec_9798_2_1_udkey_A ''TNA'')))-  , ((isoiec_9798_2_3_udkey_B, ''TNA''),-     (SumT (KnownT isoiec_9798_2_3_udkey_B_1) (NonceT isoiec_9798_2_3_udkey_A ''TNA'')))-  , ((isoiec_9798_2_3_udkey_A, ''TNB''),-     (SumT (KnownT isoiec_9798_2_3_udkey_A_2) (NonceT isoiec_9798_2_3_udkey_B ''TNB'')))-  , ((isoiec_9798_2_5_udkey_B, ''TNa''),-     (SumT (KnownT isoiec_9798_2_5_udkey_B_3) (NonceT isoiec_9798_2_5_udkey_A ''TNa'')))-  , ((isoiec_9798_2_5_udkey_A, ''TNb''),-     (SumT (KnownT isoiec_9798_2_5_udkey_A_4) (NonceT isoiec_9798_2_5_udkey_B ''TNb'')))-  , ((isoiec_9798_2_5_udkey_B, ''TNp''),-     (SumT (KnownT isoiec_9798_2_5_udkey_B_3) (NonceT isoiec_9798_2_5_udkey_P ''TNp'')))-  , ((isoiec_9798_2_5_udkey_P, ''TVPa''),-     (KnownT isoiec_9798_2_5_udkey_P_1))-  , ((isoiec_9798_2_1_udkey_A, ''Text1''),-     (KnownT isoiec_9798_2_1_udkey_A_text_1))-  , ((isoiec_9798_2_1_udkey_B, ''Text1''),-     (KnownT isoiec_9798_2_1_udkey_B_1))-  , ((isoiec_9798_2_2_udkey_A, ''Text1''),-     (KnownT isoiec_9798_2_2_udkey_A_1))-  , ((isoiec_9798_2_2_udkey_B, ''Text1''),-     (KnownT isoiec_9798_2_2_udkey_B_text_1))-  , ((isoiec_9798_2_3_udkey_A, ''Text1''),-     (KnownT isoiec_9798_2_3_udkey_A_text_1))-  , ((isoiec_9798_2_3_udkey_B, ''Text1''),-     (KnownT isoiec_9798_2_3_udkey_B_1))-  , ((isoiec_9798_2_4_udkey_A, ''Text1''),-     (KnownT isoiec_9798_2_4_udkey_A_1))-  , ((isoiec_9798_2_4_udkey_B, ''Text1''),-     (KnownT isoiec_9798_2_4_udkey_B_text_1))-  , ((isoiec_9798_2_5_udkey_A, ''Text1''),-     (KnownT isoiec_9798_2_5_udkey_A_text_1))-  , ((isoiec_9798_2_5_udkey_P, ''Text1''),-     (KnownT isoiec_9798_2_5_udkey_P_1))-  , ((isoiec_9798_2_6_udkey_A, ''Text1''),-     (KnownT isoiec_9798_2_6_udkey_A_1))-  , ((isoiec_9798_2_6_udkey_B, ''Text1''),-     (KnownT isoiec_9798_2_6_udkey_B_text_1))-  , ((isoiec_9798_2_1_udkey_A, ''Text2''),-     (KnownT isoiec_9798_2_1_udkey_A_text_1))-  , ((isoiec_9798_2_1_udkey_B, ''Text2''),-     (KnownT isoiec_9798_2_1_udkey_B_1))-  , ((isoiec_9798_2_2_udkey_A, ''Text2''),-     (KnownT isoiec_9798_2_2_udkey_A_text_2))-  , ((isoiec_9798_2_2_udkey_B, ''Text2''),-     (KnownT isoiec_9798_2_2_udkey_B_2))-  , ((isoiec_9798_2_3_udkey_A, ''Text2''),-     (KnownT isoiec_9798_2_3_udkey_A_text_1))-  , ((isoiec_9798_2_3_udkey_B, ''Text2''),-     (KnownT isoiec_9798_2_3_udkey_B_1))-  , ((isoiec_9798_2_4_udkey_A, ''Text2''),-     (KnownT isoiec_9798_2_4_udkey_A_text_2))-  , ((isoiec_9798_2_4_udkey_B, ''Text2''),-     (KnownT isoiec_9798_2_4_udkey_B_2))-  , ((isoiec_9798_2_5_udkey_B, ''Text2''),-     (KnownT isoiec_9798_2_5_udkey_B_3))-  , ((isoiec_9798_2_5_udkey_P, ''Text2''),-     (KnownT isoiec_9798_2_5_udkey_P_text_2))-  , ((isoiec_9798_2_6_udkey_A, ''Text2''),-     (KnownT isoiec_9798_2_6_udkey_A_text_2))-  , ((isoiec_9798_2_6_udkey_P, ''Text2''),-     (KnownT isoiec_9798_2_6_udkey_P_2))-  , ((isoiec_9798_2_2_udkey_A, ''Text3''),-     (KnownT isoiec_9798_2_2_udkey_A_text_2))-  , ((isoiec_9798_2_2_udkey_B, ''Text3''),-     (KnownT isoiec_9798_2_2_udkey_B_2))-  , ((isoiec_9798_2_3_udkey_A, ''Text3''),-     (KnownT isoiec_9798_2_3_udkey_A_2))-  , ((isoiec_9798_2_3_udkey_B, ''Text3''),-     (KnownT isoiec_9798_2_3_udkey_B_text_2))-  , ((isoiec_9798_2_4_udkey_A, ''Text3''),-     (KnownT isoiec_9798_2_4_udkey_A_text_2))-  , ((isoiec_9798_2_4_udkey_B, ''Text3''),-     (KnownT isoiec_9798_2_4_udkey_B_2))-  , ((isoiec_9798_2_5_udkey_A, ''Text3''),-     (KnownT isoiec_9798_2_5_udkey_A_2))-  , ((isoiec_9798_2_5_udkey_P, ''Text3''),-     (KnownT isoiec_9798_2_5_udkey_P_text_2))-  , ((isoiec_9798_2_6_udkey_B, ''Text3''),-     (KnownT isoiec_9798_2_6_udkey_B_4))-  , ((isoiec_9798_2_6_udkey_P, ''Text3''),-     (KnownT isoiec_9798_2_6_udkey_P_text_3))-  , ((isoiec_9798_2_3_udkey_A, ''Text4''),-     (KnownT isoiec_9798_2_3_udkey_A_2))-  , ((isoiec_9798_2_3_udkey_B, ''Text4''),-     (KnownT isoiec_9798_2_3_udkey_B_text_2))-  , ((isoiec_9798_2_4_udkey_A, ''Text4''),-     (KnownT isoiec_9798_2_4_udkey_A_3))-  , ((isoiec_9798_2_4_udkey_B, ''Text4''),-     (KnownT isoiec_9798_2_4_udkey_B_text_3))-  , ((isoiec_9798_2_5_udkey_A, ''Text4''),-     (KnownT isoiec_9798_2_5_udkey_A_2))-  , ((isoiec_9798_2_5_udkey_P, ''Text4''),-     (KnownT isoiec_9798_2_5_udkey_P_text_2))-  , ((isoiec_9798_2_6_udkey_A, ''Text4''),-     (KnownT isoiec_9798_2_6_udkey_A_3))-  , ((isoiec_9798_2_6_udkey_P, ''Text4''),-     (KnownT isoiec_9798_2_6_udkey_P_text_3))-  , ((isoiec_9798_2_4_udkey_A, ''Text5''),-     (KnownT isoiec_9798_2_4_udkey_A_3))-  , ((isoiec_9798_2_4_udkey_B, ''Text5''),-     (KnownT isoiec_9798_2_4_udkey_B_text_3))-  , ((isoiec_9798_2_5_udkey_A, ''Text5''),-     (KnownT isoiec_9798_2_5_udkey_A_text_3))-  , ((isoiec_9798_2_5_udkey_B, ''Text5''),-     (KnownT isoiec_9798_2_5_udkey_B_3))-  , ((isoiec_9798_2_6_udkey_A, ''Text5''),-     (KnownT isoiec_9798_2_6_udkey_A_3))-  , ((isoiec_9798_2_6_udkey_P, ''Text5''),-     (KnownT isoiec_9798_2_6_udkey_P_text_3))-  , ((isoiec_9798_2_5_udkey_A, ''Text6''),-     (KnownT isoiec_9798_2_5_udkey_A_text_3))-  , ((isoiec_9798_2_5_udkey_B, ''Text6''),-     (KnownT isoiec_9798_2_5_udkey_B_3))-  , ((isoiec_9798_2_6_udkey_A, ''Text6''),-     (KnownT isoiec_9798_2_6_udkey_A_text_4))-  , ((isoiec_9798_2_6_udkey_B, ''Text6''),-     (KnownT isoiec_9798_2_6_udkey_B_4))-  , ((isoiec_9798_2_5_udkey_A, ''Text7''),-     (KnownT isoiec_9798_2_5_udkey_A_4))-  , ((isoiec_9798_2_5_udkey_B, ''Text7''),-     (KnownT isoiec_9798_2_5_udkey_B_text_4))-  , ((isoiec_9798_2_6_udkey_A, ''Text7''),-     (KnownT isoiec_9798_2_6_udkey_A_text_4))-  , ((isoiec_9798_2_6_udkey_B, ''Text7''),-     (KnownT isoiec_9798_2_6_udkey_B_4))-  , ((isoiec_9798_2_5_udkey_A, ''Text8''),-     (KnownT isoiec_9798_2_5_udkey_A_4))-  , ((isoiec_9798_2_5_udkey_B, ''Text8''),-     (KnownT isoiec_9798_2_5_udkey_B_text_4))-  , ((isoiec_9798_2_6_udkey_A, ''Text8''),-     (KnownT isoiec_9798_2_6_udkey_A_5))-  , ((isoiec_9798_2_6_udkey_B, ''Text8''),-     (KnownT isoiec_9798_2_6_udkey_B_text_5))-  , ((isoiec_9798_2_6_udkey_A, ''Text9''),-     (KnownT isoiec_9798_2_6_udkey_A_5))-  , ((isoiec_9798_2_6_udkey_B, ''Text9''),-     (KnownT isoiec_9798_2_6_udkey_B_text_5))-  , ((isoiec_9798_2_5_udkey_A, ''TokenPA_for_B''),-     (KnownT isoiec_9798_2_5_udkey_A_2))-  , ((isoiec_9798_2_6_udkey_A, ''TokenPA_for_B''),-     (KnownT isoiec_9798_2_6_udkey_A_3))-  ]"--sublocale isoiec_9798_2_bdkey_state < isoiec_9798_2_bdkey_composed_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_2_bdkey_composed_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_2_bdkey_composed_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_2_1_udkey_A_text_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_1_udkey_A_text_1_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_1_udkey_B_1_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_1_udkey_B_1_TNA t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_1_enc_1'', s(MV ''TNA'' tid0),-               s(MV ''Text1'' tid0)-            |}-            ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_1_udkey_B_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_1_enc_1'', s(MV ''TNA'' tid0),-               s(MV ''Text1'' tid0)-            |}-            ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_1_udkey_B_1_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_2_udkey_A_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_2_udkey_A_1_RB t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_2_udkey_A_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_2_udkey_A_text_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_2_udkey_A_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_2_udkey_B_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_2_enc_2'', LN ''RB'' tid0, s(MV ''Text2'' tid0)-            |}-            ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_2_udkey_B_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_udkey_A_text_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_udkey_A_text_1_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_udkey_A_2_TNB t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_3_enc_2'', s(MV ''TNB'' tid0),-               s(MV ''Text3'' tid0)-            |}-            ( K ( s(AV ''B'' tid0) ) ( s(AV ''A'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_3_udkey_A_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_3_enc_2'', s(MV ''TNB'' tid0),-               s(MV ''Text3'' tid0)-            |}-            ( K ( s(AV ''B'' tid0) ) ( s(AV ''A'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_3_udkey_A_2_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_udkey_B_1_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_udkey_B_1_TNA t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_3_enc_1'', s(MV ''TNA'' tid0),-               s(MV ''Text1'' tid0)-            |}-            ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_3_udkey_B_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_3_enc_1'', s(MV ''TNA'' tid0),-               s(MV ''Text1'' tid0)-            |}-            ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_3_udkey_B_1_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_udkey_B_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_udkey_B_text_2_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_udkey_A_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_udkey_A_1_RB t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_udkey_A_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_udkey_A_text_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_udkey_A_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_udkey_A_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_4_enc_2'', s(MV ''RB'' tid0), LN ''RA'' tid0,-               s(MV ''Text4'' tid0)-            |}-            ( K ( s(MV ''B'' tid0) ) ( s(AV ''A'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_4_udkey_A_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_udkey_B_2_RA t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_4_enc_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,-               s(MV ''Text2'' tid0)-            |}-            ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_4_udkey_B_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_4_enc_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,-               s(MV ''Text2'' tid0)-            |}-            ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_4_udkey_B_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_udkey_B_text_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_udkey_B_text_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_A_2_Kab t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,-               s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)-            |}-            ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_udkey_A_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,-               s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)-            |}-            ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_udkey_A_2_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_A_2_TokenPA_for_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_A_text_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_A_text_3_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_A_4_TNb t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_4'', s(MV ''TNb'' tid0),-               s(AV ''A'' tid0), s(MV ''Text7'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_udkey_A_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_4'', s(MV ''TNb'' tid0),-               s(AV ''A'' tid0), s(MV ''Text7'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_udkey_A_4_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_B_3_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_B_3_Kab t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),-               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)-            |}-            ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_udkey_B_3_P t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_B_3_TNa t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid0),-               s(AV ''B'' tid0), s(MV ''Text5'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_udkey_B_3_TNp t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),-               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)-            |}-            ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_udkey_B_3_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),-               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)-            |}-            ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_udkey_B_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid0),-               s(AV ''B'' tid0), s(MV ''Text5'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_udkey_B_3_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_B_text_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_B_text_4_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_P_1_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_P_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_P_1_TVPa t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_P_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_P_text_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_P_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_P_text_2_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_A_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_A_1_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_A_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_A_3_Kab t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,-               s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)-            |}-            ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_udkey_A_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,-               s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)-            |}-            ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_udkey_A_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_A_3_TokenPA_for_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_A_text_4_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_A_text_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_A_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_5'', s(MV ''Rb'' tid0), LN ''Rpa'' tid0,-               s(MV ''Text8'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_udkey_A_5_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_B_4_Kab t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,-               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)-            |}-            ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_udkey_B_4_P t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_B_4_Rpa t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_4'', s(MV ''Rpa'' tid0), LN ''Rb'' tid0,-               s(MV ''Text6'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_udkey_B_4_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,-               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)-            |}-            ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_udkey_B_4_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_4'', s(MV ''Rpa'' tid0), LN ''Rb'' tid0,-               s(MV ''Text6'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_udkey_B_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_B_text_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_B_text_5_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_P_2_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_P_2_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_P_2_Ra t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_P_2_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_P_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_P_text_3_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_P_text_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_P_text_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_2_bdkey_composed_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_2_bdkey_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_1_udkey_B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_1_udkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_1_udkey_B_1 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_1_udkey_A &-        ( tid1, isoiec_9798_2_1_udkey_A_1 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,-           s(MV ''Text1'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),-                s(MV ''Text1'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_1_enc_1'', s(MV ''TNA'' tid0),-                          s(MV ''Text1'' tid0)-                       |}-                       ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_1_udkey_A_1_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_2_udkey_B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_2_udkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_2_udkey_B_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_2_udkey_A &-        ( tid1, isoiec_9798_2_2_udkey_A_2 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(MV ''RB'' tid1),-           s(MV ''Text2'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''RB'' tid0,-                s(MV ''Text2'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_2_enc_2'', LN ''RB'' tid0, s(MV ''Text2'' tid0)-                       |}-                       ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_2_udkey_A_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_3_udkey_A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_3_udkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_3_udkey_A_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_3_udkey_B &-        ( tid1, isoiec_9798_2_3_udkey_B_2 ) : steps t &-        {| s(MV ''A'' tid1), s(AV ''B'' tid1), LN ''TNB'' tid1,-           s(MV ''Text3'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNB'' tid0),-                s(MV ''Text3'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_3_enc_2'', s(MV ''TNB'' tid0),-                          s(MV ''Text3'' tid0)-                       |}-                       ( K ( s(AV ''B'' tid0) ) ( s(AV ''A'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_3_udkey_B_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_3_udkey_B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_3_udkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_3_udkey_B_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_3_udkey_A &-        ( tid1, isoiec_9798_2_3_udkey_A_1 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,-           s(MV ''Text1'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),-                s(MV ''Text1'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_3_enc_1'', s(MV ''TNA'' tid0),-                          s(MV ''Text1'' tid0)-                       |}-                       ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_3_udkey_A_1_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_4_udkey_A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_4_udkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_4_udkey_A_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_4_udkey_B &-        ( tid1, isoiec_9798_2_4_udkey_B_3 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''RA'' tid1), LN ''RB'' tid1,-           s(MV ''Text2'' tid1), s(MV ''Text4'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''RA'' tid0,-                s(MV ''RB'' tid0), s(MV ''Text2'' tid0), s(MV ''Text4'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_4_enc_2'', s(MV ''RB'' tid0), LN ''RA'' tid0,-                          s(MV ''Text4'' tid0)-                       |}-                       ( K ( s(MV ''B'' tid0) ) ( s(AV ''A'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_4_udkey_B_3_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_2_4_enc_1'', LN ''RA'' tid0, LN ''RB'' tid1,-                            s(MV ''Text2'' tid1)-                         |}-                         ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid1) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest!: ltk_secrecy)-    next-      case (isoiec_9798_2_4_udkey_A_2_enc tid2) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_4_udkey_B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_4_udkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_4_udkey_B_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_4_udkey_A &-        ( tid1, isoiec_9798_2_4_udkey_A_2 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''RA'' tid1, s(MV ''RB'' tid1),-           s(MV ''Text2'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''RA'' tid0),-                LN ''RB'' tid0, s(MV ''Text2'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_4_enc_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,-                          s(MV ''Text2'' tid0)-                       |}-                       ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_4_udkey_A_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_udkey_P_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_udkey_P"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "LN ''Kab'' tid0 : knows t"-  shows "False"-using facts proof(sources! " LN ''Kab'' tid0 ")-  case isoiec_9798_2_5_udkey_P_2_Kab note_unified facts = this facts-  thus ?thesis by (fastsimp dest!: ltk_secrecy)-next-  case isoiec_9798_2_5_udkey_P_2_Kab_1 note_unified facts = this facts-  thus ?thesis by (fastsimp dest!: ltk_secrecy)-qed (insert facts, fastsimp+)?--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_udkey_A_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_udkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_udkey_A_2 ) : steps t"-    "s(MV ''Kab'' tid0) : knows t"-  shows "False"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_udkey_P_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp dest: isoiec_9798_2_5_udkey_P_secret_Kab intro: event_predOrdI)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_udkey_B_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_udkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_udkey_B_3 ) : steps t"-    "s(MV ''Kab'' tid0) : knows t"-  shows "False"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),-                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)-                       |}-                       ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_udkey_P_2_enc_1 tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp dest: isoiec_9798_2_5_udkey_P_secret_Kab intro: event_predOrdI)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_udkey_A_non_injective_agreement_B:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_udkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_udkey_A_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_5_udkey_B &-        ( tid1, isoiec_9798_2_5_udkey_B_4 ) : steps t &-        {| s(MV ''A'' tid1), s(AV ''B'' tid1), s(MV ''P'' tid1),-           s(MV ''Kab'' tid1), s(MV ''TNa'' tid1), s(MV ''Text5'' tid1),-           LN ''TNb'' tid1, s(MV ''Text7'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''P'' tid0),-                s(MV ''Kab'' tid0), LN ''TNa'' tid0, s(MV ''Text5'' tid0),-                s(MV ''TNb'' tid0), s(MV ''Text7'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_udkey_P_2_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_2_5_enc_4'', s(MV ''TNb'' tid0),-                            s(AV ''A'' tid0), s(MV ''Text7'' tid0)-                         |}-                         ( LN ''Kab'' tid1 ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest: isoiec_9798_2_5_udkey_P_secret_Kab intro: event_predOrdI)-    next-      case (isoiec_9798_2_5_udkey_B_4_enc tid2) note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid2),-                              LN ''Kab'' tid1, s(AV ''A'' tid0), s(MV ''Text2'' tid2)-                           |}-                           ( K ( s(AV ''B'' tid2) ) ( s(MV ''P'' tid2) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest: isoiec_9798_2_5_udkey_P_secret_Kab intro: event_predOrdI)-      next-        case (isoiec_9798_2_5_udkey_P_2_enc_1 tid3) note_unified facts = this facts-        thus ?thesis proof(sources! "-                         Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid2),-                                s(AV ''B'' tid0), s(MV ''Text5'' tid2)-                             |}-                             ( LN ''Kab'' tid1 ) ")-          case fake note_unified facts = this facts-          thus ?thesis by (fastsimp dest: isoiec_9798_2_5_udkey_P_secret_Kab intro: event_predOrdI)-        next-          case (isoiec_9798_2_5_udkey_A_3_enc tid3) note_unified facts = this facts-          thus ?thesis proof(sources! "-                           Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid3, LN ''Kab'' tid1,-                                  s(AV ''B'' tid0), s(MV ''Text3'' tid3)-                               |}-                               ( K ( s(AV ''A'' tid3) ) ( s(AV ''P'' tid3) ) ) ")-            case fake note_unified facts = this facts-            thus ?thesis by (fastsimp dest: isoiec_9798_2_5_udkey_P_secret_Kab intro: event_predOrdI)-          next-            case (isoiec_9798_2_5_udkey_P_2_enc tid4) note_unified facts = this facts-            thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-          qed (insert facts, fastsimp+)?-        qed (insert facts, fastsimp+)?-      qed (insert facts, fastsimp+)?-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_udkey_B_non_injective_agreement_A:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_udkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_udkey_B_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_5_udkey_A &-        ( tid1, isoiec_9798_2_5_udkey_A_3 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(AV ''P'' tid1),-           s(MV ''Kab'' tid1), LN ''TNa'' tid1, s(MV ''Text5'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),-                s(MV ''Kab'' tid0), s(MV ''TNa'' tid0), s(MV ''Text5'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),-                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)-                       |}-                       ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_udkey_P_2_enc_1 tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid0),-                            s(AV ''B'' tid0), s(MV ''Text5'' tid0)-                         |}-                         ( LN ''Kab'' tid1 ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest: isoiec_9798_2_5_udkey_P_secret_Kab intro: event_predOrdI)-    next-      case (isoiec_9798_2_5_udkey_A_3_enc tid2) note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid2, LN ''Kab'' tid1,-                              s(AV ''B'' tid0), s(MV ''Text3'' tid2)-                           |}-                           ( K ( s(AV ''A'' tid2) ) ( s(AV ''P'' tid2) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest: isoiec_9798_2_5_udkey_P_secret_Kab intro: event_predOrdI)-      next-        case (isoiec_9798_2_5_udkey_P_2_enc tid3) note_unified facts = this facts-        thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-      qed (insert facts, fastsimp+)?-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_udkey_A_non_injective_agreement_P:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_udkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_udkey_A_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_5_udkey_P &-        ( tid1, isoiec_9798_2_5_udkey_P_2 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1), LN ''Kab'' tid1,-           s(MV ''TVPa'' tid1), s(MV ''Text3'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''P'' tid0),-                s(MV ''Kab'' tid0), LN ''TVPa'' tid0, s(MV ''Text3'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_udkey_P_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_udkey_B_non_injective_agreement_P:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_udkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_udkey_B_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_5_udkey_P &-        ( tid1, isoiec_9798_2_5_udkey_P_2 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1), LN ''Kab'' tid1,-           LN ''TNp'' tid1, s(MV ''Text2'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),-                s(MV ''Kab'' tid0), s(MV ''TNp'' tid0), s(MV ''Text2'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),-                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)-                       |}-                       ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_udkey_P_2_enc_1 tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_udkey_P_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_udkey_P"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "LN ''Kab'' tid0 : knows t"-  shows "False"-using facts proof(sources! " LN ''Kab'' tid0 ")-  case isoiec_9798_2_6_udkey_P_3_Kab note_unified facts = this facts-  thus ?thesis by (fastsimp dest!: ltk_secrecy)-next-  case isoiec_9798_2_6_udkey_P_3_Kab_1 note_unified facts = this facts-  thus ?thesis by (fastsimp dest!: ltk_secrecy)-qed (insert facts, fastsimp+)?--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_udkey_A_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_udkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_udkey_A_3 ) : steps t"-    "s(MV ''Kab'' tid0) : knows t"-  shows "False"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,-                          s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)-                       |}-                       ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_udkey_P_3_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp dest: isoiec_9798_2_6_udkey_P_secret_Kab intro: event_predOrdI)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_udkey_B_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_udkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_udkey_B_4 ) : steps t"-    "s(MV ''Kab'' tid0) : knows t"-  shows "False"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_udkey_P_3_enc_1 tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp dest: isoiec_9798_2_6_udkey_P_secret_Kab intro: event_predOrdI)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_udkey_A_non_injective_agreement_B:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_udkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_udkey_A_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_6_udkey_B &-        ( tid1, isoiec_9798_2_6_udkey_B_5 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''P'' tid1),-           s(MV ''Kab'' tid1), s(MV ''Rpa'' tid1), LN ''Rb'' tid1,-           s(MV ''Text6'' tid1), s(MV ''Text8'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''P'' tid0),-                s(MV ''Kab'' tid0), LN ''Rpa'' tid0, s(MV ''Rb'' tid0),-                s(MV ''Text6'' tid0), s(MV ''Text8'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,-                          s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)-                       |}-                       ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_udkey_P_3_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_2_6_enc_5'', s(MV ''Rb'' tid0), LN ''Rpa'' tid0,-                            s(MV ''Text8'' tid0)-                         |}-                         ( LN ''Kab'' tid1 ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest: isoiec_9798_2_6_udkey_P_secret_Kab intro: event_predOrdI)-    next-      case (isoiec_9798_2_6_udkey_B_5_enc tid2) note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid2, LN ''Kab'' tid1,-                              s(AV ''A'' tid2), s(MV ''Text3'' tid2)-                           |}-                           ( K ( s(AV ''B'' tid2) ) ( s(MV ''P'' tid2) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest: isoiec_9798_2_6_udkey_P_secret_Kab intro: event_predOrdI)-      next-        case (isoiec_9798_2_6_udkey_P_3_enc_1 tid3) note_unified facts = this facts-        thus ?thesis proof(sources! "-                         Enc {| LC ''isoiec_9798_2_6_enc_4'', LN ''Rpa'' tid0, LN ''Rb'' tid2,-                                s(MV ''Text6'' tid2)-                             |}-                             ( LN ''Kab'' tid1 ) ")-          case fake note_unified facts = this facts-          thus ?thesis by (fastsimp dest: isoiec_9798_2_6_udkey_P_secret_Kab intro: event_predOrdI)-        next-          case (isoiec_9798_2_6_udkey_A_4_enc tid3) note_unified facts = this facts-          thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-        qed (insert facts, fastsimp+)?-      qed (insert facts, fastsimp+)?-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_udkey_B_non_injective_agreement_A:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_udkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_udkey_B_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_6_udkey_A &-        ( tid1, isoiec_9798_2_6_udkey_A_4 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),-           s(MV ''Kab'' tid1), LN ''Rpa'' tid1, s(MV ''Rb'' tid1),-           s(MV ''Text6'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),-                s(MV ''Kab'' tid0), s(MV ''Rpa'' tid0), LN ''Rb'' tid0,-                s(MV ''Text6'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_udkey_P_3_enc_1 tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_2_6_enc_4'', s(MV ''Rpa'' tid0), LN ''Rb'' tid0,-                            s(MV ''Text6'' tid0)-                         |}-                         ( LN ''Kab'' tid1 ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest: isoiec_9798_2_6_udkey_P_secret_Kab intro: event_predOrdI)-    next-      case (isoiec_9798_2_6_udkey_A_4_enc tid2) note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid2, LN ''Kab'' tid1,-                              s(MV ''B'' tid2), s(MV ''Text4'' tid2)-                           |}-                           ( K ( s(AV ''A'' tid2) ) ( s(AV ''P'' tid2) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest: isoiec_9798_2_6_udkey_P_secret_Kab intro: event_predOrdI)-      next-        case (isoiec_9798_2_6_udkey_P_3_enc tid3) note_unified facts = this facts-        thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-      qed (insert facts, fastsimp+)?-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_udkey_A_non_injective_agreement_P:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_udkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_udkey_A_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_6_udkey_P &-        ( tid1, isoiec_9798_2_6_udkey_P_3 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),-           s(MV ''Ra'' tid1), LN ''Kab'' tid1, s(MV ''Text4'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''P'' tid0),-                LN ''Ra'' tid0, s(MV ''Kab'' tid0), s(MV ''Text4'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,-                          s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)-                       |}-                       ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_udkey_P_3_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_udkey_B_non_injective_agreement_P:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_udkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_udkey_B_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_6_udkey_P &-        ( tid1, isoiec_9798_2_6_udkey_P_3 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),-           s(MV ''Rb'' tid1), LN ''Kab'' tid1, s(MV ''Text3'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),-                LN ''Rb'' tid0, s(MV ''Kab'' tid0), s(MV ''Text3'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_udkey_P_3_enc_1 tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?+  "ESPLogic"+begin++role isoiec_9798_2_1_udkey_A+where "isoiec_9798_2_1_udkey_A =+  [ Send ''leak_A'' ( sN ''TNA'' )+  , Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>+  , Send ''1'' <| sAV ''A'', sAV ''B'', sMV ''Text2'',+                  PEnc <| sC ''isoiec_9798_2_1_enc_1'', sN ''TNA'', sMV ''Text1'' |>+                       ( sK ''A'' ''B'' )+               |>+  ]"++role isoiec_9798_2_1_udkey_B+where "isoiec_9798_2_1_udkey_B =+  [ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Text2'',+                  PEnc <| sC ''isoiec_9798_2_1_enc_1'', sMV ''TNA'', sMV ''Text1'' |>+                       ( PSymK ( sMV ''A'' ) ( sAV ''B'' ) )+               |>+  ]"++role isoiec_9798_2_2_udkey_A+where "isoiec_9798_2_2_udkey_A =+  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''RB'', sMV ''Text1'' |>+  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>+  , Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'',+                  PEnc <| sC ''isoiec_9798_2_2_enc_2'', sMV ''RB'', sMV ''Text2'' |>+                       ( PSymK ( sAV ''A'' ) ( sMV ''B'' ) )+               |>+  ]"++role isoiec_9798_2_2_udkey_B+where "isoiec_9798_2_2_udkey_B =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''RB'', sMV ''Text1'' |>+  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'',+                  PEnc <| sC ''isoiec_9798_2_2_enc_2'', sN ''RB'', sMV ''Text2'' |>+                       ( sK ''A'' ''B'' )+               |>+  ]"++role isoiec_9798_2_3_udkey_A+where "isoiec_9798_2_3_udkey_A =+  [ Send ''leak_A'' ( sN ''TNA'' )+  , Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>+  , Send ''1'' <| sAV ''A'', sAV ''B'', sMV ''Text2'',+                  PEnc <| sC ''isoiec_9798_2_3_enc_1'', sN ''TNA'', sMV ''Text1'' |>+                       ( sK ''A'' ''B'' )+               |>+  , Recv ''2'' <| sAV ''B'', sAV ''A'', sMV ''Text4'',+                  PEnc <| sC ''isoiec_9798_2_3_enc_2'', sMV ''TNB'', sMV ''Text3'' |>+                       ( sK ''B'' ''A'' )+               |>+  ]"++role isoiec_9798_2_3_udkey_B+where "isoiec_9798_2_3_udkey_B =+  [ Send ''leak_B'' ( sN ''TNB'' )+  , Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Text2'',+                  PEnc <| sC ''isoiec_9798_2_3_enc_1'', sMV ''TNA'', sMV ''Text1'' |>+                       ( PSymK ( sMV ''A'' ) ( sAV ''B'' ) )+               |>+  , Recv ''text_2'' <| sMV ''Text3'', sMV ''Text4'' |>+  , Send ''2'' <| sAV ''B'', sMV ''A'', sMV ''Text4'',+                  PEnc <| sC ''isoiec_9798_2_3_enc_2'', sN ''TNB'', sMV ''Text3'' |>+                       ( PSymK ( sAV ''B'' ) ( sMV ''A'' ) )+               |>+  ]"++role isoiec_9798_2_4_udkey_A+where "isoiec_9798_2_4_udkey_A =+  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''RB'', sMV ''Text1'' |>+  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>+  , Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'',+                  PEnc <| sC ''isoiec_9798_2_4_enc_1'', sN ''RA'', sMV ''RB'',+                          sMV ''Text2''+                       |>+                       ( PSymK ( sAV ''A'' ) ( sMV ''B'' ) )+               |>+  , Recv ''3'' <| sMV ''B'', sAV ''A'', sMV ''Text5'',+                  PEnc <| sC ''isoiec_9798_2_4_enc_2'', sMV ''RB'', sN ''RA'',+                          sMV ''Text4''+                       |>+                       ( PSymK ( sMV ''B'' ) ( sAV ''A'' ) )+               |>+  ]"++role isoiec_9798_2_4_udkey_B+where "isoiec_9798_2_4_udkey_B =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''RB'', sMV ''Text1'' |>+  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'',+                  PEnc <| sC ''isoiec_9798_2_4_enc_1'', sMV ''RA'', sN ''RB'',+                          sMV ''Text2''+                       |>+                       ( sK ''A'' ''B'' )+               |>+  , Recv ''text_3'' <| sMV ''Text4'', sMV ''Text5'' |>+  , Send ''3'' <| sAV ''B'', sAV ''A'', sMV ''Text5'',+                  PEnc <| sC ''isoiec_9798_2_4_enc_2'', sN ''RB'', sMV ''RA'',+                          sMV ''Text4''+                       |>+                       ( sK ''B'' ''A'' )+               |>+  ]"++role isoiec_9798_2_5_udkey_A+where "isoiec_9798_2_5_udkey_A =+  [ Send ''leak_A'' <| sN ''TVPa'', sN ''TNa'' |>+  , Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''A'', sAV ''P'', sN ''TVPa'', sAV ''B'',+                  sMV ''Text1''+               |>+  , Recv ''2'' <| sAV ''P'', sAV ''A'', sMV ''Text4'',+                  PEnc <| sC ''isoiec_9798_2_5_enc_2_1'', sN ''TVPa'', sMV ''Kab'',+                          sAV ''B'', sMV ''Text3''+                       |>+                       ( sK ''A'' ''P'' ),+                  sMV ''TokenPA_for_B''+               |>+  , Recv ''text_3'' <| sMV ''Text5'', sMV ''Text6'' |>+  , Send ''3'' <| sAV ''A'', sAV ''B'', sMV ''Text6'', sAV ''P'',+                  sMV ''TokenPA_for_B'',+                  PEnc <| sC ''isoiec_9798_2_5_enc_3'', sN ''TNa'', sAV ''B'',+                          sMV ''Text5''+                       |>+                       ( sMV ''Kab'' )+               |>+  , Recv ''4'' <| sAV ''B'', sAV ''A'', sMV ''Text8'',+                  PEnc <| sC ''isoiec_9798_2_5_enc_4'', sMV ''TNb'', sAV ''A'',+                          sMV ''Text7''+                       |>+                       ( sMV ''Kab'' )+               |>+  ]"++role isoiec_9798_2_5_udkey_B+where "isoiec_9798_2_5_udkey_B =+  [ Send ''leak_B'' ( sN ''TNb'' )+  , Recv ''3'' <| sMV ''A'', sAV ''B'', sMV ''Text6'', sMV ''P'',+                  PEnc <| sC ''isoiec_9798_2_5_enc_2_2'', sMV ''TNp'', sMV ''Kab'',+                          sMV ''A'', sMV ''Text2''+                       |>+                       ( PSymK ( sAV ''B'' ) ( sMV ''P'' ) ),+                  PEnc <| sC ''isoiec_9798_2_5_enc_3'', sMV ''TNa'', sAV ''B'',+                          sMV ''Text5''+                       |>+                       ( sMV ''Kab'' )+               |>+  , Recv ''text_4'' <| sMV ''Text7'', sMV ''Text8'' |>+  , Send ''4'' <| sAV ''B'', sMV ''A'', sMV ''Text8'',+                  PEnc <| sC ''isoiec_9798_2_5_enc_4'', sN ''TNb'', sMV ''A'',+                          sMV ''Text7''+                       |>+                       ( sMV ''Kab'' )+               |>+  ]"++role isoiec_9798_2_5_udkey_P+where "isoiec_9798_2_5_udkey_P =+  [ Send ''leak_P'' ( sN ''TNp'' )+  , Recv ''1'' <| sMV ''A'', sAV ''P'', sMV ''TVPa'', sMV ''B'',+                  sMV ''Text1''+               |>+  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'', sMV ''Text4'' |>+  , Send ''2'' <| sAV ''P'', sMV ''A'', sMV ''Text4'',+                  PEnc <| sC ''isoiec_9798_2_5_enc_2_1'', sMV ''TVPa'', sN ''Kab'',+                          sMV ''B'', sMV ''Text3''+                       |>+                       ( PSymK ( sMV ''A'' ) ( sAV ''P'' ) ),+                  PEnc <| sC ''isoiec_9798_2_5_enc_2_2'', sN ''TNp'', sN ''Kab'',+                          sMV ''A'', sMV ''Text2''+                       |>+                       ( PSymK ( sMV ''B'' ) ( sAV ''P'' ) )+               |>+  ]"++role isoiec_9798_2_6_udkey_A+where "isoiec_9798_2_6_udkey_A =+  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>+  , Recv ''text_2'' ( sMV ''Text2'' )+  , Send ''2'' <| sAV ''A'', sAV ''P'', sN ''Ra'', sMV ''Rb'', sMV ''B'',+                  sMV ''Text2''+               |>+  , Recv ''3'' <| sAV ''P'', sAV ''A'', sMV ''Text5'',+                  PEnc <| sC ''isoiec_9798_2_6_enc_3_1'', sN ''Ra'', sMV ''Kab'',+                          sMV ''B'', sMV ''Text4''+                       |>+                       ( sK ''A'' ''P'' ),+                  sMV ''TokenPA_for_B''+               |>+  , Recv ''text_4'' <| sMV ''Text6'', sMV ''Text7'' |>+  , Send ''4'' <| sAV ''A'', sMV ''B'', sMV ''Text7'', sAV ''P'',+                  sMV ''TokenPA_for_B'',+                  PEnc <| sC ''isoiec_9798_2_6_enc_4'', sN ''Rpa'', sMV ''Rb'',+                          sMV ''Text6''+                       |>+                       ( sMV ''Kab'' )+               |>+  , Recv ''5'' <| sMV ''B'', sAV ''A'', sMV ''Text9'',+                  PEnc <| sC ''isoiec_9798_2_6_enc_5'', sMV ''Rb'', sN ''Rpa'',+                          sMV ''Text8''+                       |>+                       ( sMV ''Kab'' )+               |>+  ]"++role isoiec_9798_2_6_udkey_B+where "isoiec_9798_2_6_udkey_B =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>+  , Recv ''4'' <| sAV ''A'', sAV ''B'', sMV ''Text7'', sMV ''P'',+                  PEnc <| sC ''isoiec_9798_2_6_enc_3_2'', sN ''Rb'', sMV ''Kab'',+                          sAV ''A'', sMV ''Text3''+                       |>+                       ( PSymK ( sAV ''B'' ) ( sMV ''P'' ) ),+                  PEnc <| sC ''isoiec_9798_2_6_enc_4'', sMV ''Rpa'', sN ''Rb'',+                          sMV ''Text6''+                       |>+                       ( sMV ''Kab'' )+               |>+  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>+  , Send ''5'' <| sAV ''B'', sAV ''A'', sMV ''Text9'',+                  PEnc <| sC ''isoiec_9798_2_6_enc_5'', sN ''Rb'', sMV ''Rpa'',+                          sMV ''Text8''+                       |>+                       ( sMV ''Kab'' )+               |>+  ]"++role isoiec_9798_2_6_udkey_P+where "isoiec_9798_2_6_udkey_P =+  [ Recv ''2'' <| sMV ''A'', sAV ''P'', sMV ''Ra'', sMV ''Rb'', sMV ''B'',+                  sMV ''Text2''+               |>+  , Recv ''text_3'' <| sMV ''Text3'', sMV ''Text4'', sMV ''Text5'' |>+  , Send ''3'' <| sAV ''P'', sMV ''A'', sMV ''Text5'',+                  PEnc <| sC ''isoiec_9798_2_6_enc_3_1'', sMV ''Ra'', sN ''Kab'',+                          sMV ''B'', sMV ''Text4''+                       |>+                       ( PSymK ( sMV ''A'' ) ( sAV ''P'' ) ),+                  PEnc <| sC ''isoiec_9798_2_6_enc_3_2'', sMV ''Rb'', sN ''Kab'',+                          sMV ''A'', sMV ''Text3''+                       |>+                       ( PSymK ( sMV ''B'' ) ( sAV ''P'' ) )+               |>+  ]"++protocol isoiec_9798_2_bdkey+where "isoiec_9798_2_bdkey =+{ isoiec_9798_2_1_udkey_A, isoiec_9798_2_1_udkey_B,+  isoiec_9798_2_2_udkey_A, isoiec_9798_2_2_udkey_B,+  isoiec_9798_2_3_udkey_A, isoiec_9798_2_3_udkey_B,+  isoiec_9798_2_4_udkey_A, isoiec_9798_2_4_udkey_B,+  isoiec_9798_2_5_udkey_A, isoiec_9798_2_5_udkey_B,+  isoiec_9798_2_5_udkey_P, isoiec_9798_2_6_udkey_A,+  isoiec_9798_2_6_udkey_B, isoiec_9798_2_6_udkey_P+}"++locale restricted_isoiec_9798_2_bdkey_state = isoiec_9798_2_bdkey_state++type_invariant isoiec_9798_2_bdkey_composed_typing for isoiec_9798_2_bdkey+where "isoiec_9798_2_bdkey_composed_typing = mk_typing+  [ ((isoiec_9798_2_1_udkey_B, ''A''), (KnownT isoiec_9798_2_1_udkey_B_1))+  , ((isoiec_9798_2_3_udkey_B, ''A''), (KnownT isoiec_9798_2_3_udkey_B_1))+  , ((isoiec_9798_2_5_udkey_B, ''A''), (KnownT isoiec_9798_2_5_udkey_B_3))+  , ((isoiec_9798_2_5_udkey_P, ''A''), (KnownT isoiec_9798_2_5_udkey_P_1))+  , ((isoiec_9798_2_6_udkey_P, ''A''), (KnownT isoiec_9798_2_6_udkey_P_2))+  , ((isoiec_9798_2_2_udkey_A, ''B''), (KnownT isoiec_9798_2_2_udkey_A_1))+  , ((isoiec_9798_2_4_udkey_A, ''B''), (KnownT isoiec_9798_2_4_udkey_A_1))+  , ((isoiec_9798_2_5_udkey_P, ''B''), (KnownT isoiec_9798_2_5_udkey_P_1))+  , ((isoiec_9798_2_6_udkey_A, ''B''), (KnownT isoiec_9798_2_6_udkey_A_1))+  , ((isoiec_9798_2_6_udkey_P, ''B''), (KnownT isoiec_9798_2_6_udkey_P_2))+  , ((isoiec_9798_2_5_udkey_A, ''Kab''),+     (SumT (KnownT isoiec_9798_2_5_udkey_A_2) (NonceT isoiec_9798_2_5_udkey_P ''Kab'')))+  , ((isoiec_9798_2_5_udkey_B, ''Kab''),+     (SumT (KnownT isoiec_9798_2_5_udkey_B_3) (NonceT isoiec_9798_2_5_udkey_P ''Kab'')))+  , ((isoiec_9798_2_6_udkey_A, ''Kab''),+     (SumT (KnownT isoiec_9798_2_6_udkey_A_3) (NonceT isoiec_9798_2_6_udkey_P ''Kab'')))+  , ((isoiec_9798_2_6_udkey_B, ''Kab''),+     (SumT (KnownT isoiec_9798_2_6_udkey_B_4) (NonceT isoiec_9798_2_6_udkey_P ''Kab'')))+  , ((isoiec_9798_2_5_udkey_B, ''P''), (KnownT isoiec_9798_2_5_udkey_B_3))+  , ((isoiec_9798_2_6_udkey_B, ''P''), (KnownT isoiec_9798_2_6_udkey_B_4))+  , ((isoiec_9798_2_4_udkey_B, ''RA''),+     (SumT (KnownT isoiec_9798_2_4_udkey_B_2) (NonceT isoiec_9798_2_4_udkey_A ''RA'')))+  , ((isoiec_9798_2_2_udkey_A, ''RB''), (KnownT isoiec_9798_2_2_udkey_A_1))+  , ((isoiec_9798_2_4_udkey_A, ''RB''), (KnownT isoiec_9798_2_4_udkey_A_1))+  , ((isoiec_9798_2_6_udkey_P, ''Ra''), (KnownT isoiec_9798_2_6_udkey_P_2))+  , ((isoiec_9798_2_6_udkey_A, ''Rb''), (KnownT isoiec_9798_2_6_udkey_A_1))+  , ((isoiec_9798_2_6_udkey_P, ''Rb''), (KnownT isoiec_9798_2_6_udkey_P_2))+  , ((isoiec_9798_2_6_udkey_B, ''Rpa''),+     (SumT (KnownT isoiec_9798_2_6_udkey_B_4) (NonceT isoiec_9798_2_6_udkey_A ''Rpa'')))+  , ((isoiec_9798_2_1_udkey_B, ''TNA''),+     (SumT (KnownT isoiec_9798_2_1_udkey_B_1) (NonceT isoiec_9798_2_1_udkey_A ''TNA'')))+  , ((isoiec_9798_2_3_udkey_B, ''TNA''),+     (SumT (KnownT isoiec_9798_2_3_udkey_B_1) (NonceT isoiec_9798_2_3_udkey_A ''TNA'')))+  , ((isoiec_9798_2_3_udkey_A, ''TNB''),+     (SumT (KnownT isoiec_9798_2_3_udkey_A_2) (NonceT isoiec_9798_2_3_udkey_B ''TNB'')))+  , ((isoiec_9798_2_5_udkey_B, ''TNa''),+     (SumT (KnownT isoiec_9798_2_5_udkey_B_3) (NonceT isoiec_9798_2_5_udkey_A ''TNa'')))+  , ((isoiec_9798_2_5_udkey_A, ''TNb''),+     (SumT (KnownT isoiec_9798_2_5_udkey_A_4) (NonceT isoiec_9798_2_5_udkey_B ''TNb'')))+  , ((isoiec_9798_2_5_udkey_B, ''TNp''),+     (SumT (KnownT isoiec_9798_2_5_udkey_B_3) (NonceT isoiec_9798_2_5_udkey_P ''TNp'')))+  , ((isoiec_9798_2_5_udkey_P, ''TVPa''),+     (KnownT isoiec_9798_2_5_udkey_P_1))+  , ((isoiec_9798_2_1_udkey_A, ''Text1''),+     (KnownT isoiec_9798_2_1_udkey_A_text_1))+  , ((isoiec_9798_2_1_udkey_B, ''Text1''),+     (KnownT isoiec_9798_2_1_udkey_B_1))+  , ((isoiec_9798_2_2_udkey_A, ''Text1''),+     (KnownT isoiec_9798_2_2_udkey_A_1))+  , ((isoiec_9798_2_2_udkey_B, ''Text1''),+     (KnownT isoiec_9798_2_2_udkey_B_text_1))+  , ((isoiec_9798_2_3_udkey_A, ''Text1''),+     (KnownT isoiec_9798_2_3_udkey_A_text_1))+  , ((isoiec_9798_2_3_udkey_B, ''Text1''),+     (KnownT isoiec_9798_2_3_udkey_B_1))+  , ((isoiec_9798_2_4_udkey_A, ''Text1''),+     (KnownT isoiec_9798_2_4_udkey_A_1))+  , ((isoiec_9798_2_4_udkey_B, ''Text1''),+     (KnownT isoiec_9798_2_4_udkey_B_text_1))+  , ((isoiec_9798_2_5_udkey_A, ''Text1''),+     (KnownT isoiec_9798_2_5_udkey_A_text_1))+  , ((isoiec_9798_2_5_udkey_P, ''Text1''),+     (KnownT isoiec_9798_2_5_udkey_P_1))+  , ((isoiec_9798_2_6_udkey_A, ''Text1''),+     (KnownT isoiec_9798_2_6_udkey_A_1))+  , ((isoiec_9798_2_6_udkey_B, ''Text1''),+     (KnownT isoiec_9798_2_6_udkey_B_text_1))+  , ((isoiec_9798_2_1_udkey_A, ''Text2''),+     (KnownT isoiec_9798_2_1_udkey_A_text_1))+  , ((isoiec_9798_2_1_udkey_B, ''Text2''),+     (KnownT isoiec_9798_2_1_udkey_B_1))+  , ((isoiec_9798_2_2_udkey_A, ''Text2''),+     (KnownT isoiec_9798_2_2_udkey_A_text_2))+  , ((isoiec_9798_2_2_udkey_B, ''Text2''),+     (KnownT isoiec_9798_2_2_udkey_B_2))+  , ((isoiec_9798_2_3_udkey_A, ''Text2''),+     (KnownT isoiec_9798_2_3_udkey_A_text_1))+  , ((isoiec_9798_2_3_udkey_B, ''Text2''),+     (KnownT isoiec_9798_2_3_udkey_B_1))+  , ((isoiec_9798_2_4_udkey_A, ''Text2''),+     (KnownT isoiec_9798_2_4_udkey_A_text_2))+  , ((isoiec_9798_2_4_udkey_B, ''Text2''),+     (KnownT isoiec_9798_2_4_udkey_B_2))+  , ((isoiec_9798_2_5_udkey_B, ''Text2''),+     (KnownT isoiec_9798_2_5_udkey_B_3))+  , ((isoiec_9798_2_5_udkey_P, ''Text2''),+     (KnownT isoiec_9798_2_5_udkey_P_text_2))+  , ((isoiec_9798_2_6_udkey_A, ''Text2''),+     (KnownT isoiec_9798_2_6_udkey_A_text_2))+  , ((isoiec_9798_2_6_udkey_P, ''Text2''),+     (KnownT isoiec_9798_2_6_udkey_P_2))+  , ((isoiec_9798_2_2_udkey_A, ''Text3''),+     (KnownT isoiec_9798_2_2_udkey_A_text_2))+  , ((isoiec_9798_2_2_udkey_B, ''Text3''),+     (KnownT isoiec_9798_2_2_udkey_B_2))+  , ((isoiec_9798_2_3_udkey_A, ''Text3''),+     (KnownT isoiec_9798_2_3_udkey_A_2))+  , ((isoiec_9798_2_3_udkey_B, ''Text3''),+     (KnownT isoiec_9798_2_3_udkey_B_text_2))+  , ((isoiec_9798_2_4_udkey_A, ''Text3''),+     (KnownT isoiec_9798_2_4_udkey_A_text_2))+  , ((isoiec_9798_2_4_udkey_B, ''Text3''),+     (KnownT isoiec_9798_2_4_udkey_B_2))+  , ((isoiec_9798_2_5_udkey_A, ''Text3''),+     (KnownT isoiec_9798_2_5_udkey_A_2))+  , ((isoiec_9798_2_5_udkey_P, ''Text3''),+     (KnownT isoiec_9798_2_5_udkey_P_text_2))+  , ((isoiec_9798_2_6_udkey_B, ''Text3''),+     (KnownT isoiec_9798_2_6_udkey_B_4))+  , ((isoiec_9798_2_6_udkey_P, ''Text3''),+     (KnownT isoiec_9798_2_6_udkey_P_text_3))+  , ((isoiec_9798_2_3_udkey_A, ''Text4''),+     (KnownT isoiec_9798_2_3_udkey_A_2))+  , ((isoiec_9798_2_3_udkey_B, ''Text4''),+     (KnownT isoiec_9798_2_3_udkey_B_text_2))+  , ((isoiec_9798_2_4_udkey_A, ''Text4''),+     (KnownT isoiec_9798_2_4_udkey_A_3))+  , ((isoiec_9798_2_4_udkey_B, ''Text4''),+     (KnownT isoiec_9798_2_4_udkey_B_text_3))+  , ((isoiec_9798_2_5_udkey_A, ''Text4''),+     (KnownT isoiec_9798_2_5_udkey_A_2))+  , ((isoiec_9798_2_5_udkey_P, ''Text4''),+     (KnownT isoiec_9798_2_5_udkey_P_text_2))+  , ((isoiec_9798_2_6_udkey_A, ''Text4''),+     (KnownT isoiec_9798_2_6_udkey_A_3))+  , ((isoiec_9798_2_6_udkey_P, ''Text4''),+     (KnownT isoiec_9798_2_6_udkey_P_text_3))+  , ((isoiec_9798_2_4_udkey_A, ''Text5''),+     (KnownT isoiec_9798_2_4_udkey_A_3))+  , ((isoiec_9798_2_4_udkey_B, ''Text5''),+     (KnownT isoiec_9798_2_4_udkey_B_text_3))+  , ((isoiec_9798_2_5_udkey_A, ''Text5''),+     (KnownT isoiec_9798_2_5_udkey_A_text_3))+  , ((isoiec_9798_2_5_udkey_B, ''Text5''),+     (KnownT isoiec_9798_2_5_udkey_B_3))+  , ((isoiec_9798_2_6_udkey_A, ''Text5''),+     (KnownT isoiec_9798_2_6_udkey_A_3))+  , ((isoiec_9798_2_6_udkey_P, ''Text5''),+     (KnownT isoiec_9798_2_6_udkey_P_text_3))+  , ((isoiec_9798_2_5_udkey_A, ''Text6''),+     (KnownT isoiec_9798_2_5_udkey_A_text_3))+  , ((isoiec_9798_2_5_udkey_B, ''Text6''),+     (KnownT isoiec_9798_2_5_udkey_B_3))+  , ((isoiec_9798_2_6_udkey_A, ''Text6''),+     (KnownT isoiec_9798_2_6_udkey_A_text_4))+  , ((isoiec_9798_2_6_udkey_B, ''Text6''),+     (KnownT isoiec_9798_2_6_udkey_B_4))+  , ((isoiec_9798_2_5_udkey_A, ''Text7''),+     (KnownT isoiec_9798_2_5_udkey_A_4))+  , ((isoiec_9798_2_5_udkey_B, ''Text7''),+     (KnownT isoiec_9798_2_5_udkey_B_text_4))+  , ((isoiec_9798_2_6_udkey_A, ''Text7''),+     (KnownT isoiec_9798_2_6_udkey_A_text_4))+  , ((isoiec_9798_2_6_udkey_B, ''Text7''),+     (KnownT isoiec_9798_2_6_udkey_B_4))+  , ((isoiec_9798_2_5_udkey_A, ''Text8''),+     (KnownT isoiec_9798_2_5_udkey_A_4))+  , ((isoiec_9798_2_5_udkey_B, ''Text8''),+     (KnownT isoiec_9798_2_5_udkey_B_text_4))+  , ((isoiec_9798_2_6_udkey_A, ''Text8''),+     (KnownT isoiec_9798_2_6_udkey_A_5))+  , ((isoiec_9798_2_6_udkey_B, ''Text8''),+     (KnownT isoiec_9798_2_6_udkey_B_text_5))+  , ((isoiec_9798_2_6_udkey_A, ''Text9''),+     (KnownT isoiec_9798_2_6_udkey_A_5))+  , ((isoiec_9798_2_6_udkey_B, ''Text9''),+     (KnownT isoiec_9798_2_6_udkey_B_text_5))+  , ((isoiec_9798_2_5_udkey_A, ''TokenPA_for_B''),+     (KnownT isoiec_9798_2_5_udkey_A_2))+  , ((isoiec_9798_2_6_udkey_A, ''TokenPA_for_B''),+     (KnownT isoiec_9798_2_6_udkey_A_3))+  ]"++sublocale isoiec_9798_2_bdkey_state < isoiec_9798_2_bdkey_composed_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_2_bdkey_composed_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_2_bdkey_composed_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_2_1_udkey_A_text_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_1_udkey_A_text_1_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_1_udkey_B_1_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_1_udkey_B_1_TNA t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_1_enc_1'', s(MV ''TNA'' tid0),+               s(MV ''Text1'' tid0)+            |}+            ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_1_udkey_B_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_1_enc_1'', s(MV ''TNA'' tid0),+               s(MV ''Text1'' tid0)+            |}+            ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_1_udkey_B_1_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_2_udkey_A_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_2_udkey_A_1_RB t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_2_udkey_A_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_2_udkey_A_text_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_2_udkey_A_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_2_udkey_B_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_2_enc_2'', LN ''RB'' tid0, s(MV ''Text2'' tid0)+            |}+            ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_2_udkey_B_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_udkey_A_text_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_udkey_A_text_1_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_udkey_A_2_TNB t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_3_enc_2'', s(MV ''TNB'' tid0),+               s(MV ''Text3'' tid0)+            |}+            ( K ( s(AV ''B'' tid0) ) ( s(AV ''A'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_3_udkey_A_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_3_enc_2'', s(MV ''TNB'' tid0),+               s(MV ''Text3'' tid0)+            |}+            ( K ( s(AV ''B'' tid0) ) ( s(AV ''A'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_3_udkey_A_2_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_udkey_B_1_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_udkey_B_1_TNA t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_3_enc_1'', s(MV ''TNA'' tid0),+               s(MV ''Text1'' tid0)+            |}+            ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_3_udkey_B_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_3_enc_1'', s(MV ''TNA'' tid0),+               s(MV ''Text1'' tid0)+            |}+            ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_3_udkey_B_1_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_udkey_B_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_udkey_B_text_2_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_udkey_A_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_udkey_A_1_RB t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_udkey_A_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_udkey_A_text_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_udkey_A_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_udkey_A_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_4_enc_2'', s(MV ''RB'' tid0), LN ''RA'' tid0,+               s(MV ''Text4'' tid0)+            |}+            ( K ( s(MV ''B'' tid0) ) ( s(AV ''A'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_4_udkey_A_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_udkey_B_2_RA t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_4_enc_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,+               s(MV ''Text2'' tid0)+            |}+            ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_4_udkey_B_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_4_enc_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,+               s(MV ''Text2'' tid0)+            |}+            ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_4_udkey_B_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_udkey_B_text_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_udkey_B_text_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_A_2_Kab t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,+               s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)+            |}+            ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_udkey_A_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,+               s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)+            |}+            ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_udkey_A_2_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_A_2_TokenPA_for_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_A_text_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_A_text_3_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_A_4_TNb t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_4'', s(MV ''TNb'' tid0),+               s(AV ''A'' tid0), s(MV ''Text7'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_udkey_A_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_4'', s(MV ''TNb'' tid0),+               s(AV ''A'' tid0), s(MV ''Text7'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_udkey_A_4_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_B_3_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_B_3_Kab t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),+               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)+            |}+            ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_udkey_B_3_P t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_B_3_TNa t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid0),+               s(AV ''B'' tid0), s(MV ''Text5'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_udkey_B_3_TNp t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),+               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)+            |}+            ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_udkey_B_3_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),+               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)+            |}+            ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_udkey_B_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid0),+               s(AV ''B'' tid0), s(MV ''Text5'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_udkey_B_3_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_B_text_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_B_text_4_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_P_1_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_P_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_P_1_TVPa t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_P_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_P_text_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_P_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_P_text_2_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_A_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_A_1_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_A_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_A_3_Kab t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,+               s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)+            |}+            ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_udkey_A_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,+               s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)+            |}+            ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_udkey_A_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_A_3_TokenPA_for_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_A_text_4_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_A_text_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_A_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_5'', s(MV ''Rb'' tid0), LN ''Rpa'' tid0,+               s(MV ''Text8'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_udkey_A_5_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_B_4_Kab t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,+               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)+            |}+            ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_udkey_B_4_P t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_B_4_Rpa t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_4'', s(MV ''Rpa'' tid0), LN ''Rb'' tid0,+               s(MV ''Text6'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_udkey_B_4_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,+               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)+            |}+            ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_udkey_B_4_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_4'', s(MV ''Rpa'' tid0), LN ''Rb'' tid0,+               s(MV ''Text6'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_udkey_B_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_B_text_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_B_text_5_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_P_2_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_P_2_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_P_2_Ra t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_P_2_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_P_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_P_text_3_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_P_text_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_P_text_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_2_bdkey_composed_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_2_bdkey_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_1_udkey_B_non_injective_agreement:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_1_udkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_1_udkey_B_1 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_2_1_udkey_A &+        ( tid1, isoiec_9798_2_1_udkey_A_1 ) : steps t &+        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,+           s(MV ''Text1'' tid1)+        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),+                s(MV ''Text1'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_1_enc_1'', s(MV ''TNA'' tid0),+                          s(MV ''Text1'' tid0)+                       |}+                       ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_1_udkey_A_1_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_2_udkey_B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_2_udkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_2_udkey_B_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_2_udkey_A &+          ( tid1, isoiec_9798_2_2_udkey_A_2 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(MV ''RB'' tid1),+             s(MV ''Text2'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''RB'' tid0,+                  s(MV ''Text2'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_2_enc_2'', LN ''RB'' tid0, s(MV ''Text2'' tid0)+                           |}+                           ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_2_udkey_A_2_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_3_udkey_A_non_injective_agreement:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_3_udkey_A"+    "RLKR(s(AV ''A'' tid0)) ~: reveals t"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_3_udkey_A_2 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_2_3_udkey_B &+        ( tid1, isoiec_9798_2_3_udkey_B_2 ) : steps t &+        {| s(MV ''A'' tid1), s(AV ''B'' tid1), LN ''TNB'' tid1,+           s(MV ''Text3'' tid1)+        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNB'' tid0),+                s(MV ''Text3'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_3_enc_2'', s(MV ''TNB'' tid0),+                          s(MV ''Text3'' tid0)+                       |}+                       ( K ( s(AV ''B'' tid0) ) ( s(AV ''A'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_3_udkey_B_2_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_3_udkey_B_non_injective_agreement:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_3_udkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_3_udkey_B_2 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_2_3_udkey_A &+        ( tid1, isoiec_9798_2_3_udkey_A_1 ) : steps t &+        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,+           s(MV ''Text1'' tid1)+        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),+                s(MV ''Text1'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_3_enc_1'', s(MV ''TNA'' tid0),+                          s(MV ''Text1'' tid0)+                       |}+                       ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_3_udkey_A_1_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_4_udkey_A_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_4_udkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_4_udkey_A_3 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_4_udkey_B &+          ( tid1, isoiec_9798_2_4_udkey_B_3 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''RA'' tid1), LN ''RB'' tid1,+             s(MV ''Text2'' tid1), s(MV ''Text4'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''RA'' tid0,+                  s(MV ''RB'' tid0), s(MV ''Text2'' tid0), s(MV ''Text4'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_4_enc_2'', s(MV ''RB'' tid0), LN ''RA'' tid0,+                              s(MV ''Text4'' tid0)+                           |}+                           ( K ( s(MV ''B'' tid0) ) ( s(AV ''A'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_4_udkey_B_3_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_2_4_enc_1'', LN ''RA'' tid0, LN ''RB'' tid1,+                                s(MV ''Text2'' tid1)+                             |}+                             ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid1) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_2_4_udkey_A_2_enc tid2) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_4_udkey_B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_4_udkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_4_udkey_B_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_4_udkey_A &+          ( tid1, isoiec_9798_2_4_udkey_A_2 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''RA'' tid1, s(MV ''RB'' tid1),+             s(MV ''Text2'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''RA'' tid0),+                  LN ''RB'' tid0, s(MV ''Text2'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_4_enc_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,+                              s(MV ''Text2'' tid0)+                           |}+                           ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_4_udkey_A_2_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_udkey_P_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_udkey_P"+    "RLKR(s(AV ''P'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''B'' tid0)) ~: reveals t"+    "LN ''Kab'' tid0 : knows t"+  shows "False"+using facts proof(sources! " LN ''Kab'' tid0 ")+  case isoiec_9798_2_5_udkey_P_2_Kab note_unified facts = this facts+  thus ?thesis by (fastforce dest!: ltk_secrecy)+next+  case isoiec_9798_2_5_udkey_P_2_Kab_1 note_unified facts = this facts+  thus ?thesis by (fastforce dest!: ltk_secrecy)+qed (insert facts, fastforce+)?++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_udkey_A_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_udkey_A"+    "RLKR(s(AV ''A'' tid0)) ~: reveals t"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(AV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_5_udkey_A_2 ) : steps t"+    "s(MV ''Kab'' tid0) : knows t"+  shows "False"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,+                          s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)+                       |}+                       ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_5_udkey_P_2_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce dest: isoiec_9798_2_5_udkey_P_secret_Kab intro: event_predOrdI)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_udkey_B_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_udkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_5_udkey_B_3 ) : steps t"+    "s(MV ''Kab'' tid0) : knows t"+  shows "False"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),+                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)+                       |}+                       ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_5_udkey_P_2_enc_1 tid1) note_unified facts = this facts+    thus ?thesis by (fastforce dest: isoiec_9798_2_5_udkey_P_secret_Kab intro: event_predOrdI)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_udkey_A_injective_agreement_B:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_5_udkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(AV ''P'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_5_udkey_A_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_5_udkey_B &+          ( tid1, isoiec_9798_2_5_udkey_B_4 ) : steps t &+          {| s(MV ''A'' tid1), s(AV ''B'' tid1), s(MV ''P'' tid1),+             s(MV ''Kab'' tid1), s(MV ''TNa'' tid1), s(MV ''Text5'' tid1),+             LN ''TNb'' tid1, s(MV ''Text7'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''P'' tid0),+                  s(MV ''Kab'' tid0), LN ''TNa'' tid0, s(MV ''Text5'' tid0),+                  s(MV ''TNb'' tid0), s(MV ''Text7'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_5_udkey_P_2_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_2_5_enc_4'', s(MV ''TNb'' tid0),+                                s(AV ''A'' tid0), s(MV ''Text7'' tid0)+                             |}+                             ( LN ''Kab'' tid1 ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest: isoiec_9798_2_5_udkey_P_secret_Kab intro: event_predOrdI)+        next+          case (isoiec_9798_2_5_udkey_B_4_enc tid2) note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid2),+                                  LN ''Kab'' tid1, s(AV ''A'' tid0), s(MV ''Text2'' tid2)+                               |}+                               ( K ( s(AV ''B'' tid2) ) ( s(MV ''P'' tid2) ) ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest: isoiec_9798_2_5_udkey_P_secret_Kab intro: event_predOrdI)+          next+            case (isoiec_9798_2_5_udkey_P_2_enc_1 tid3) note_unified facts = this facts+            thus ?thesis proof(sources! "+                             Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid2),+                                    s(AV ''B'' tid0), s(MV ''Text5'' tid2)+                                 |}+                                 ( LN ''Kab'' tid1 ) ")+              case fake note_unified facts = this facts+              thus ?thesis by (fastforce dest: isoiec_9798_2_5_udkey_P_secret_Kab intro: event_predOrdI)+            next+              case (isoiec_9798_2_5_udkey_A_3_enc tid3) note_unified facts = this facts+              thus ?thesis proof(sources! "+                               Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid3, LN ''Kab'' tid1,+                                      s(AV ''B'' tid0), s(MV ''Text3'' tid3)+                                   |}+                                   ( K ( s(AV ''A'' tid3) ) ( s(AV ''P'' tid3) ) ) ")+                case fake note_unified facts = this facts+                thus ?thesis by (fastforce dest: isoiec_9798_2_5_udkey_P_secret_Kab intro: event_predOrdI)+              next+                case (isoiec_9798_2_5_udkey_P_2_enc tid4) note_unified facts = this facts+                thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+              qed (insert facts, fastforce+)?+            qed (insert facts, fastforce+)?+          qed (insert facts, fastforce+)?+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_udkey_B_non_injective_agreement_A:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_udkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_5_udkey_B_3 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_2_5_udkey_A &+        ( tid1, isoiec_9798_2_5_udkey_A_3 ) : steps t &+        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(AV ''P'' tid1),+           s(MV ''Kab'' tid1), LN ''TNa'' tid1, s(MV ''Text5'' tid1)+        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),+                s(MV ''Kab'' tid0), s(MV ''TNa'' tid0), s(MV ''Text5'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),+                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)+                       |}+                       ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_5_udkey_P_2_enc_1 tid1) note_unified facts = this facts+    thus ?thesis proof(sources! "+                     Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid0),+                            s(AV ''B'' tid0), s(MV ''Text5'' tid0)+                         |}+                         ( LN ''Kab'' tid1 ) ")+      case fake note_unified facts = this facts+      thus ?thesis by (fastforce dest: isoiec_9798_2_5_udkey_P_secret_Kab intro: event_predOrdI)+    next+      case (isoiec_9798_2_5_udkey_A_3_enc tid2) note_unified facts = this facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid2, LN ''Kab'' tid1,+                              s(AV ''B'' tid0), s(MV ''Text3'' tid2)+                           |}+                           ( K ( s(AV ''A'' tid2) ) ( s(AV ''P'' tid2) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest: isoiec_9798_2_5_udkey_P_secret_Kab intro: event_predOrdI)+      next+        case (isoiec_9798_2_5_udkey_P_2_enc tid3) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed (insert facts, fastforce+)?+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_udkey_A_injective_agreement_P:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_5_udkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(AV ''P'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_5_udkey_A_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_5_udkey_P &+          ( tid1, isoiec_9798_2_5_udkey_P_2 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1), LN ''Kab'' tid1,+             s(MV ''TVPa'' tid1), s(MV ''Text3'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''P'' tid0),+                  s(MV ''Kab'' tid0), LN ''TVPa'' tid0, s(MV ''Text3'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_5_udkey_P_2_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_udkey_B_non_injective_agreement_P:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_udkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_5_udkey_B_3 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_2_5_udkey_P &+        ( tid1, isoiec_9798_2_5_udkey_P_2 ) : steps t &+        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1), LN ''Kab'' tid1,+           LN ''TNp'' tid1, s(MV ''Text2'' tid1)+        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),+                s(MV ''Kab'' tid0), s(MV ''TNp'' tid0), s(MV ''Text2'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),+                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)+                       |}+                       ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_5_udkey_P_2_enc_1 tid1) note_unified facts = this facts+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_udkey_P_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_6_udkey_P"+    "RLKR(s(AV ''P'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''B'' tid0)) ~: reveals t"+    "LN ''Kab'' tid0 : knows t"+  shows "False"+using facts proof(sources! " LN ''Kab'' tid0 ")+  case isoiec_9798_2_6_udkey_P_3_Kab note_unified facts = this facts+  thus ?thesis by (fastforce dest!: ltk_secrecy)+next+  case isoiec_9798_2_6_udkey_P_3_Kab_1 note_unified facts = this facts+  thus ?thesis by (fastforce dest!: ltk_secrecy)+qed (insert facts, fastforce+)?++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_udkey_A_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_6_udkey_A"+    "RLKR(s(AV ''A'' tid0)) ~: reveals t"+    "RLKR(s(AV ''P'' tid0)) ~: reveals t"+    "RLKR(s(MV ''B'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_6_udkey_A_3 ) : steps t"+    "s(MV ''Kab'' tid0) : knows t"+  shows "False"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,+                          s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)+                       |}+                       ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_6_udkey_P_3_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce dest: isoiec_9798_2_6_udkey_P_secret_Kab intro: event_predOrdI)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_udkey_B_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_6_udkey_B"+    "RLKR(s(AV ''A'' tid0)) ~: reveals t"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_6_udkey_B_4 ) : steps t"+    "s(MV ''Kab'' tid0) : knows t"+  shows "False"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,+                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)+                       |}+                       ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_6_udkey_P_3_enc_1 tid1) note_unified facts = this facts+    thus ?thesis by (fastforce dest: isoiec_9798_2_6_udkey_P_secret_Kab intro: event_predOrdI)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_udkey_A_injective_agreement_B:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_6_udkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''P'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_6_udkey_A_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_6_udkey_B &+          ( tid1, isoiec_9798_2_6_udkey_B_5 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''P'' tid1),+             s(MV ''Kab'' tid1), s(MV ''Rpa'' tid1), LN ''Rb'' tid1,+             s(MV ''Text6'' tid1), s(MV ''Text8'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''P'' tid0),+                  s(MV ''Kab'' tid0), LN ''Rpa'' tid0, s(MV ''Rb'' tid0),+                  s(MV ''Text6'' tid0), s(MV ''Text8'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,+                              s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)+                           |}+                           ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_6_udkey_P_3_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_2_6_enc_5'', s(MV ''Rb'' tid0), LN ''Rpa'' tid0,+                                s(MV ''Text8'' tid0)+                             |}+                             ( LN ''Kab'' tid1 ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest: isoiec_9798_2_6_udkey_P_secret_Kab intro: event_predOrdI)+        next+          case (isoiec_9798_2_6_udkey_B_5_enc tid2) note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid2, LN ''Kab'' tid1,+                                  s(AV ''A'' tid2), s(MV ''Text3'' tid2)+                               |}+                               ( K ( s(AV ''B'' tid2) ) ( s(MV ''P'' tid2) ) ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest: isoiec_9798_2_6_udkey_P_secret_Kab intro: event_predOrdI)+          next+            case (isoiec_9798_2_6_udkey_P_3_enc_1 tid3) note_unified facts = this facts+            thus ?thesis proof(sources! "+                             Enc {| LC ''isoiec_9798_2_6_enc_4'', LN ''Rpa'' tid0, LN ''Rb'' tid2,+                                    s(MV ''Text6'' tid2)+                                 |}+                                 ( LN ''Kab'' tid1 ) ")+              case fake note_unified facts = this facts+              thus ?thesis by (fastforce dest: isoiec_9798_2_6_udkey_P_secret_Kab intro: event_predOrdI)+            next+              case (isoiec_9798_2_6_udkey_A_4_enc tid3) note_unified facts = this facts+              thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+            qed (insert facts, fastforce+)?+          qed (insert facts, fastforce+)?+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_udkey_B_injective_agreement_A:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_6_udkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(MV ''P'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_6_udkey_B_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_6_udkey_A &+          ( tid1, isoiec_9798_2_6_udkey_A_4 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),+             s(MV ''Kab'' tid1), LN ''Rpa'' tid1, s(MV ''Rb'' tid1),+             s(MV ''Text6'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),+                  s(MV ''Kab'' tid0), s(MV ''Rpa'' tid0), LN ''Rb'' tid0,+                  s(MV ''Text6'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_6_udkey_P_3_enc_1 tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_2_6_enc_4'', s(MV ''Rpa'' tid0), LN ''Rb'' tid0,+                                s(MV ''Text6'' tid0)+                             |}+                             ( LN ''Kab'' tid1 ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest: isoiec_9798_2_6_udkey_P_secret_Kab intro: event_predOrdI)+        next+          case (isoiec_9798_2_6_udkey_A_4_enc tid2) note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid2, LN ''Kab'' tid1,+                                  s(MV ''B'' tid2), s(MV ''Text4'' tid2)+                               |}+                               ( K ( s(AV ''A'' tid2) ) ( s(AV ''P'' tid2) ) ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest: isoiec_9798_2_6_udkey_P_secret_Kab intro: event_predOrdI)+          next+            case (isoiec_9798_2_6_udkey_P_3_enc tid3) note_unified facts = this facts+            thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+          qed (insert facts, fastforce+)?+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_udkey_A_injective_agreement_P:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_6_udkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''P'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_6_udkey_A_3 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_6_udkey_P &+          ( tid1, isoiec_9798_2_6_udkey_P_3 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),+             s(MV ''Ra'' tid1), LN ''Kab'' tid1, s(MV ''Text4'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''P'' tid0),+                  LN ''Ra'' tid0, s(MV ''Kab'' tid0), s(MV ''Text4'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,+                              s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)+                           |}+                           ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_6_udkey_P_3_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_udkey_B_injective_agreement_P:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_6_udkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(MV ''P'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_6_udkey_B_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_6_udkey_P &+          ( tid1, isoiec_9798_2_6_udkey_P_3 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),+             s(MV ''Rb'' tid1), LN ''Kab'' tid1, s(MV ''Text3'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),+                  LN ''Rb'' tid0, s(MV ''Kab'' tid0), s(MV ''Text3'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_6_udkey_P_3_enc_1 tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj) qed  end
data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-3_cert_auto.thy view
@@ -1,2773 +1,3179 @@ theory "isoiec-9798-3_cert_auto" imports-  "../ESPLogic"-begin--role isoiec_9798_3_1_A-where "isoiec_9798_3_1_A =-  [ Send ''leak_A'' ( sN ''TNA'' )-  , Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>-  , Send ''1'' <| sAV ''A'', sAV ''B'', sMV ''Text2'',-                  PSign <| sC ''isoiec_9798_3_1_sig_1'', sN ''TNA'', sAV ''B'',-                           sMV ''Text1''-                        |>-                        ( sPK ''A'' )-               |>-  ]"--role isoiec_9798_3_1_B-where "isoiec_9798_3_1_B =-  [ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Text2'',-                  PSign <| sC ''isoiec_9798_3_1_sig_1'', sMV ''TNA'', sAV ''B'',-                           sMV ''Text1''-                        |>-                        ( PAsymPK ( sMV ''A'' ) )-               |>-  ]"--role isoiec_9798_3_2_A-where "isoiec_9798_3_2_A =-  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>-  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>-  , Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'',-                  PSign <| sC ''isoiec_9798_3_2_sig_2'', sN ''Ra'', sMV ''Rb'', sMV ''B'',-                           sMV ''Text2''-                        |>-                        ( sPK ''A'' )-               |>-  ]"--role isoiec_9798_3_2_B-where "isoiec_9798_3_2_B =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>-  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'',-                  PSign <| sC ''isoiec_9798_3_2_sig_2'', sMV ''Ra'', sN ''Rb'', sAV ''B'',-                           sMV ''Text2''-                        |>-                        ( sPK ''A'' )-               |>-  ]"--role isoiec_9798_3_3_A-where "isoiec_9798_3_3_A =-  [ Send ''leak_A'' ( sN ''TNA'' )-  , Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>-  , Send ''1'' <| sAV ''A'', sAV ''B'', sMV ''Text2'',-                  PSign <| sC ''isoiec_9798_3_3_sig_1'', sN ''TNA'', sAV ''B'',-                           sMV ''Text1''-                        |>-                        ( sPK ''A'' )-               |>-  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text4'',-                  PSign <| sC ''isoiec_9798_3_3_sig_2'', sMV ''TNB'', sAV ''A'',-                           sMV ''Text3''-                        |>-                        ( sPK ''B'' )-               |>-  ]"--role isoiec_9798_3_3_B-where "isoiec_9798_3_3_B =-  [ Send ''leak_B'' ( sN ''TNB'' )-  , Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Text2'',-                  PSign <| sC ''isoiec_9798_3_3_sig_1'', sMV ''TNA'', sAV ''B'',-                           sMV ''Text1''-                        |>-                        ( PAsymPK ( sMV ''A'' ) )-               |>-  , Recv ''text_2'' <| sMV ''Text3'', sMV ''Text4'' |>-  , Send ''2'' <| sMV ''A'', sAV ''B'', sMV ''Text4'',-                  PSign <| sC ''isoiec_9798_3_3_sig_2'', sN ''TNB'', sMV ''A'',-                           sMV ''Text3''-                        |>-                        ( sPK ''B'' )-               |>-  ]"--role isoiec_9798_3_4_A-where "isoiec_9798_3_4_A =-  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''RB'', sMV ''Text1'' |>-  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>-  , Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'',-                  PSign <| sC ''isoiec_9798_3_4_sig_1'', sN ''RA'', sMV ''RB'', sMV ''B'',-                           sMV ''Text2''-                        |>-                        ( sPK ''A'' )-               |>-  , Recv ''3'' <| sMV ''B'', sAV ''A'', sMV ''Text5'',-                  PSign <| sC ''isoiec_9798_3_4_sig_2'', sMV ''RB'', sN ''RA'', sAV ''A'',-                           sMV ''Text4''-                        |>-                        ( PAsymPK ( sMV ''B'' ) )-               |>-  ]"--role isoiec_9798_3_4_B-where "isoiec_9798_3_4_B =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''RB'', sMV ''Text1'' |>-  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'',-                  PSign <| sC ''isoiec_9798_3_4_sig_1'', sMV ''RA'', sN ''RB'', sAV ''B'',-                           sMV ''Text2''-                        |>-                        ( sPK ''A'' )-               |>-  , Recv ''text_3'' <| sMV ''Text4'', sMV ''Text5'' |>-  , Send ''3'' <| sAV ''B'', sAV ''A'', sMV ''Text5'',-                  PSign <| sC ''isoiec_9798_3_4_sig_2'', sN ''RB'', sMV ''RA'', sAV ''A'',-                           sMV ''Text4''-                        |>-                        ( sPK ''B'' )-               |>-  ]"--role isoiec_9798_3_5_A-where "isoiec_9798_3_5_A =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''A'', sAV ''B'', sN ''RA'', sMV ''Text1'' |>-  , Recv ''2'' <| sAV ''B'', sAV ''A'', sMV ''RB'', sMV ''Text2'' |>-  , Recv ''3'' <| sAV ''B'', sAV ''A'', sMV ''Text6'',-                  PSign <| sC ''isoiec_9798_3_5_sig_1'', sMV ''RB'', sN ''RA'', sAV ''A'',-                           sMV ''Text5''-                        |>-                        ( sPK ''B'' )-               |>-  , Recv ''text_4'' <| sMV ''Text3'', sMV ''Text4'' |>-  , Send ''4'' <| sAV ''A'', sAV ''B'', sMV ''Text4'',-                  PSign <| sC ''isoiec_9798_3_5_sig_2'', sN ''RA'', sMV ''RB'', sAV ''B'',-                           sMV ''Text3''-                        |>-                        ( sPK ''A'' )-               |>-  ]"--role isoiec_9798_3_5_B-where "isoiec_9798_3_5_B =-  [ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''RA'', sMV ''Text1'' |>-  , Recv ''text_2'' ( sMV ''Text2'' )-  , Send ''2'' <| sAV ''B'', sMV ''A'', sN ''RB'', sMV ''Text2'' |>-  , Recv ''text_3'' <| sMV ''Text5'', sMV ''Text6'' |>-  , Send ''3'' <| sAV ''B'', sMV ''A'', sMV ''Text6'',-                  PSign <| sC ''isoiec_9798_3_5_sig_1'', sN ''RB'', sMV ''RA'', sMV ''A'',-                           sMV ''Text5''-                        |>-                        ( sPK ''B'' )-               |>-  , Recv ''4'' <| sMV ''A'', sAV ''B'', sMV ''Text4'',-                  PSign <| sC ''isoiec_9798_3_5_sig_2'', sMV ''RA'', sN ''RB'', sAV ''B'',-                           sMV ''Text3''-                        |>-                        ( PAsymPK ( sMV ''A'' ) )-               |>-  ]"--role isoiec_9798_3_6_1_A-where "isoiec_9798_3_6_1_A =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''A'', sAV ''B'', sN ''Ra'', sMV ''Text1'' |>-  , Recv ''2'' <| sAV ''A'', sAV ''B'', sN ''Ra'', sMV ''Rb'',-                  sMV ''Text3'', sMV ''TokenBA''-               |>-  , Recv ''text_3'' ( sMV ''Text4'' )-  , Send ''3'' <| sAV ''A'', sAV ''T'', sN ''Rpa'', sMV ''Rb'', sAV ''B'',-                  sMV ''Text4''-               |>-  , Recv ''4'' <| sAV ''T'', sAV ''A'', sMV ''Text7'', sAV ''A'',-                  sPK ''A'', sAV ''B'', sMV ''pkB'',-                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_4_1'', sN ''Rpa'', sAV ''B'',-                           sMV ''pkB'', sMV ''Text6''-                        |>-                        ( sPK ''T'' ),-                  sMV ''TokenTA_for_B''-               |>-  , Send ''check_4_out'' ( PEnc <| sC ''check_4'', sMV ''TokenBA'' |>-                                ( sN ''check_nonce_4'' )-                         )-  , Recv ''check_4_in'' ( PEnc <| sC ''check_4'',-                                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_2'', sAV ''B'', sN ''Ra'',-                                           sMV ''Rb'', sAV ''A'', sMV ''Text2''-                                        |>-                                        ( sMV ''pkB'' )-                               |>-                               ( sN ''check_nonce_4'' )-                        )-  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>-  , Send ''5'' <| sAV ''A'', sAV ''B'', sMV ''Text9'', sAV ''T'',-                  sMV ''TokenTA_for_B'',-                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_5'', sMV ''Rb'', sN ''Ra'',-                           sAV ''B'', sAV ''A'', sMV ''Text8''-                        |>-                        ( sPK ''A'' )-               |>-  ]"--role isoiec_9798_3_6_1_B-where "isoiec_9798_3_6_1_B =-  [ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Ra'', sMV ''Text1'' |>-  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>-  , Send ''2'' <| sMV ''A'', sAV ''B'', sMV ''Ra'', sN ''Rb'',-                  sMV ''Text3'',-                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_2'', sAV ''B'', sMV ''Ra'',-                           sN ''Rb'', sMV ''A'', sMV ''Text2''-                        |>-                        ( sPK ''B'' )-               |>-  , Recv ''5'' <| sMV ''A'', sAV ''B'', sMV ''Text9'', sMV ''T'',-                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_4_2'', sN ''Rb'', sMV ''A'',-                           sMV ''pkA'', sMV ''Text5''-                        |>-                        ( PAsymPK ( sMV ''T'' ) ),-                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_5'', sN ''Rb'', sMV ''Ra5'',-                           sAV ''B'', sMV ''A'', sMV ''Text8''-                        |>-                        ( sMV ''pkA'' )-               |>-  ]"--role isoiec_9798_3_6_1_T-where "isoiec_9798_3_6_1_T =-  [ Recv ''3'' <| sMV ''A'', sAV ''T'', sMV ''Rpa'', sMV ''Rb'', sMV ''B'',-                  sMV ''Text4''-               |>-  , Recv ''text_4'' <| sMV ''Text5'', sMV ''Text6'', sMV ''Text7'' |>-  , Send ''4'' <| sAV ''T'', sMV ''A'', sMV ''Text7'', sMV ''A'',-                  PAsymPK ( sMV ''A'' ), sMV ''B'', PAsymPK ( sMV ''B'' ),-                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_4_1'', sMV ''Rpa'', sMV ''B'',-                           PAsymPK ( sMV ''B'' ), sMV ''Text6''-                        |>-                        ( sPK ''T'' ),-                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_4_2'', sMV ''Rb'', sMV ''A'',-                           PAsymPK ( sMV ''A'' ), sMV ''Text5''-                        |>-                        ( sPK ''T'' )-               |>-  ]"--role isoiec_9798_3_6_2_A-where "isoiec_9798_3_6_2_A =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''A'', sAV ''B'', sN ''Ra'', sMV ''Text1'' |>-  , Recv ''2'' <| sAV ''A'', sAV ''B'', sN ''Ra'', sMV ''Rb'',-                  sMV ''Text3'', sMV ''TokenBA''-               |>-  , Recv ''text_3'' ( sMV ''Text4'' )-  , Send ''3'' <| sAV ''A'', sAV ''T'', sN ''Rpa'', sMV ''Rb'', sAV ''B'',-                  sMV ''Text4''-               |>-  , Recv ''4'' <| sAV ''T'', sAV ''A'', sMV ''Text7'', sAV ''A'',-                  sPK ''A'', sAV ''B'', sMV ''pkB'', sMV ''TokenTA''-               |>-  , Send ''check_4_out'' ( PEnc <| sC ''check_4'', sMV ''TokenTA'',-                                   sMV ''TokenBA''-                                |>-                                ( sN ''check_nonce_4'' )-                         )-  , Recv ''check_4_in'' ( PEnc <| sC ''check_4'',-                                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_4'', sN ''Rpa'', sMV ''Rb'',-                                           sAV ''A'', sMV ''pkA'', sAV ''B'', sMV ''pkB'', sMV ''Text5''-                                        |>-                                        ( sPK ''T'' ),-                                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_2'', sAV ''B'', sN ''Ra'',-                                           sMV ''Rb'', sAV ''A'', sMV ''Text2''-                                        |>-                                        ( sMV ''pkB'' )-                               |>-                               ( sN ''check_nonce_4'' )-                        )-  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>-  , Send ''5'' <| sAV ''A'', sAV ''B'', sN ''Rpa'', sMV ''Text9'',-                  sAV ''T'', sMV ''TokenTA'',-                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_5'', sMV ''Rb'', sN ''Ra'',-                           sAV ''B'', sAV ''A'', sMV ''Text8''-                        |>-                        ( sPK ''A'' )-               |>-  ]"--role isoiec_9798_3_6_2_B-where "isoiec_9798_3_6_2_B =-  [ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Ra'', sMV ''Text1'' |>-  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>-  , Send ''2'' <| sMV ''A'', sAV ''B'', sMV ''Ra'', sN ''Rb'',-                  sMV ''Text3'',-                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_2'', sAV ''B'', sMV ''Ra'',-                           sN ''Rb'', sMV ''A'', sMV ''Text2''-                        |>-                        ( sPK ''B'' )-               |>-  , Recv ''5'' <| sMV ''A'', sAV ''B'', sMV ''Rpa'', sMV ''Text9'',-                  sMV ''T'',-                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_4'', sMV ''Rpa'', sN ''Rb'',-                           sMV ''A'', sMV ''pkA'', sAV ''B'', sMV ''pkB'', sMV ''Text5''-                        |>-                        ( PAsymPK ( sMV ''T'' ) ),-                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_5'', sN ''Rb'', sMV ''Ra5'',-                           sAV ''B'', sMV ''A'', sMV ''Text8''-                        |>-                        ( sMV ''pkA'' )-               |>-  ]"--role isoiec_9798_3_6_2_T-where "isoiec_9798_3_6_2_T =-  [ Recv ''3'' <| sMV ''A'', sAV ''T'', sMV ''Rpa'', sMV ''Rb'', sMV ''B'',-                  sMV ''Text4''-               |>-  , Recv ''text_4'' <| sMV ''Text5'', sMV ''Text7'' |>-  , Send ''4'' <| sAV ''T'', sMV ''A'', sMV ''Text7'', sMV ''A'',-                  PAsymPK ( sMV ''A'' ), sMV ''B'', PAsymPK ( sMV ''B'' ),-                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_4'', sMV ''Rpa'', sMV ''Rb'',-                           sMV ''A'', PAsymPK ( sMV ''A'' ), sMV ''B'', PAsymPK ( sMV ''B'' ),-                           sMV ''Text5''-                        |>-                        ( sPK ''T'' )-               |>-  ]"--role isoiec_9798_3_7_1_A-where "isoiec_9798_3_7_1_A =-  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>-  , Recv ''text_2'' ( sMV ''Text2'' )-  , Send ''2'' <| sAV ''A'', sAV ''T'', sN ''Rpa'', sMV ''Rb'', sAV ''A'',-                  sMV ''B'', sMV ''Text2''-               |>-  , Recv ''3'' <| sAV ''T'', sAV ''A'', sMV ''Text5'', sAV ''A'',-                  sPK ''A'', sMV ''B'', sMV ''pkB'',-                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_3_1'', sN ''Rpa'', sMV ''B'',-                           sMV ''pkB'', sMV ''Text4''-                        |>-                        ( sPK ''T'' ),-                  sMV ''TokenTA_for_B''-               |>-  , Recv ''text_4'' <| sMV ''Text6'', sMV ''Text7'' |>-  , Send ''4'' <| sAV ''A'', sMV ''B'', sN ''Rpa'', sMV ''Text7'',-                  sAV ''T'', sMV ''TokenTA_for_B'',-                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_4'', sMV ''Rb'', sN ''Ra'',-                           sMV ''B'', sAV ''A'', sMV ''Text6''-                        |>-                        ( sPK ''A'' )-               |>-  , Recv ''5'' <| sAV ''A'', sMV ''B'', sN ''Ra'', sMV ''Rb'',-                  sMV ''Text9'',-                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_5'', sN ''Ra'', sMV ''Rb'',-                           sAV ''A'', sMV ''B'', sMV ''Text8''-                        |>-                        ( sMV ''pkB'' )-               |>-  ]"--role isoiec_9798_3_7_1_B-where "isoiec_9798_3_7_1_B =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>-  , Recv ''4'' <| sAV ''A'', sAV ''B'', sMV ''Rpa'', sMV ''Text9'',-                  sMV ''T'',-                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_3_2'', sN ''Rb'', sAV ''A'',-                           sMV ''pkA'', sMV ''Text3''-                        |>-                        ( PAsymPK ( sMV ''T'' ) ),-                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_4'', sN ''Rb'', sMV ''Ra'',-                           sAV ''B'', sAV ''A'', sMV ''Text6''-                        |>-                        ( sMV ''pkA'' )-               |>-  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>-  , Send ''5'' <| sAV ''A'', sAV ''B'', sMV ''Ra'', sN ''Rb'',-                  sMV ''Text9'',-                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_5'', sMV ''Ra'', sN ''Rb'',-                           sAV ''A'', sAV ''B'', sMV ''Text8''-                        |>-                        ( sPK ''B'' )-               |>-  ]"--role isoiec_9798_3_7_1_T-where "isoiec_9798_3_7_1_T =-  [ Recv ''2'' <| sMV ''A'', sAV ''T'', sMV ''Rpa'', sMV ''Rb'', sMV ''A'',-                  sMV ''B'', sMV ''Text2''-               |>-  , Recv ''text_3'' <| sMV ''Text3'', sMV ''Text4'', sMV ''Text5'' |>-  , Send ''3'' <| sAV ''T'', sMV ''A'', sMV ''Text5'', sMV ''A'',-                  PAsymPK ( sMV ''A'' ), sMV ''B'', PAsymPK ( sMV ''B'' ),-                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_3_1'', sMV ''Rpa'', sMV ''B'',-                           PAsymPK ( sMV ''B'' ), sMV ''Text4''-                        |>-                        ( sPK ''T'' ),-                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_3_2'', sMV ''Rb'', sMV ''A'',-                           PAsymPK ( sMV ''A'' ), sMV ''Text3''-                        |>-                        ( sPK ''T'' )-               |>-  ]"--role isoiec_9798_3_7_2_A-where "isoiec_9798_3_7_2_A =-  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>-  , Recv ''text_2'' ( sMV ''Text2'' )-  , Send ''2'' <| sAV ''A'', sAV ''T'', sN ''Rpa'', sMV ''Rb'', sAV ''A'',-                  sMV ''B'', sMV ''Text2''-               |>-  , Recv ''3'' <| sAV ''T'', sAV ''A'', sMV ''Text5'', sAV ''A'',-                  sPK ''A'', sMV ''B'', sMV ''pkB'', sMV ''TokenTA''-               |>-  , Send ''check_3_out'' ( PEnc <| sC ''check_4'', sMV ''TokenTA'' |>-                                ( sN ''check_nonce_4'' )-                         )-  , Recv ''check_3_in'' ( PEnc <| sC ''check_4'',-                                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_3'', sN ''Rpa'', sMV ''Rb'',-                                           sAV ''A'', sMV ''pkA'', sMV ''B'', sMV ''pkB'', sMV ''Text3''-                                        |>-                                        ( sPK ''T'' )-                               |>-                               ( sN ''check_nonce_4'' )-                        )-  , Recv ''text_4'' <| sMV ''Text6'', sMV ''Text7'' |>-  , Send ''4'' <| sAV ''A'', sMV ''B'', sN ''Rpa'', sMV ''Text7'',-                  sAV ''T'', sMV ''TokenTA'',-                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_4'', sMV ''Rb'', sN ''Ra'',-                           sMV ''B'', sAV ''A'', sMV ''Text6''-                        |>-                        ( sPK ''A'' )-               |>-  , Recv ''5'' <| sAV ''A'', sMV ''B'', sN ''Ra'', sMV ''Rb'',-                  sMV ''Text9'',-                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_5'', sN ''Ra'', sMV ''Rb'',-                           sAV ''A'', sMV ''B'', sMV ''Text8''-                        |>-                        ( sMV ''pkB'' )-               |>-  ]"--role isoiec_9798_3_7_2_B-where "isoiec_9798_3_7_2_B =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>-  , Recv ''4'' <| sAV ''A'', sAV ''B'', sMV ''Rpa'', sMV ''Text9'',-                  sMV ''T'',-                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_3'', sMV ''Rpa'', sN ''Rb'',-                           sAV ''A'', sMV ''pkA'', sAV ''B'', sMV ''pkB'', sMV ''Text3''-                        |>-                        ( PAsymPK ( sMV ''T'' ) ),-                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_4'', sN ''Rb'', sMV ''Ra'',-                           sAV ''B'', sAV ''A'', sMV ''Text6''-                        |>-                        ( sMV ''pkA'' )-               |>-  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>-  , Send ''5'' <| sAV ''A'', sAV ''B'', sMV ''Ra'', sN ''Rb'',-                  sMV ''Text9'',-                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_5'', sMV ''Ra'', sN ''Rb'',-                           sAV ''A'', sAV ''B'', sMV ''Text8''-                        |>-                        ( sPK ''B'' )-               |>-  ]"--role isoiec_9798_3_7_2_T-where "isoiec_9798_3_7_2_T =-  [ Recv ''2'' <| sMV ''A'', sAV ''T'', sMV ''Rpa'', sMV ''Rb'', sMV ''A'',-                  sMV ''B'', sMV ''Text2''-               |>-  , Recv ''text_3'' <| sMV ''Text3'', sMV ''Text5'' |>-  , Send ''3'' <| sAV ''T'', sMV ''A'', sMV ''Text5'', sMV ''A'',-                  PAsymPK ( sMV ''A'' ), sMV ''B'', PAsymPK ( sMV ''B'' ),-                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_3'', sMV ''Rpa'', sMV ''Rb'',-                           sMV ''A'', PAsymPK ( sMV ''A'' ), sMV ''B'', PAsymPK ( sMV ''B'' ),-                           sMV ''Text3''-                        |>-                        ( sPK ''T'' )-               |>-  ]"--protocol isoiec_9798_3-where "isoiec_9798_3 =-{ isoiec_9798_3_1_A, isoiec_9798_3_1_B, isoiec_9798_3_2_A,-  isoiec_9798_3_2_B, isoiec_9798_3_3_A, isoiec_9798_3_3_B,-  isoiec_9798_3_4_A, isoiec_9798_3_4_B, isoiec_9798_3_5_A,-  isoiec_9798_3_5_B, isoiec_9798_3_6_1_A, isoiec_9798_3_6_1_B,-  isoiec_9798_3_6_1_T, isoiec_9798_3_6_2_A, isoiec_9798_3_6_2_B,-  isoiec_9798_3_6_2_T, isoiec_9798_3_7_1_A, isoiec_9798_3_7_1_B,-  isoiec_9798_3_7_1_T, isoiec_9798_3_7_2_A, isoiec_9798_3_7_2_B,-  isoiec_9798_3_7_2_T-}"--locale restricted_isoiec_9798_3_state = isoiec_9798_3_state--type_invariant isoiec_9798_3_composed_typing for isoiec_9798_3-where "isoiec_9798_3_composed_typing = mk_typing-  [ ((isoiec_9798_3_1_B, ''A''), (KnownT isoiec_9798_3_1_B_1))-  , ((isoiec_9798_3_3_B, ''A''), (KnownT isoiec_9798_3_3_B_1))-  , ((isoiec_9798_3_5_B, ''A''), (KnownT isoiec_9798_3_5_B_1))-  , ((isoiec_9798_3_6_1_B, ''A''), (KnownT isoiec_9798_3_6_1_B_1))-  , ((isoiec_9798_3_6_1_T, ''A''), (KnownT isoiec_9798_3_6_1_T_3))-  , ((isoiec_9798_3_6_2_B, ''A''), (KnownT isoiec_9798_3_6_2_B_1))-  , ((isoiec_9798_3_6_2_T, ''A''), (KnownT isoiec_9798_3_6_2_T_3))-  , ((isoiec_9798_3_7_1_T, ''A''), (KnownT isoiec_9798_3_7_1_T_2))-  , ((isoiec_9798_3_7_2_T, ''A''), (KnownT isoiec_9798_3_7_2_T_2))-  , ((isoiec_9798_3_2_A, ''B''), (KnownT isoiec_9798_3_2_A_1))-  , ((isoiec_9798_3_4_A, ''B''), (KnownT isoiec_9798_3_4_A_1))-  , ((isoiec_9798_3_6_1_T, ''B''), (KnownT isoiec_9798_3_6_1_T_3))-  , ((isoiec_9798_3_6_2_T, ''B''), (KnownT isoiec_9798_3_6_2_T_3))-  , ((isoiec_9798_3_7_1_A, ''B''), (KnownT isoiec_9798_3_7_1_A_1))-  , ((isoiec_9798_3_7_1_T, ''B''), (KnownT isoiec_9798_3_7_1_T_2))-  , ((isoiec_9798_3_7_2_A, ''B''), (KnownT isoiec_9798_3_7_2_A_1))-  , ((isoiec_9798_3_7_2_T, ''B''), (KnownT isoiec_9798_3_7_2_T_2))-  , ((isoiec_9798_3_4_B, ''RA''), (KnownT isoiec_9798_3_4_B_2))-  , ((isoiec_9798_3_5_B, ''RA''), (KnownT isoiec_9798_3_5_B_1))-  , ((isoiec_9798_3_4_A, ''RB''), (KnownT isoiec_9798_3_4_A_1))-  , ((isoiec_9798_3_5_A, ''RB''), (KnownT isoiec_9798_3_5_A_2))-  , ((isoiec_9798_3_2_B, ''Ra''), (KnownT isoiec_9798_3_2_B_2))-  , ((isoiec_9798_3_6_1_B, ''Ra''), (KnownT isoiec_9798_3_6_1_B_1))-  , ((isoiec_9798_3_6_2_B, ''Ra''), (KnownT isoiec_9798_3_6_2_B_1))-  , ((isoiec_9798_3_7_1_B, ''Ra''), (KnownT isoiec_9798_3_7_1_B_4))-  , ((isoiec_9798_3_7_2_B, ''Ra''), (KnownT isoiec_9798_3_7_2_B_4))-  , ((isoiec_9798_3_6_1_B, ''Ra5''), (KnownT isoiec_9798_3_6_1_B_5))-  , ((isoiec_9798_3_6_2_B, ''Ra5''), (KnownT isoiec_9798_3_6_2_B_5))-  , ((isoiec_9798_3_2_A, ''Rb''), (KnownT isoiec_9798_3_2_A_1))-  , ((isoiec_9798_3_6_1_A, ''Rb''), (KnownT isoiec_9798_3_6_1_A_2))-  , ((isoiec_9798_3_6_1_T, ''Rb''), (KnownT isoiec_9798_3_6_1_T_3))-  , ((isoiec_9798_3_6_2_A, ''Rb''), (KnownT isoiec_9798_3_6_2_A_2))-  , ((isoiec_9798_3_6_2_T, ''Rb''), (KnownT isoiec_9798_3_6_2_T_3))-  , ((isoiec_9798_3_7_1_A, ''Rb''), (KnownT isoiec_9798_3_7_1_A_1))-  , ((isoiec_9798_3_7_1_T, ''Rb''), (KnownT isoiec_9798_3_7_1_T_2))-  , ((isoiec_9798_3_7_2_A, ''Rb''), (KnownT isoiec_9798_3_7_2_A_1))-  , ((isoiec_9798_3_7_2_T, ''Rb''), (KnownT isoiec_9798_3_7_2_T_2))-  , ((isoiec_9798_3_6_1_T, ''Rpa''), (KnownT isoiec_9798_3_6_1_T_3))-  , ((isoiec_9798_3_6_2_B, ''Rpa''), (KnownT isoiec_9798_3_6_2_B_5))-  , ((isoiec_9798_3_6_2_T, ''Rpa''), (KnownT isoiec_9798_3_6_2_T_3))-  , ((isoiec_9798_3_7_1_B, ''Rpa''), (KnownT isoiec_9798_3_7_1_B_4))-  , ((isoiec_9798_3_7_1_T, ''Rpa''), (KnownT isoiec_9798_3_7_1_T_2))-  , ((isoiec_9798_3_7_2_B, ''Rpa''), (KnownT isoiec_9798_3_7_2_B_4))-  , ((isoiec_9798_3_7_2_T, ''Rpa''), (KnownT isoiec_9798_3_7_2_T_2))-  , ((isoiec_9798_3_6_1_B, ''T''), (KnownT isoiec_9798_3_6_1_B_5))-  , ((isoiec_9798_3_6_2_B, ''T''), (KnownT isoiec_9798_3_6_2_B_5))-  , ((isoiec_9798_3_7_1_B, ''T''), (KnownT isoiec_9798_3_7_1_B_4))-  , ((isoiec_9798_3_7_2_B, ''T''), (KnownT isoiec_9798_3_7_2_B_4))-  , ((isoiec_9798_3_1_B, ''TNA''), (KnownT isoiec_9798_3_1_B_1))-  , ((isoiec_9798_3_3_B, ''TNA''), (KnownT isoiec_9798_3_3_B_1))-  , ((isoiec_9798_3_3_A, ''TNB''), (KnownT isoiec_9798_3_3_A_2))-  , ((isoiec_9798_3_1_A, ''Text1''), (KnownT isoiec_9798_3_1_A_text_1))-  , ((isoiec_9798_3_1_B, ''Text1''), (KnownT isoiec_9798_3_1_B_1))-  , ((isoiec_9798_3_2_A, ''Text1''), (KnownT isoiec_9798_3_2_A_1))-  , ((isoiec_9798_3_2_B, ''Text1''), (KnownT isoiec_9798_3_2_B_text_1))-  , ((isoiec_9798_3_3_A, ''Text1''), (KnownT isoiec_9798_3_3_A_text_1))-  , ((isoiec_9798_3_3_B, ''Text1''), (KnownT isoiec_9798_3_3_B_1))-  , ((isoiec_9798_3_4_A, ''Text1''), (KnownT isoiec_9798_3_4_A_1))-  , ((isoiec_9798_3_4_B, ''Text1''), (KnownT isoiec_9798_3_4_B_text_1))-  , ((isoiec_9798_3_5_A, ''Text1''), (KnownT isoiec_9798_3_5_A_text_1))-  , ((isoiec_9798_3_5_B, ''Text1''), (KnownT isoiec_9798_3_5_B_1))-  , ((isoiec_9798_3_6_1_A, ''Text1''), (KnownT isoiec_9798_3_6_1_A_text_1))-  , ((isoiec_9798_3_6_1_B, ''Text1''), (KnownT isoiec_9798_3_6_1_B_1))-  , ((isoiec_9798_3_6_2_A, ''Text1''), (KnownT isoiec_9798_3_6_2_A_text_1))-  , ((isoiec_9798_3_6_2_B, ''Text1''), (KnownT isoiec_9798_3_6_2_B_1))-  , ((isoiec_9798_3_7_1_A, ''Text1''), (KnownT isoiec_9798_3_7_1_A_1))-  , ((isoiec_9798_3_7_1_B, ''Text1''), (KnownT isoiec_9798_3_7_1_B_text_1))-  , ((isoiec_9798_3_7_2_A, ''Text1''), (KnownT isoiec_9798_3_7_2_A_1))-  , ((isoiec_9798_3_7_2_B, ''Text1''), (KnownT isoiec_9798_3_7_2_B_text_1))-  , ((isoiec_9798_3_1_A, ''Text2''), (KnownT isoiec_9798_3_1_A_text_1))-  , ((isoiec_9798_3_1_B, ''Text2''), (KnownT isoiec_9798_3_1_B_1))-  , ((isoiec_9798_3_2_A, ''Text2''), (KnownT isoiec_9798_3_2_A_text_2))-  , ((isoiec_9798_3_2_B, ''Text2''), (KnownT isoiec_9798_3_2_B_2))-  , ((isoiec_9798_3_3_A, ''Text2''), (KnownT isoiec_9798_3_3_A_text_1))-  , ((isoiec_9798_3_3_B, ''Text2''), (KnownT isoiec_9798_3_3_B_1))-  , ((isoiec_9798_3_4_A, ''Text2''), (KnownT isoiec_9798_3_4_A_text_2))-  , ((isoiec_9798_3_4_B, ''Text2''), (KnownT isoiec_9798_3_4_B_2))-  , ((isoiec_9798_3_5_A, ''Text2''), (KnownT isoiec_9798_3_5_A_2))-  , ((isoiec_9798_3_5_B, ''Text2''), (KnownT isoiec_9798_3_5_B_text_2))-  , ((isoiec_9798_3_6_1_A, ''Text2''),-     (KnownT isoiec_9798_3_6_1_A_check_4_in))-  , ((isoiec_9798_3_6_1_B, ''Text2''), (KnownT isoiec_9798_3_6_1_B_text_2))-  , ((isoiec_9798_3_6_2_A, ''Text2''),-     (KnownT isoiec_9798_3_6_2_A_check_4_in))-  , ((isoiec_9798_3_6_2_B, ''Text2''), (KnownT isoiec_9798_3_6_2_B_text_2))-  , ((isoiec_9798_3_7_1_A, ''Text2''), (KnownT isoiec_9798_3_7_1_A_text_2))-  , ((isoiec_9798_3_7_1_T, ''Text2''), (KnownT isoiec_9798_3_7_1_T_2))-  , ((isoiec_9798_3_7_2_A, ''Text2''), (KnownT isoiec_9798_3_7_2_A_text_2))-  , ((isoiec_9798_3_7_2_T, ''Text2''), (KnownT isoiec_9798_3_7_2_T_2))-  , ((isoiec_9798_3_2_A, ''Text3''), (KnownT isoiec_9798_3_2_A_text_2))-  , ((isoiec_9798_3_2_B, ''Text3''), (KnownT isoiec_9798_3_2_B_2))-  , ((isoiec_9798_3_3_A, ''Text3''), (KnownT isoiec_9798_3_3_A_2))-  , ((isoiec_9798_3_3_B, ''Text3''), (KnownT isoiec_9798_3_3_B_text_2))-  , ((isoiec_9798_3_4_A, ''Text3''), (KnownT isoiec_9798_3_4_A_text_2))-  , ((isoiec_9798_3_4_B, ''Text3''), (KnownT isoiec_9798_3_4_B_2))-  , ((isoiec_9798_3_5_A, ''Text3''), (KnownT isoiec_9798_3_5_A_text_4))-  , ((isoiec_9798_3_5_B, ''Text3''), (KnownT isoiec_9798_3_5_B_4))-  , ((isoiec_9798_3_6_1_A, ''Text3''), (KnownT isoiec_9798_3_6_1_A_2))-  , ((isoiec_9798_3_6_1_B, ''Text3''), (KnownT isoiec_9798_3_6_1_B_text_2))-  , ((isoiec_9798_3_6_2_A, ''Text3''), (KnownT isoiec_9798_3_6_2_A_2))-  , ((isoiec_9798_3_6_2_B, ''Text3''), (KnownT isoiec_9798_3_6_2_B_text_2))-  , ((isoiec_9798_3_7_1_B, ''Text3''), (KnownT isoiec_9798_3_7_1_B_4))-  , ((isoiec_9798_3_7_1_T, ''Text3''), (KnownT isoiec_9798_3_7_1_T_text_3))-  , ((isoiec_9798_3_7_2_A, ''Text3''),-     (KnownT isoiec_9798_3_7_2_A_check_3_in))-  , ((isoiec_9798_3_7_2_B, ''Text3''), (KnownT isoiec_9798_3_7_2_B_4))-  , ((isoiec_9798_3_7_2_T, ''Text3''), (KnownT isoiec_9798_3_7_2_T_text_3))-  , ((isoiec_9798_3_3_A, ''Text4''), (KnownT isoiec_9798_3_3_A_2))-  , ((isoiec_9798_3_3_B, ''Text4''), (KnownT isoiec_9798_3_3_B_text_2))-  , ((isoiec_9798_3_4_A, ''Text4''), (KnownT isoiec_9798_3_4_A_3))-  , ((isoiec_9798_3_4_B, ''Text4''), (KnownT isoiec_9798_3_4_B_text_3))-  , ((isoiec_9798_3_5_A, ''Text4''), (KnownT isoiec_9798_3_5_A_text_4))-  , ((isoiec_9798_3_5_B, ''Text4''), (KnownT isoiec_9798_3_5_B_4))-  , ((isoiec_9798_3_6_1_A, ''Text4''), (KnownT isoiec_9798_3_6_1_A_text_3))-  , ((isoiec_9798_3_6_1_T, ''Text4''), (KnownT isoiec_9798_3_6_1_T_3))-  , ((isoiec_9798_3_6_2_A, ''Text4''), (KnownT isoiec_9798_3_6_2_A_text_3))-  , ((isoiec_9798_3_6_2_T, ''Text4''), (KnownT isoiec_9798_3_6_2_T_3))-  , ((isoiec_9798_3_7_1_A, ''Text4''), (KnownT isoiec_9798_3_7_1_A_3))-  , ((isoiec_9798_3_7_1_T, ''Text4''), (KnownT isoiec_9798_3_7_1_T_text_3))-  , ((isoiec_9798_3_4_A, ''Text5''), (KnownT isoiec_9798_3_4_A_3))-  , ((isoiec_9798_3_4_B, ''Text5''), (KnownT isoiec_9798_3_4_B_text_3))-  , ((isoiec_9798_3_5_A, ''Text5''), (KnownT isoiec_9798_3_5_A_3))-  , ((isoiec_9798_3_5_B, ''Text5''), (KnownT isoiec_9798_3_5_B_text_3))-  , ((isoiec_9798_3_6_1_B, ''Text5''), (KnownT isoiec_9798_3_6_1_B_5))-  , ((isoiec_9798_3_6_1_T, ''Text5''), (KnownT isoiec_9798_3_6_1_T_text_4))-  , ((isoiec_9798_3_6_2_A, ''Text5''),-     (KnownT isoiec_9798_3_6_2_A_check_4_in))-  , ((isoiec_9798_3_6_2_B, ''Text5''), (KnownT isoiec_9798_3_6_2_B_5))-  , ((isoiec_9798_3_6_2_T, ''Text5''), (KnownT isoiec_9798_3_6_2_T_text_4))-  , ((isoiec_9798_3_7_1_A, ''Text5''), (KnownT isoiec_9798_3_7_1_A_3))-  , ((isoiec_9798_3_7_1_T, ''Text5''), (KnownT isoiec_9798_3_7_1_T_text_3))-  , ((isoiec_9798_3_7_2_A, ''Text5''), (KnownT isoiec_9798_3_7_2_A_3))-  , ((isoiec_9798_3_7_2_T, ''Text5''), (KnownT isoiec_9798_3_7_2_T_text_3))-  , ((isoiec_9798_3_5_A, ''Text6''), (KnownT isoiec_9798_3_5_A_3))-  , ((isoiec_9798_3_5_B, ''Text6''), (KnownT isoiec_9798_3_5_B_text_3))-  , ((isoiec_9798_3_6_1_A, ''Text6''), (KnownT isoiec_9798_3_6_1_A_4))-  , ((isoiec_9798_3_6_1_T, ''Text6''), (KnownT isoiec_9798_3_6_1_T_text_4))-  , ((isoiec_9798_3_7_1_A, ''Text6''), (KnownT isoiec_9798_3_7_1_A_text_4))-  , ((isoiec_9798_3_7_1_B, ''Text6''), (KnownT isoiec_9798_3_7_1_B_4))-  , ((isoiec_9798_3_7_2_A, ''Text6''), (KnownT isoiec_9798_3_7_2_A_text_4))-  , ((isoiec_9798_3_7_2_B, ''Text6''), (KnownT isoiec_9798_3_7_2_B_4))-  , ((isoiec_9798_3_6_1_A, ''Text7''), (KnownT isoiec_9798_3_6_1_A_4))-  , ((isoiec_9798_3_6_1_T, ''Text7''), (KnownT isoiec_9798_3_6_1_T_text_4))-  , ((isoiec_9798_3_6_2_A, ''Text7''), (KnownT isoiec_9798_3_6_2_A_4))-  , ((isoiec_9798_3_6_2_T, ''Text7''), (KnownT isoiec_9798_3_6_2_T_text_4))-  , ((isoiec_9798_3_7_1_A, ''Text7''), (KnownT isoiec_9798_3_7_1_A_text_4))-  , ((isoiec_9798_3_7_2_A, ''Text7''), (KnownT isoiec_9798_3_7_2_A_text_4))-  , ((isoiec_9798_3_6_1_A, ''Text8''), (KnownT isoiec_9798_3_6_1_A_text_5))-  , ((isoiec_9798_3_6_1_B, ''Text8''), (KnownT isoiec_9798_3_6_1_B_5))-  , ((isoiec_9798_3_6_2_A, ''Text8''), (KnownT isoiec_9798_3_6_2_A_text_5))-  , ((isoiec_9798_3_6_2_B, ''Text8''), (KnownT isoiec_9798_3_6_2_B_5))-  , ((isoiec_9798_3_7_1_A, ''Text8''), (KnownT isoiec_9798_3_7_1_A_5))-  , ((isoiec_9798_3_7_1_B, ''Text8''), (KnownT isoiec_9798_3_7_1_B_text_5))-  , ((isoiec_9798_3_7_2_A, ''Text8''), (KnownT isoiec_9798_3_7_2_A_5))-  , ((isoiec_9798_3_7_2_B, ''Text8''), (KnownT isoiec_9798_3_7_2_B_text_5))-  , ((isoiec_9798_3_6_1_A, ''Text9''), (KnownT isoiec_9798_3_6_1_A_text_5))-  , ((isoiec_9798_3_6_1_B, ''Text9''), (KnownT isoiec_9798_3_6_1_B_5))-  , ((isoiec_9798_3_6_2_A, ''Text9''), (KnownT isoiec_9798_3_6_2_A_text_5))-  , ((isoiec_9798_3_6_2_B, ''Text9''), (KnownT isoiec_9798_3_6_2_B_5))-  , ((isoiec_9798_3_7_1_A, ''Text9''), (KnownT isoiec_9798_3_7_1_A_5))-  , ((isoiec_9798_3_7_1_B, ''Text9''), (KnownT isoiec_9798_3_7_1_B_4))-  , ((isoiec_9798_3_7_2_A, ''Text9''), (KnownT isoiec_9798_3_7_2_A_5))-  , ((isoiec_9798_3_7_2_B, ''Text9''), (KnownT isoiec_9798_3_7_2_B_4))-  , ((isoiec_9798_3_6_1_A, ''TokenBA''), (KnownT isoiec_9798_3_6_1_A_2))-  , ((isoiec_9798_3_6_2_A, ''TokenBA''), (KnownT isoiec_9798_3_6_2_A_2))-  , ((isoiec_9798_3_6_2_A, ''TokenTA''), (KnownT isoiec_9798_3_6_2_A_4))-  , ((isoiec_9798_3_7_2_A, ''TokenTA''), (KnownT isoiec_9798_3_7_2_A_3))-  , ((isoiec_9798_3_6_1_A, ''TokenTA_for_B''),-     (KnownT isoiec_9798_3_6_1_A_4))-  , ((isoiec_9798_3_7_1_A, ''TokenTA_for_B''),-     (KnownT isoiec_9798_3_7_1_A_3))-  , ((isoiec_9798_3_6_1_B, ''pkA''), (KnownT isoiec_9798_3_6_1_B_5))-  , ((isoiec_9798_3_6_2_A, ''pkA''),-     (KnownT isoiec_9798_3_6_2_A_check_4_in))-  , ((isoiec_9798_3_6_2_B, ''pkA''), (KnownT isoiec_9798_3_6_2_B_5))-  , ((isoiec_9798_3_7_1_B, ''pkA''), (KnownT isoiec_9798_3_7_1_B_4))-  , ((isoiec_9798_3_7_2_A, ''pkA''),-     (KnownT isoiec_9798_3_7_2_A_check_3_in))-  , ((isoiec_9798_3_7_2_B, ''pkA''), (KnownT isoiec_9798_3_7_2_B_4))-  , ((isoiec_9798_3_6_1_A, ''pkB''), (KnownT isoiec_9798_3_6_1_A_4))-  , ((isoiec_9798_3_6_2_A, ''pkB''), (KnownT isoiec_9798_3_6_2_A_4))-  , ((isoiec_9798_3_6_2_B, ''pkB''), (KnownT isoiec_9798_3_6_2_B_5))-  , ((isoiec_9798_3_7_1_A, ''pkB''), (KnownT isoiec_9798_3_7_1_A_3))-  , ((isoiec_9798_3_7_2_A, ''pkB''), (KnownT isoiec_9798_3_7_2_A_3))-  , ((isoiec_9798_3_7_2_B, ''pkB''), (KnownT isoiec_9798_3_7_2_B_4))-  ]"--sublocale isoiec_9798_3_state < isoiec_9798_3_composed_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_3_composed_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_3_composed_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_3_1_A_text_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_1_A_text_1_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_1_B_1_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_1_B_1_TNA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_1_B_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_1_B_1_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_2_A_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_2_A_1_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_2_A_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_2_A_text_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_2_A_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_2_B_2_Ra t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_2_B_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_2_B_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_3_A_text_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_3_A_text_1_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_3_A_2_TNB t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_3_A_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_3_A_2_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_3_B_1_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_3_B_1_TNA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_3_B_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_3_B_1_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_3_B_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_3_B_text_2_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_4_A_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_4_A_1_RB t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_4_A_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_4_A_text_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_4_A_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_4_A_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_4_A_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_4_B_2_RA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_4_B_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_4_B_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_4_B_text_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_4_B_text_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_A_2_RB t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_A_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_A_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_A_3_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_A_text_4_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_A_text_4_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_B_1_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_B_1_RA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_B_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_B_text_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_B_text_3_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_B_4_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_B_4_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_A_2_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_A_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_A_2_TokenBA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_A_4_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_A_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_A_4_TokenTA_for_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_A_4_pkB t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_A_check_4_in_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''check_4'',-               {| LC ''isoiec_9798_3_6_opt_1_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,-                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-               |},-               Enc {| LC ''isoiec_9798_3_6_opt_1_sig_2'', s(AV ''B'' tid0),-                      LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-                   |}-                   ( inv(s(MV ''pkB'' tid0)) )-            |}-            ( LN ''check_nonce_4'' tid0 ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_3_6_1_A_text_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_A_text_5_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_B_1_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_B_1_Ra t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_B_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_B_text_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_B_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_B_5_Ra5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_B_5_T t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_B_5_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_B_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_B_5_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_B_5_pkA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_T_3_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_T_3_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_T_3_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_T_3_Rpa t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_T_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_T_text_4_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_T_text_4_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_T_text_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_A_2_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_A_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_A_2_TokenBA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_A_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_A_4_TokenTA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_A_4_pkB t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_A_check_4_in_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''check_4'',-               {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,-                     s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                     s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                  |},-                  Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,-                         s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                         s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                      |}-                      ( SK ( s(AV ''T'' tid0) ) )-               |},-               {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,-                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-               |},-               Enc {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0),-                      LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-                   |}-                   ( inv(s(MV ''pkB'' tid0)) )-            |}-            ( LN ''check_nonce_4'' tid0 ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_3_6_2_A_check_4_in_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''check_4'',-               {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,-                     s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                     s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                  |},-                  Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,-                         s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                         s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                      |}-                      ( SK ( s(AV ''T'' tid0) ) )-               |},-               {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,-                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-               |},-               Enc {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0),-                      LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-                   |}-                   ( inv(s(MV ''pkB'' tid0)) )-            |}-            ( LN ''check_nonce_4'' tid0 ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_3_6_2_A_check_4_in_pkA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''check_4'',-               {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,-                     s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                     s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                  |},-                  Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,-                         s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                         s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                      |}-                      ( SK ( s(AV ''T'' tid0) ) )-               |},-               {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,-                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-               |},-               Enc {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0),-                      LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-                   |}-                   ( inv(s(MV ''pkB'' tid0)) )-            |}-            ( LN ''check_nonce_4'' tid0 ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_3_6_2_A_text_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_A_text_5_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_1_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_1_Ra t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_text_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_5_Ra5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_5_Rpa t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_5_T t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_5_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_5_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_5_pkA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_5_pkB t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_T_3_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_T_3_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_T_3_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_T_3_Rpa t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_T_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_T_text_4_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_T_text_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_A_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_A_1_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_A_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_A_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_A_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_A_3_TokenTA_for_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_A_3_pkB t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_A_text_4_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_A_text_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_A_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_A_5_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_B_4_Ra t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_B_4_Rpa t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_B_4_T t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_B_4_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_B_4_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_B_4_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_B_4_pkA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_B_text_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_T_2_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_T_2_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_T_2_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_T_2_Rpa t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_T_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_T_text_3_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_T_text_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_T_text_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_A_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_A_1_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_A_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_A_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_A_3_TokenTA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_A_3_pkB t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_A_check_3_in_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''check_4'',-               {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,-                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                  s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-               |},-               Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,-                      s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                      s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-                   |}-                   ( SK ( s(AV ''T'' tid0) ) )-            |}-            ( LN ''check_nonce_4'' tid0 ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_3_7_2_A_check_3_in_pkA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''check_4'',-               {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,-                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                  s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-               |},-               Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,-                      s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                      s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-                   |}-                   ( SK ( s(AV ''T'' tid0) ) )-            |}-            ( LN ''check_nonce_4'' tid0 ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_3_7_2_A_text_4_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_A_text_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_A_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_A_5_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_B_4_Ra t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_B_4_Rpa t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_B_4_T t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_B_4_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_B_4_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_B_4_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_B_4_pkA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_B_4_pkB t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_B_text_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_T_2_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_T_2_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_T_2_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_T_2_Rpa t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_T_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_T_text_3_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_T_text_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_composed_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_3_composed_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_3_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end--lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_1_B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_1_B"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_1_B_1 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_1_A &-        ( tid1, isoiec_9798_3_1_A_1 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,-           s(MV ''Text1'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),-                s(MV ''Text1'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_1_sig_1'', s(MV ''TNA'' tid0),-                          s(AV ''B'' tid0), s(MV ''Text1'' tid0)-                       |}-                       ( SK ( s(MV ''A'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_1_A_1_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_2_B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_2_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_2_B_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_2_A &-        ( tid1, isoiec_9798_3_2_A_2 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),-           s(MV ''Text2'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),-                LN ''Rb'' tid0, s(MV ''Text2'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_2_sig_2'', s(MV ''Ra'' tid0), LN ''Rb'' tid0,-                          s(AV ''B'' tid0), s(MV ''Text2'' tid0)-                       |}-                       ( SK ( s(AV ''A'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_2_A_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_3_A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_3_A"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_3_A_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_3_B &-        ( tid1, isoiec_9798_3_3_B_2 ) : steps t &-        {| s(MV ''A'' tid1), s(AV ''B'' tid1), LN ''TNB'' tid1,-           s(MV ''Text3'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNB'' tid0),-                s(MV ''Text3'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_3_sig_2'', s(MV ''TNB'' tid0),-                          s(AV ''A'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( SK ( s(AV ''B'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_3_B_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_3_B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_3_B"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_3_B_1 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_3_A &-        ( tid1, isoiec_9798_3_3_A_1 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,-           s(MV ''Text1'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),-                s(MV ''Text1'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_3_sig_1'', s(MV ''TNA'' tid0),-                          s(AV ''B'' tid0), s(MV ''Text1'' tid0)-                       |}-                       ( SK ( s(MV ''A'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_3_A_1_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_4_A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_4_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_4_A_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_4_B &-        ( tid1, isoiec_9798_3_4_B_3 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''RA'' tid1), LN ''RB'' tid1,-           s(MV ''Text2'' tid1), s(MV ''Text4'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''RA'' tid0,-                s(MV ''RB'' tid0), s(MV ''Text2'' tid0), s(MV ''Text4'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_4_sig_2'', s(MV ''RB'' tid0), LN ''RA'' tid0,-                          s(AV ''A'' tid0), s(MV ''Text4'' tid0)-                       |}-                       ( SK ( s(MV ''B'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_4_B_3_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_3_4_sig_1'', LN ''RA'' tid0, LN ''RB'' tid1,-                            s(AV ''B'' tid1), s(MV ''Text2'' tid1)-                         |}-                         ( SK ( s(AV ''A'' tid0) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest!: ltk_secrecy)-    next-      case (isoiec_9798_3_4_A_2_enc tid2) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_4_B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_4_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_4_B_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_4_A &-        ( tid1, isoiec_9798_3_4_A_2 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''RA'' tid1, s(MV ''RB'' tid1),-           s(MV ''Text2'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''RA'' tid0),-                LN ''RB'' tid0, s(MV ''Text2'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_4_sig_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,-                          s(AV ''B'' tid0), s(MV ''Text2'' tid0)-                       |}-                       ( SK ( s(AV ''A'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_4_A_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_5_A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_5_A"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_5_A_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_5_B &-        ( tid1, isoiec_9798_3_5_B_3 ) : steps t &-        {| s(MV ''A'' tid1), s(AV ''B'' tid1), s(MV ''RA'' tid1), LN ''RB'' tid1,-           s(MV ''Text5'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''RA'' tid0,-                s(MV ''RB'' tid0), s(MV ''Text5'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_5_sig_1'', s(MV ''RB'' tid0), LN ''RA'' tid0,-                          s(AV ''A'' tid0), s(MV ''Text5'' tid0)-                       |}-                       ( SK ( s(AV ''B'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_5_B_3_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_5_B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_5_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_5_B_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_5_A &-        ( tid1, isoiec_9798_3_5_A_4 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''RA'' tid1, s(MV ''RB'' tid1),-           s(MV ''Text3'' tid1), s(MV ''Text5'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''RA'' tid0),-                LN ''RB'' tid0, s(MV ''Text3'' tid0), s(MV ''Text5'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_5_sig_2'', s(MV ''RA'' tid0), LN ''RB'' tid0,-                          s(AV ''B'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( SK ( s(MV ''A'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_5_A_4_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_3_5_sig_1'', LN ''RB'' tid0, LN ''RA'' tid1,-                            s(AV ''A'' tid1), s(MV ''Text5'' tid1)-                         |}-                         ( SK ( s(AV ''B'' tid0) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest!: ltk_secrecy)-    next-      case (isoiec_9798_3_5_B_3_enc tid2) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_6_1_A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_6_1_A"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(AV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_6_1_A_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_6_1_B &-        ( tid1, isoiec_9798_3_6_1_B_2 ) : steps t &-        {| s(MV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,-           s(MV ''Text2'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''Ra'' tid0,-                s(MV ''Rb'' tid0), s(MV ''Text2'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''check_4'',-                          {| LC ''isoiec_9798_3_6_opt_1_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,-                             s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-                          |},-                          Enc {| LC ''isoiec_9798_3_6_opt_1_sig_2'', s(AV ''B'' tid0),-                                 LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-                              |}-                              ( inv(s(MV ''pkB'' tid0)) )-                       |}-                       ( LN ''check_nonce_4'' tid0 ) ")-    case fake note_unified facts = this facts-    thus ?thesis proof(sources! " LN ''check_nonce_4'' tid0 ")-    qed (insert facts, fastsimp+)?-  next-    case (isoiec_9798_3_6_1_A_check_4_out_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_3_6_opt_1_sig_2'', s(AV ''B'' tid0),-                            LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-                         |}-                         ( inv(s(MV ''pkB'' tid0)) ) ")-      case fake note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_3_6_opt_1_sig_4_1'', LN ''Rpa'' tid0,-                              s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text6'' tid0)-                           |}-                           ( SK ( s(AV ''T'' tid0) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest!: ltk_secrecy)-      next-        case (isoiec_9798_3_6_1_T_4_enc tid1) note_unified facts = this facts-        thus ?thesis by (fastsimp dest!: ltk_secrecy)-      qed (insert facts, fastsimp+)?-    next-      case (isoiec_9798_3_6_1_B_2_enc tid1) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_6_1_B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_6_1_B"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_6_1_B_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_6_1_A &-        ( tid1, isoiec_9798_3_6_1_A_5 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),-           s(MV ''Text8'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra5'' tid0),-                LN ''Rb'' tid0, s(MV ''Text8'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_6_opt_1_sig_4_2'', LN ''Rb'' tid0,-                          s(MV ''A'' tid0), s(MV ''pkA'' tid0), s(MV ''Text5'' tid0)-                       |}-                       ( SK ( s(MV ''T'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_6_1_T_4_enc_1 tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_3_6_opt_1_sig_5'', LN ''Rb'' tid0,-                            s(MV ''Ra5'' tid0), s(AV ''B'' tid0), s(MV ''A'' tid0),-                            s(MV ''Text8'' tid0)-                         |}-                         ( SK ( s(MV ''A'' tid0) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest!: ltk_secrecy)-    next-      case (isoiec_9798_3_6_1_A_5_enc tid2) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_6_1_A_non_injective_agreement_T:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_6_1_A"-    "RLKR(s(AV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_6_1_A_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_6_1_T &-        ( tid1, isoiec_9798_3_6_1_T_4 ) : steps t &-        {| s(MV ''B'' tid1), s(AV ''T'' tid1), s(MV ''Rpa'' tid1),-           PK ( s(MV ''B'' tid1) ), s(MV ''Text6'' tid1)-        |} = {| s(AV ''B'' tid0), s(AV ''T'' tid0), LN ''Rpa'' tid0,-                s(MV ''pkB'' tid0), s(MV ''Text6'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_6_opt_1_sig_4_1'', LN ''Rpa'' tid0,-                          s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text6'' tid0)-                       |}-                       ( SK ( s(AV ''T'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_6_1_T_4_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_6_1_B_non_injective_agreement_T:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_6_1_B"-    "RLKR(s(MV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_6_1_B_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_6_1_T &-        ( tid1, isoiec_9798_3_6_1_T_4 ) : steps t &-        {| s(MV ''A'' tid1), s(AV ''T'' tid1), s(MV ''Rb'' tid1),-           PK ( s(MV ''A'' tid1) ), s(MV ''Text5'' tid1)-        |} = {| s(MV ''A'' tid0), s(MV ''T'' tid0), LN ''Rb'' tid0,-                s(MV ''pkA'' tid0), s(MV ''Text5'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_6_opt_1_sig_4_2'', LN ''Rb'' tid0,-                          s(MV ''A'' tid0), s(MV ''pkA'' tid0), s(MV ''Text5'' tid0)-                       |}-                       ( SK ( s(MV ''T'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_6_1_T_4_enc_1 tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_6_2_A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_6_2_A"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(AV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_6_2_A_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_6_2_B &-        ( tid1, isoiec_9798_3_6_2_B_2 ) : steps t &-        {| s(MV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,-           s(MV ''Text2'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''Ra'' tid0,-                s(MV ''Rb'' tid0), s(MV ''Text2'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''check_4'',-                          {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,-                                s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                                s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                             |},-                             Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,-                                    s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                                    s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                                 |}-                                 ( SK ( s(AV ''T'' tid0) ) )-                          |},-                          {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,-                             s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-                          |},-                          Enc {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0),-                                 LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-                              |}-                              ( inv(s(MV ''pkB'' tid0)) )-                       |}-                       ( LN ''check_nonce_4'' tid0 ) ")-    case fake note_unified facts = this facts-    thus ?thesis proof(sources! " LN ''check_nonce_4'' tid0 ")-    qed (insert facts, fastsimp+)?-  next-    case (isoiec_9798_3_6_2_A_check_4_out_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0),-                            LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-                         |}-                         ( inv(s(MV ''pkB'' tid0)) ) ")-      case fake note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,-                              s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                              s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                           |}-                           ( SK ( s(AV ''T'' tid0) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest!: ltk_secrecy)-      next-        case (isoiec_9798_3_6_2_T_4_enc tid1) note_unified facts = this facts-        thus ?thesis by (fastsimp dest!: ltk_secrecy)-      qed (insert facts, fastsimp+)?-    next-      case (isoiec_9798_3_6_2_B_2_enc tid1) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_6_2_B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_6_2_B"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_6_2_B_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_6_2_A &-        ( tid1, isoiec_9798_3_6_2_A_5 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),-           s(MV ''Text8'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra5'' tid0),-                LN ''Rb'' tid0, s(MV ''Text8'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', s(MV ''Rpa'' tid0),-                          LN ''Rb'' tid0, s(MV ''A'' tid0), s(MV ''pkA'' tid0), s(AV ''B'' tid0),-                          s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                       |}-                       ( SK ( s(MV ''T'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_6_2_T_4_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_3_6_opt_2_sig_5'', LN ''Rb'' tid0,-                            s(MV ''Ra5'' tid0), s(AV ''B'' tid0), s(MV ''A'' tid0),-                            s(MV ''Text8'' tid0)-                         |}-                         ( SK ( s(MV ''A'' tid0) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest!: ltk_secrecy)-    next-      case (isoiec_9798_3_6_2_A_5_enc tid2) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_6_2_A_non_injective_agreement_T:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_6_2_A"-    "RLKR(s(AV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_6_2_A_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_6_2_T &-        ( tid1, isoiec_9798_3_6_2_T_4 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''T'' tid1),-           s(MV ''Rpa'' tid1), s(MV ''Rb'' tid1), PK ( s(MV ''A'' tid1) ),-           PK ( s(MV ''B'' tid1) ), s(MV ''Text5'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''T'' tid0),-                LN ''Rpa'' tid0, s(MV ''Rb'' tid0), s(MV ''pkA'' tid0),-                s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''check_4'',-                          {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,-                                s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                                s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                             |},-                             Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,-                                    s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                                    s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                                 |}-                                 ( SK ( s(AV ''T'' tid0) ) )-                          |},-                          {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,-                             s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-                          |},-                          Enc {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0),-                                 LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-                              |}-                              ( inv(s(MV ''pkB'' tid0)) )-                       |}-                       ( LN ''check_nonce_4'' tid0 ) ")-    case fake note_unified facts = this facts-    thus ?thesis proof(sources! " LN ''check_nonce_4'' tid0 ")-    qed (insert facts, fastsimp+)?-  next-    case (isoiec_9798_3_6_2_A_check_4_out_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,-                            s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                            s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                         |}-                         ( SK ( s(AV ''T'' tid0) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest!: ltk_secrecy)-    next-      case (isoiec_9798_3_6_2_T_4_enc tid1) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_6_2_B_non_injective_agreement_T:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_6_2_B"-    "RLKR(s(MV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_6_2_B_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_6_2_T &-        ( tid1, isoiec_9798_3_6_2_T_4 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''T'' tid1),-           s(MV ''Rpa'' tid1), s(MV ''Rb'' tid1), PK ( s(MV ''A'' tid1) ),-           PK ( s(MV ''B'' tid1) ), s(MV ''Text5'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''T'' tid0),-                s(MV ''Rpa'' tid0), LN ''Rb'' tid0, s(MV ''pkA'' tid0),-                s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', s(MV ''Rpa'' tid0),-                          LN ''Rb'' tid0, s(MV ''A'' tid0), s(MV ''pkA'' tid0), s(AV ''B'' tid0),-                          s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                       |}-                       ( SK ( s(MV ''T'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_6_2_T_4_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_7_1_A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_7_1_A"-    "RLKR(s(AV ''T'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_7_1_A_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_7_1_B &-        ( tid1, isoiec_9798_3_7_1_B_5 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,-           s(MV ''Text8'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''Ra'' tid0,-                s(MV ''Rb'' tid0), s(MV ''Text8'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_7_opt_1_sig_3_1'', LN ''Rpa'' tid0,-                          s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text4'' tid0)-                       |}-                       ( SK ( s(AV ''T'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_7_1_T_3_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_3_7_opt_1_sig_5'', LN ''Ra'' tid0,-                            s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),-                            s(MV ''Text8'' tid0)-                         |}-                         ( SK ( s(MV ''B'' tid0) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest!: ltk_secrecy)-    next-      case (isoiec_9798_3_7_1_B_5_enc tid2) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_7_1_B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_7_1_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_7_1_B_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_7_1_A &-        ( tid1, isoiec_9798_3_7_1_A_4 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),-           s(MV ''Text6'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),-                LN ''Rb'' tid0, s(MV ''Text6'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_7_opt_1_sig_3_2'', LN ''Rb'' tid0,-                          s(AV ''A'' tid0), s(MV ''pkA'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( SK ( s(MV ''T'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_7_1_T_3_enc_1 tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_3_7_opt_1_sig_4'', LN ''Rb'' tid0,-                            s(MV ''Ra'' tid0), s(AV ''B'' tid0), s(AV ''A'' tid0),-                            s(MV ''Text6'' tid0)-                         |}-                         ( SK ( s(AV ''A'' tid0) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest!: ltk_secrecy)-    next-      case (isoiec_9798_3_7_1_A_4_enc tid2) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_7_1_A_non_injective_agreement_T:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_7_1_A"-    "RLKR(s(AV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_7_1_A_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_7_1_T &-        ( tid1, isoiec_9798_3_7_1_T_3 ) : steps t &-        {| s(MV ''B'' tid1), s(AV ''T'' tid1), s(MV ''Rpa'' tid1),-           PK ( s(MV ''B'' tid1) ), s(MV ''Text4'' tid1)-        |} = {| s(MV ''B'' tid0), s(AV ''T'' tid0), LN ''Rpa'' tid0,-                s(MV ''pkB'' tid0), s(MV ''Text4'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_7_opt_1_sig_3_1'', LN ''Rpa'' tid0,-                          s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text4'' tid0)-                       |}-                       ( SK ( s(AV ''T'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_7_1_T_3_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_7_1_B_non_injective_agreement_T:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_7_1_B"-    "RLKR(s(MV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_7_1_B_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_7_1_T &-        ( tid1, isoiec_9798_3_7_1_T_3 ) : steps t &-        {| s(MV ''A'' tid1), s(AV ''T'' tid1), s(MV ''Rb'' tid1),-           PK ( s(MV ''A'' tid1) ), s(MV ''Text3'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''T'' tid0), LN ''Rb'' tid0,-                s(MV ''pkA'' tid0), s(MV ''Text3'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_7_opt_1_sig_3_2'', LN ''Rb'' tid0,-                          s(AV ''A'' tid0), s(MV ''pkA'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( SK ( s(MV ''T'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_7_1_T_3_enc_1 tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_7_2_A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_7_2_A"-    "RLKR(s(AV ''T'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_7_2_A_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_7_2_B &-        ( tid1, isoiec_9798_3_7_2_B_5 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,-           s(MV ''Text8'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''Ra'' tid0,-                s(MV ''Rb'' tid0), s(MV ''Text8'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''check_4'',-                          {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,-                             s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                             s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-                          |},-                          Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,-                                 s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                                 s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-                              |}-                              ( SK ( s(AV ''T'' tid0) ) )-                       |}-                       ( LN ''check_nonce_4'' tid0 ) ")-    case fake note_unified facts = this facts-    thus ?thesis proof(sources! " LN ''check_nonce_4'' tid0 ")-    qed (insert facts, fastsimp+)?-  next-    case (isoiec_9798_3_7_2_A_check_3_out_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,-                            s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                            s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-                         |}-                         ( SK ( s(AV ''T'' tid0) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest!: ltk_secrecy)-    next-      case (isoiec_9798_3_7_2_T_3_enc tid1) note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_3_7_opt_2_sig_5'', LN ''Ra'' tid0,-                              s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),-                              s(MV ''Text8'' tid0)-                           |}-                           ( SK ( s(MV ''B'' tid0) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest!: ltk_secrecy)-      next-        case (isoiec_9798_3_7_2_B_5_enc tid2) note_unified facts = this facts-        thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-      qed (insert facts, fastsimp+)?-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_7_2_B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_7_2_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_7_2_B_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_7_2_A &-        ( tid1, isoiec_9798_3_7_2_A_4 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),-           s(MV ''Text6'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),-                LN ''Rb'' tid0, s(MV ''Text6'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', s(MV ''Rpa'' tid0),-                          LN ''Rb'' tid0, s(AV ''A'' tid0), s(MV ''pkA'' tid0), s(AV ''B'' tid0),-                          s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( SK ( s(MV ''T'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_7_2_T_3_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_3_7_opt_2_sig_4'', LN ''Rb'' tid0,-                            s(MV ''Ra'' tid0), s(AV ''B'' tid0), s(AV ''A'' tid0),-                            s(MV ''Text6'' tid0)-                         |}-                         ( SK ( s(AV ''A'' tid0) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest!: ltk_secrecy)-    next-      case (isoiec_9798_3_7_2_A_4_enc tid2) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_7_2_A_non_injective_agreement_T:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_7_2_A"-    "RLKR(s(AV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_7_2_A_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_7_2_T &-        ( tid1, isoiec_9798_3_7_2_T_3 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''T'' tid1),-           s(MV ''Rpa'' tid1), s(MV ''Rb'' tid1), PK ( s(MV ''A'' tid1) ),-           PK ( s(MV ''B'' tid1) ), s(MV ''Text3'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''T'' tid0),-                LN ''Rpa'' tid0, s(MV ''Rb'' tid0), s(MV ''pkA'' tid0),-                s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''check_4'',-                          {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,-                             s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                             s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-                          |},-                          Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,-                                 s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                                 s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-                              |}-                              ( SK ( s(AV ''T'' tid0) ) )-                       |}-                       ( LN ''check_nonce_4'' tid0 ) ")-    case fake note_unified facts = this facts-    thus ?thesis proof(sources! " LN ''check_nonce_4'' tid0 ")-    qed (insert facts, fastsimp+)?-  next-    case (isoiec_9798_3_7_2_A_check_3_out_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,-                            s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                            s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-                         |}-                         ( SK ( s(AV ''T'' tid0) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest!: ltk_secrecy)-    next-      case (isoiec_9798_3_7_2_T_3_enc tid1) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_7_2_B_non_injective_agreement_T:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_7_2_B"-    "RLKR(s(MV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_7_2_B_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_7_2_T &-        ( tid1, isoiec_9798_3_7_2_T_3 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''T'' tid1),-           s(MV ''Rpa'' tid1), s(MV ''Rb'' tid1), PK ( s(MV ''A'' tid1) ),-           PK ( s(MV ''B'' tid1) ), s(MV ''Text3'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''T'' tid0),-                s(MV ''Rpa'' tid0), LN ''Rb'' tid0, s(MV ''pkA'' tid0),-                s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', s(MV ''Rpa'' tid0),-                          LN ''Rb'' tid0, s(AV ''A'' tid0), s(MV ''pkA'' tid0), s(AV ''B'' tid0),-                          s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( SK ( s(MV ''T'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_7_2_T_3_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?+  "ESPLogic"+begin++role isoiec_9798_3_1_A+where "isoiec_9798_3_1_A =+  [ Send ''leak_A'' ( sN ''TNA'' )+  , Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>+  , Send ''1'' <| sAV ''A'', sAV ''B'', sMV ''Text2'',+                  PSign <| sC ''isoiec_9798_3_1_sig_1'', sN ''TNA'', sAV ''B'',+                           sMV ''Text1''+                        |>+                        ( sPK ''A'' )+               |>+  ]"++role isoiec_9798_3_1_B+where "isoiec_9798_3_1_B =+  [ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Text2'',+                  PSign <| sC ''isoiec_9798_3_1_sig_1'', sMV ''TNA'', sAV ''B'',+                           sMV ''Text1''+                        |>+                        ( PAsymPK ( sMV ''A'' ) )+               |>+  ]"++role isoiec_9798_3_2_A+where "isoiec_9798_3_2_A =+  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>+  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>+  , Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'',+                  PSign <| sC ''isoiec_9798_3_2_sig_2'', sN ''Ra'', sMV ''Rb'', sMV ''B'',+                           sMV ''Text2''+                        |>+                        ( sPK ''A'' )+               |>+  ]"++role isoiec_9798_3_2_B+where "isoiec_9798_3_2_B =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>+  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'',+                  PSign <| sC ''isoiec_9798_3_2_sig_2'', sMV ''Ra'', sN ''Rb'', sAV ''B'',+                           sMV ''Text2''+                        |>+                        ( sPK ''A'' )+               |>+  ]"++role isoiec_9798_3_3_A+where "isoiec_9798_3_3_A =+  [ Send ''leak_A'' ( sN ''TNA'' )+  , Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>+  , Send ''1'' <| sAV ''A'', sAV ''B'', sMV ''Text2'',+                  PSign <| sC ''isoiec_9798_3_3_sig_1'', sN ''TNA'', sAV ''B'',+                           sMV ''Text1''+                        |>+                        ( sPK ''A'' )+               |>+  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text4'',+                  PSign <| sC ''isoiec_9798_3_3_sig_2'', sMV ''TNB'', sAV ''A'',+                           sMV ''Text3''+                        |>+                        ( sPK ''B'' )+               |>+  ]"++role isoiec_9798_3_3_B+where "isoiec_9798_3_3_B =+  [ Send ''leak_B'' ( sN ''TNB'' )+  , Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Text2'',+                  PSign <| sC ''isoiec_9798_3_3_sig_1'', sMV ''TNA'', sAV ''B'',+                           sMV ''Text1''+                        |>+                        ( PAsymPK ( sMV ''A'' ) )+               |>+  , Recv ''text_2'' <| sMV ''Text3'', sMV ''Text4'' |>+  , Send ''2'' <| sMV ''A'', sAV ''B'', sMV ''Text4'',+                  PSign <| sC ''isoiec_9798_3_3_sig_2'', sN ''TNB'', sMV ''A'',+                           sMV ''Text3''+                        |>+                        ( sPK ''B'' )+               |>+  ]"++role isoiec_9798_3_4_A+where "isoiec_9798_3_4_A =+  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''RB'', sMV ''Text1'' |>+  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>+  , Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'',+                  PSign <| sC ''isoiec_9798_3_4_sig_1'', sN ''RA'', sMV ''RB'', sMV ''B'',+                           sMV ''Text2''+                        |>+                        ( sPK ''A'' )+               |>+  , Recv ''3'' <| sMV ''B'', sAV ''A'', sMV ''Text5'',+                  PSign <| sC ''isoiec_9798_3_4_sig_2'', sMV ''RB'', sN ''RA'', sAV ''A'',+                           sMV ''Text4''+                        |>+                        ( PAsymPK ( sMV ''B'' ) )+               |>+  ]"++role isoiec_9798_3_4_B+where "isoiec_9798_3_4_B =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''RB'', sMV ''Text1'' |>+  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'',+                  PSign <| sC ''isoiec_9798_3_4_sig_1'', sMV ''RA'', sN ''RB'', sAV ''B'',+                           sMV ''Text2''+                        |>+                        ( sPK ''A'' )+               |>+  , Recv ''text_3'' <| sMV ''Text4'', sMV ''Text5'' |>+  , Send ''3'' <| sAV ''B'', sAV ''A'', sMV ''Text5'',+                  PSign <| sC ''isoiec_9798_3_4_sig_2'', sN ''RB'', sMV ''RA'', sAV ''A'',+                           sMV ''Text4''+                        |>+                        ( sPK ''B'' )+               |>+  ]"++role isoiec_9798_3_5_A+where "isoiec_9798_3_5_A =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''A'', sAV ''B'', sN ''RA'', sMV ''Text1'' |>+  , Recv ''2'' <| sAV ''B'', sAV ''A'', sMV ''RB'', sMV ''Text2'' |>+  , Recv ''3'' <| sAV ''B'', sAV ''A'', sMV ''Text6'',+                  PSign <| sC ''isoiec_9798_3_5_sig_1'', sMV ''RB'', sN ''RA'', sAV ''A'',+                           sMV ''Text5''+                        |>+                        ( sPK ''B'' )+               |>+  , Recv ''text_4'' <| sMV ''Text3'', sMV ''Text4'' |>+  , Send ''4'' <| sAV ''A'', sAV ''B'', sMV ''Text4'',+                  PSign <| sC ''isoiec_9798_3_5_sig_2'', sN ''RA'', sMV ''RB'', sAV ''B'',+                           sMV ''Text3''+                        |>+                        ( sPK ''A'' )+               |>+  ]"++role isoiec_9798_3_5_B+where "isoiec_9798_3_5_B =+  [ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''RA'', sMV ''Text1'' |>+  , Recv ''text_2'' ( sMV ''Text2'' )+  , Send ''2'' <| sAV ''B'', sMV ''A'', sN ''RB'', sMV ''Text2'' |>+  , Recv ''text_3'' <| sMV ''Text5'', sMV ''Text6'' |>+  , Send ''3'' <| sAV ''B'', sMV ''A'', sMV ''Text6'',+                  PSign <| sC ''isoiec_9798_3_5_sig_1'', sN ''RB'', sMV ''RA'', sMV ''A'',+                           sMV ''Text5''+                        |>+                        ( sPK ''B'' )+               |>+  , Recv ''4'' <| sMV ''A'', sAV ''B'', sMV ''Text4'',+                  PSign <| sC ''isoiec_9798_3_5_sig_2'', sMV ''RA'', sN ''RB'', sAV ''B'',+                           sMV ''Text3''+                        |>+                        ( PAsymPK ( sMV ''A'' ) )+               |>+  ]"++role isoiec_9798_3_6_1_A+where "isoiec_9798_3_6_1_A =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''A'', sAV ''B'', sN ''Ra'', sMV ''Text1'' |>+  , Recv ''2'' <| sAV ''A'', sAV ''B'', sN ''Ra'', sMV ''Rb'',+                  sMV ''Text3'', sMV ''TokenBA''+               |>+  , Recv ''text_3'' ( sMV ''Text4'' )+  , Send ''3'' <| sAV ''A'', sAV ''T'', sN ''Rpa'', sMV ''Rb'', sAV ''B'',+                  sMV ''Text4''+               |>+  , Recv ''4'' <| sAV ''T'', sAV ''A'', sMV ''Text7'', sAV ''A'',+                  sPK ''A'', sAV ''B'', sMV ''pkB'',+                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_4_1'', sN ''Rpa'', sAV ''B'',+                           sMV ''pkB'', sMV ''Text6''+                        |>+                        ( sPK ''T'' ),+                  sMV ''TokenTA_for_B''+               |>+  , Send ''check_4_out'' ( PEnc <| sC ''check_4'', sMV ''TokenBA'' |>+                                ( sN ''check_nonce_4'' )+                         )+  , Recv ''check_4_in'' ( PEnc <| sC ''check_4'',+                                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_2'', sAV ''B'', sN ''Ra'',+                                           sMV ''Rb'', sAV ''A'', sMV ''Text2''+                                        |>+                                        ( sMV ''pkB'' )+                               |>+                               ( sN ''check_nonce_4'' )+                        )+  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>+  , Send ''5'' <| sAV ''A'', sAV ''B'', sMV ''Text9'', sAV ''T'',+                  sMV ''TokenTA_for_B'',+                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_5'', sMV ''Rb'', sN ''Ra'',+                           sAV ''B'', sAV ''A'', sMV ''Text8''+                        |>+                        ( sPK ''A'' )+               |>+  ]"++role isoiec_9798_3_6_1_B+where "isoiec_9798_3_6_1_B =+  [ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Ra'', sMV ''Text1'' |>+  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>+  , Send ''2'' <| sMV ''A'', sAV ''B'', sMV ''Ra'', sN ''Rb'',+                  sMV ''Text3'',+                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_2'', sAV ''B'', sMV ''Ra'',+                           sN ''Rb'', sMV ''A'', sMV ''Text2''+                        |>+                        ( sPK ''B'' )+               |>+  , Recv ''5'' <| sMV ''A'', sAV ''B'', sMV ''Text9'', sMV ''T'',+                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_4_2'', sN ''Rb'', sMV ''A'',+                           sMV ''pkA'', sMV ''Text5''+                        |>+                        ( PAsymPK ( sMV ''T'' ) ),+                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_5'', sN ''Rb'', sMV ''Ra'',+                           sAV ''B'', sMV ''A'', sMV ''Text8''+                        |>+                        ( sMV ''pkA'' )+               |>+  ]"++role isoiec_9798_3_6_1_T+where "isoiec_9798_3_6_1_T =+  [ Recv ''3'' <| sMV ''A'', sAV ''T'', sMV ''Rpa'', sMV ''Rb'', sMV ''B'',+                  sMV ''Text4''+               |>+  , Recv ''text_4'' <| sMV ''Text5'', sMV ''Text6'', sMV ''Text7'' |>+  , Send ''4'' <| sAV ''T'', sMV ''A'', sMV ''Text7'', sMV ''A'',+                  PAsymPK ( sMV ''A'' ), sMV ''B'', PAsymPK ( sMV ''B'' ),+                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_4_1'', sMV ''Rpa'', sMV ''B'',+                           PAsymPK ( sMV ''B'' ), sMV ''Text6''+                        |>+                        ( sPK ''T'' ),+                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_4_2'', sMV ''Rb'', sMV ''A'',+                           PAsymPK ( sMV ''A'' ), sMV ''Text5''+                        |>+                        ( sPK ''T'' )+               |>+  ]"++role isoiec_9798_3_6_2_A+where "isoiec_9798_3_6_2_A =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''A'', sAV ''B'', sN ''Ra'', sMV ''Text1'' |>+  , Recv ''2'' <| sAV ''A'', sAV ''B'', sN ''Ra'', sMV ''Rb'',+                  sMV ''Text3'', sMV ''TokenBA''+               |>+  , Recv ''text_3'' ( sMV ''Text4'' )+  , Send ''3'' <| sAV ''A'', sAV ''T'', sN ''Rpa'', sMV ''Rb'', sAV ''B'',+                  sMV ''Text4''+               |>+  , Recv ''4'' <| sAV ''T'', sAV ''A'', sMV ''Text7'', sAV ''A'',+                  sPK ''A'', sAV ''B'', sMV ''pkB'', sMV ''TokenTA''+               |>+  , Send ''check_4_out'' ( PEnc <| sC ''check_4'', sMV ''TokenTA'',+                                   sMV ''TokenBA''+                                |>+                                ( sN ''check_nonce_4'' )+                         )+  , Recv ''check_4_in'' ( PEnc <| sC ''check_4'',+                                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_4'', sN ''Rpa'', sMV ''Rb'',+                                           sAV ''A'', sMV ''pkA'', sAV ''B'', sMV ''pkB'', sMV ''Text5''+                                        |>+                                        ( sPK ''T'' ),+                                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_2'', sAV ''B'', sN ''Ra'',+                                           sMV ''Rb'', sAV ''A'', sMV ''Text2''+                                        |>+                                        ( sMV ''pkB'' )+                               |>+                               ( sN ''check_nonce_4'' )+                        )+  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>+  , Send ''5'' <| sAV ''A'', sAV ''B'', sN ''Rpa'', sMV ''Text9'',+                  sAV ''T'', sMV ''TokenTA'',+                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_5'', sMV ''Rb'', sN ''Ra'',+                           sAV ''B'', sAV ''A'', sMV ''Text8''+                        |>+                        ( sPK ''A'' )+               |>+  ]"++role isoiec_9798_3_6_2_B+where "isoiec_9798_3_6_2_B =+  [ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Ra'', sMV ''Text1'' |>+  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>+  , Send ''2'' <| sMV ''A'', sAV ''B'', sMV ''Ra'', sN ''Rb'',+                  sMV ''Text3'',+                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_2'', sAV ''B'', sMV ''Ra'',+                           sN ''Rb'', sMV ''A'', sMV ''Text2''+                        |>+                        ( sPK ''B'' )+               |>+  , Recv ''5'' <| sMV ''A'', sAV ''B'', sMV ''Rpa'', sMV ''Text9'',+                  sMV ''T'',+                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_4'', sMV ''Rpa'', sN ''Rb'',+                           sMV ''A'', sMV ''pkA'', sAV ''B'', sMV ''pkB'', sMV ''Text5''+                        |>+                        ( PAsymPK ( sMV ''T'' ) ),+                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_5'', sN ''Rb'', sMV ''Ra'',+                           sAV ''B'', sMV ''A'', sMV ''Text8''+                        |>+                        ( sMV ''pkA'' )+               |>+  ]"++role isoiec_9798_3_6_2_T+where "isoiec_9798_3_6_2_T =+  [ Recv ''3'' <| sMV ''A'', sAV ''T'', sMV ''Rpa'', sMV ''Rb'', sMV ''B'',+                  sMV ''Text4''+               |>+  , Recv ''text_4'' <| sMV ''Text5'', sMV ''Text7'' |>+  , Send ''4'' <| sAV ''T'', sMV ''A'', sMV ''Text7'', sMV ''A'',+                  PAsymPK ( sMV ''A'' ), sMV ''B'', PAsymPK ( sMV ''B'' ),+                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_4'', sMV ''Rpa'', sMV ''Rb'',+                           sMV ''A'', PAsymPK ( sMV ''A'' ), sMV ''B'', PAsymPK ( sMV ''B'' ),+                           sMV ''Text5''+                        |>+                        ( sPK ''T'' )+               |>+  ]"++role isoiec_9798_3_7_1_A+where "isoiec_9798_3_7_1_A =+  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>+  , Recv ''text_2'' ( sMV ''Text2'' )+  , Send ''2'' <| sAV ''A'', sAV ''T'', sN ''Rpa'', sMV ''Rb'', sAV ''A'',+                  sMV ''B'', sMV ''Text2''+               |>+  , Recv ''3'' <| sAV ''T'', sAV ''A'', sMV ''Text5'', sAV ''A'',+                  sPK ''A'', sMV ''B'', sMV ''pkB'',+                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_3_1'', sN ''Rpa'', sMV ''B'',+                           sMV ''pkB'', sMV ''Text4''+                        |>+                        ( sPK ''T'' ),+                  sMV ''TokenTA_for_B''+               |>+  , Recv ''text_4'' <| sMV ''Text6'', sMV ''Text7'' |>+  , Send ''4'' <| sAV ''A'', sMV ''B'', sN ''Rpa'', sMV ''Text7'',+                  sAV ''T'', sMV ''TokenTA_for_B'',+                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_4'', sMV ''Rb'', sN ''Ra'',+                           sMV ''B'', sAV ''A'', sMV ''Text6''+                        |>+                        ( sPK ''A'' )+               |>+  , Recv ''5'' <| sAV ''A'', sMV ''B'', sN ''Ra'', sMV ''Rb'',+                  sMV ''Text9'',+                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_5'', sN ''Ra'', sMV ''Rb'',+                           sAV ''A'', sMV ''B'', sMV ''Text8''+                        |>+                        ( sMV ''pkB'' )+               |>+  ]"++role isoiec_9798_3_7_1_B+where "isoiec_9798_3_7_1_B =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>+  , Recv ''4'' <| sAV ''A'', sAV ''B'', sMV ''Rpa'', sMV ''Text9'',+                  sMV ''T'',+                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_3_2'', sN ''Rb'', sAV ''A'',+                           sMV ''pkA'', sMV ''Text3''+                        |>+                        ( PAsymPK ( sMV ''T'' ) ),+                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_4'', sN ''Rb'', sMV ''Ra'',+                           sAV ''B'', sAV ''A'', sMV ''Text6''+                        |>+                        ( sMV ''pkA'' )+               |>+  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>+  , Send ''5'' <| sAV ''A'', sAV ''B'', sMV ''Ra'', sN ''Rb'',+                  sMV ''Text9'',+                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_5'', sMV ''Ra'', sN ''Rb'',+                           sAV ''A'', sAV ''B'', sMV ''Text8''+                        |>+                        ( sPK ''B'' )+               |>+  ]"++role isoiec_9798_3_7_1_T+where "isoiec_9798_3_7_1_T =+  [ Recv ''2'' <| sMV ''A'', sAV ''T'', sMV ''Rpa'', sMV ''Rb'', sMV ''A'',+                  sMV ''B'', sMV ''Text2''+               |>+  , Recv ''text_3'' <| sMV ''Text3'', sMV ''Text4'', sMV ''Text5'' |>+  , Send ''3'' <| sAV ''T'', sMV ''A'', sMV ''Text5'', sMV ''A'',+                  PAsymPK ( sMV ''A'' ), sMV ''B'', PAsymPK ( sMV ''B'' ),+                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_3_1'', sMV ''Rpa'', sMV ''B'',+                           PAsymPK ( sMV ''B'' ), sMV ''Text4''+                        |>+                        ( sPK ''T'' ),+                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_3_2'', sMV ''Rb'', sMV ''A'',+                           PAsymPK ( sMV ''A'' ), sMV ''Text3''+                        |>+                        ( sPK ''T'' )+               |>+  ]"++role isoiec_9798_3_7_2_A+where "isoiec_9798_3_7_2_A =+  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>+  , Recv ''text_2'' ( sMV ''Text2'' )+  , Send ''2'' <| sAV ''A'', sAV ''T'', sN ''Rpa'', sMV ''Rb'', sAV ''A'',+                  sMV ''B'', sMV ''Text2''+               |>+  , Recv ''3'' <| sAV ''T'', sAV ''A'', sMV ''Text5'', sAV ''A'',+                  sPK ''A'', sMV ''B'', sMV ''pkB'', sMV ''TokenTA''+               |>+  , Send ''check_3_out'' ( PEnc <| sC ''check_4'', sMV ''TokenTA'' |>+                                ( sN ''check_nonce_4'' )+                         )+  , Recv ''check_3_in'' ( PEnc <| sC ''check_4'',+                                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_3'', sN ''Rpa'', sMV ''Rb'',+                                           sAV ''A'', sMV ''pkA'', sMV ''B'', sMV ''pkB'', sMV ''Text3''+                                        |>+                                        ( sPK ''T'' )+                               |>+                               ( sN ''check_nonce_4'' )+                        )+  , Recv ''text_4'' <| sMV ''Text6'', sMV ''Text7'' |>+  , Send ''4'' <| sAV ''A'', sMV ''B'', sN ''Rpa'', sMV ''Text7'',+                  sAV ''T'', sMV ''TokenTA'',+                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_4'', sMV ''Rb'', sN ''Ra'',+                           sMV ''B'', sAV ''A'', sMV ''Text6''+                        |>+                        ( sPK ''A'' )+               |>+  , Recv ''5'' <| sAV ''A'', sMV ''B'', sN ''Ra'', sMV ''Rb'',+                  sMV ''Text9'',+                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_5'', sN ''Ra'', sMV ''Rb'',+                           sAV ''A'', sMV ''B'', sMV ''Text8''+                        |>+                        ( sMV ''pkB'' )+               |>+  ]"++role isoiec_9798_3_7_2_B+where "isoiec_9798_3_7_2_B =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>+  , Recv ''4'' <| sAV ''A'', sAV ''B'', sMV ''Rpa'', sMV ''Text9'',+                  sMV ''T'',+                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_3'', sMV ''Rpa'', sN ''Rb'',+                           sAV ''A'', sMV ''pkA'', sAV ''B'', sMV ''pkB'', sMV ''Text3''+                        |>+                        ( PAsymPK ( sMV ''T'' ) ),+                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_4'', sN ''Rb'', sMV ''Ra'',+                           sAV ''B'', sAV ''A'', sMV ''Text6''+                        |>+                        ( sMV ''pkA'' )+               |>+  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>+  , Send ''5'' <| sAV ''A'', sAV ''B'', sMV ''Ra'', sN ''Rb'',+                  sMV ''Text9'',+                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_5'', sMV ''Ra'', sN ''Rb'',+                           sAV ''A'', sAV ''B'', sMV ''Text8''+                        |>+                        ( sPK ''B'' )+               |>+  ]"++role isoiec_9798_3_7_2_T+where "isoiec_9798_3_7_2_T =+  [ Recv ''2'' <| sMV ''A'', sAV ''T'', sMV ''Rpa'', sMV ''Rb'', sMV ''A'',+                  sMV ''B'', sMV ''Text2''+               |>+  , Recv ''text_3'' <| sMV ''Text3'', sMV ''Text5'' |>+  , Send ''3'' <| sAV ''T'', sMV ''A'', sMV ''Text5'', sMV ''A'',+                  PAsymPK ( sMV ''A'' ), sMV ''B'', PAsymPK ( sMV ''B'' ),+                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_3'', sMV ''Rpa'', sMV ''Rb'',+                           sMV ''A'', PAsymPK ( sMV ''A'' ), sMV ''B'', PAsymPK ( sMV ''B'' ),+                           sMV ''Text3''+                        |>+                        ( sPK ''T'' )+               |>+  ]"++protocol isoiec_9798_3+where "isoiec_9798_3 =+{ isoiec_9798_3_1_A, isoiec_9798_3_1_B, isoiec_9798_3_2_A,+  isoiec_9798_3_2_B, isoiec_9798_3_3_A, isoiec_9798_3_3_B,+  isoiec_9798_3_4_A, isoiec_9798_3_4_B, isoiec_9798_3_5_A,+  isoiec_9798_3_5_B, isoiec_9798_3_6_1_A, isoiec_9798_3_6_1_B,+  isoiec_9798_3_6_1_T, isoiec_9798_3_6_2_A, isoiec_9798_3_6_2_B,+  isoiec_9798_3_6_2_T, isoiec_9798_3_7_1_A, isoiec_9798_3_7_1_B,+  isoiec_9798_3_7_1_T, isoiec_9798_3_7_2_A, isoiec_9798_3_7_2_B,+  isoiec_9798_3_7_2_T+}"++locale restricted_isoiec_9798_3_state = isoiec_9798_3_state++type_invariant isoiec_9798_3_composed_typing for isoiec_9798_3+where "isoiec_9798_3_composed_typing = mk_typing+  [ ((isoiec_9798_3_1_B, ''A''), (KnownT isoiec_9798_3_1_B_1))+  , ((isoiec_9798_3_3_B, ''A''), (KnownT isoiec_9798_3_3_B_1))+  , ((isoiec_9798_3_5_B, ''A''), (KnownT isoiec_9798_3_5_B_1))+  , ((isoiec_9798_3_6_1_B, ''A''), (KnownT isoiec_9798_3_6_1_B_1))+  , ((isoiec_9798_3_6_1_T, ''A''), (KnownT isoiec_9798_3_6_1_T_3))+  , ((isoiec_9798_3_6_2_B, ''A''), (KnownT isoiec_9798_3_6_2_B_1))+  , ((isoiec_9798_3_6_2_T, ''A''), (KnownT isoiec_9798_3_6_2_T_3))+  , ((isoiec_9798_3_7_1_T, ''A''), (KnownT isoiec_9798_3_7_1_T_2))+  , ((isoiec_9798_3_7_2_T, ''A''), (KnownT isoiec_9798_3_7_2_T_2))+  , ((isoiec_9798_3_2_A, ''B''), (KnownT isoiec_9798_3_2_A_1))+  , ((isoiec_9798_3_4_A, ''B''), (KnownT isoiec_9798_3_4_A_1))+  , ((isoiec_9798_3_6_1_T, ''B''), (KnownT isoiec_9798_3_6_1_T_3))+  , ((isoiec_9798_3_6_2_T, ''B''), (KnownT isoiec_9798_3_6_2_T_3))+  , ((isoiec_9798_3_7_1_A, ''B''), (KnownT isoiec_9798_3_7_1_A_1))+  , ((isoiec_9798_3_7_1_T, ''B''), (KnownT isoiec_9798_3_7_1_T_2))+  , ((isoiec_9798_3_7_2_A, ''B''), (KnownT isoiec_9798_3_7_2_A_1))+  , ((isoiec_9798_3_7_2_T, ''B''), (KnownT isoiec_9798_3_7_2_T_2))+  , ((isoiec_9798_3_4_B, ''RA''), (KnownT isoiec_9798_3_4_B_2))+  , ((isoiec_9798_3_5_B, ''RA''), (KnownT isoiec_9798_3_5_B_1))+  , ((isoiec_9798_3_4_A, ''RB''), (KnownT isoiec_9798_3_4_A_1))+  , ((isoiec_9798_3_5_A, ''RB''), (KnownT isoiec_9798_3_5_A_2))+  , ((isoiec_9798_3_2_B, ''Ra''), (KnownT isoiec_9798_3_2_B_2))+  , ((isoiec_9798_3_6_1_B, ''Ra''), (KnownT isoiec_9798_3_6_1_B_1))+  , ((isoiec_9798_3_6_2_B, ''Ra''), (KnownT isoiec_9798_3_6_2_B_1))+  , ((isoiec_9798_3_7_1_B, ''Ra''), (KnownT isoiec_9798_3_7_1_B_4))+  , ((isoiec_9798_3_7_2_B, ''Ra''), (KnownT isoiec_9798_3_7_2_B_4))+  , ((isoiec_9798_3_2_A, ''Rb''), (KnownT isoiec_9798_3_2_A_1))+  , ((isoiec_9798_3_6_1_A, ''Rb''), (KnownT isoiec_9798_3_6_1_A_2))+  , ((isoiec_9798_3_6_1_T, ''Rb''), (KnownT isoiec_9798_3_6_1_T_3))+  , ((isoiec_9798_3_6_2_A, ''Rb''), (KnownT isoiec_9798_3_6_2_A_2))+  , ((isoiec_9798_3_6_2_T, ''Rb''), (KnownT isoiec_9798_3_6_2_T_3))+  , ((isoiec_9798_3_7_1_A, ''Rb''), (KnownT isoiec_9798_3_7_1_A_1))+  , ((isoiec_9798_3_7_1_T, ''Rb''), (KnownT isoiec_9798_3_7_1_T_2))+  , ((isoiec_9798_3_7_2_A, ''Rb''), (KnownT isoiec_9798_3_7_2_A_1))+  , ((isoiec_9798_3_7_2_T, ''Rb''), (KnownT isoiec_9798_3_7_2_T_2))+  , ((isoiec_9798_3_6_1_T, ''Rpa''), (KnownT isoiec_9798_3_6_1_T_3))+  , ((isoiec_9798_3_6_2_B, ''Rpa''), (KnownT isoiec_9798_3_6_2_B_5))+  , ((isoiec_9798_3_6_2_T, ''Rpa''), (KnownT isoiec_9798_3_6_2_T_3))+  , ((isoiec_9798_3_7_1_B, ''Rpa''), (KnownT isoiec_9798_3_7_1_B_4))+  , ((isoiec_9798_3_7_1_T, ''Rpa''), (KnownT isoiec_9798_3_7_1_T_2))+  , ((isoiec_9798_3_7_2_B, ''Rpa''), (KnownT isoiec_9798_3_7_2_B_4))+  , ((isoiec_9798_3_7_2_T, ''Rpa''), (KnownT isoiec_9798_3_7_2_T_2))+  , ((isoiec_9798_3_6_1_B, ''T''), (KnownT isoiec_9798_3_6_1_B_5))+  , ((isoiec_9798_3_6_2_B, ''T''), (KnownT isoiec_9798_3_6_2_B_5))+  , ((isoiec_9798_3_7_1_B, ''T''), (KnownT isoiec_9798_3_7_1_B_4))+  , ((isoiec_9798_3_7_2_B, ''T''), (KnownT isoiec_9798_3_7_2_B_4))+  , ((isoiec_9798_3_1_B, ''TNA''), (KnownT isoiec_9798_3_1_B_1))+  , ((isoiec_9798_3_3_B, ''TNA''), (KnownT isoiec_9798_3_3_B_1))+  , ((isoiec_9798_3_3_A, ''TNB''), (KnownT isoiec_9798_3_3_A_2))+  , ((isoiec_9798_3_1_A, ''Text1''), (KnownT isoiec_9798_3_1_A_text_1))+  , ((isoiec_9798_3_1_B, ''Text1''), (KnownT isoiec_9798_3_1_B_1))+  , ((isoiec_9798_3_2_A, ''Text1''), (KnownT isoiec_9798_3_2_A_1))+  , ((isoiec_9798_3_2_B, ''Text1''), (KnownT isoiec_9798_3_2_B_text_1))+  , ((isoiec_9798_3_3_A, ''Text1''), (KnownT isoiec_9798_3_3_A_text_1))+  , ((isoiec_9798_3_3_B, ''Text1''), (KnownT isoiec_9798_3_3_B_1))+  , ((isoiec_9798_3_4_A, ''Text1''), (KnownT isoiec_9798_3_4_A_1))+  , ((isoiec_9798_3_4_B, ''Text1''), (KnownT isoiec_9798_3_4_B_text_1))+  , ((isoiec_9798_3_5_A, ''Text1''), (KnownT isoiec_9798_3_5_A_text_1))+  , ((isoiec_9798_3_5_B, ''Text1''), (KnownT isoiec_9798_3_5_B_1))+  , ((isoiec_9798_3_6_1_A, ''Text1''), (KnownT isoiec_9798_3_6_1_A_text_1))+  , ((isoiec_9798_3_6_1_B, ''Text1''), (KnownT isoiec_9798_3_6_1_B_1))+  , ((isoiec_9798_3_6_2_A, ''Text1''), (KnownT isoiec_9798_3_6_2_A_text_1))+  , ((isoiec_9798_3_6_2_B, ''Text1''), (KnownT isoiec_9798_3_6_2_B_1))+  , ((isoiec_9798_3_7_1_A, ''Text1''), (KnownT isoiec_9798_3_7_1_A_1))+  , ((isoiec_9798_3_7_1_B, ''Text1''), (KnownT isoiec_9798_3_7_1_B_text_1))+  , ((isoiec_9798_3_7_2_A, ''Text1''), (KnownT isoiec_9798_3_7_2_A_1))+  , ((isoiec_9798_3_7_2_B, ''Text1''), (KnownT isoiec_9798_3_7_2_B_text_1))+  , ((isoiec_9798_3_1_A, ''Text2''), (KnownT isoiec_9798_3_1_A_text_1))+  , ((isoiec_9798_3_1_B, ''Text2''), (KnownT isoiec_9798_3_1_B_1))+  , ((isoiec_9798_3_2_A, ''Text2''), (KnownT isoiec_9798_3_2_A_text_2))+  , ((isoiec_9798_3_2_B, ''Text2''), (KnownT isoiec_9798_3_2_B_2))+  , ((isoiec_9798_3_3_A, ''Text2''), (KnownT isoiec_9798_3_3_A_text_1))+  , ((isoiec_9798_3_3_B, ''Text2''), (KnownT isoiec_9798_3_3_B_1))+  , ((isoiec_9798_3_4_A, ''Text2''), (KnownT isoiec_9798_3_4_A_text_2))+  , ((isoiec_9798_3_4_B, ''Text2''), (KnownT isoiec_9798_3_4_B_2))+  , ((isoiec_9798_3_5_A, ''Text2''), (KnownT isoiec_9798_3_5_A_2))+  , ((isoiec_9798_3_5_B, ''Text2''), (KnownT isoiec_9798_3_5_B_text_2))+  , ((isoiec_9798_3_6_1_A, ''Text2''),+     (KnownT isoiec_9798_3_6_1_A_check_4_in))+  , ((isoiec_9798_3_6_1_B, ''Text2''), (KnownT isoiec_9798_3_6_1_B_text_2))+  , ((isoiec_9798_3_6_2_A, ''Text2''),+     (KnownT isoiec_9798_3_6_2_A_check_4_in))+  , ((isoiec_9798_3_6_2_B, ''Text2''), (KnownT isoiec_9798_3_6_2_B_text_2))+  , ((isoiec_9798_3_7_1_A, ''Text2''), (KnownT isoiec_9798_3_7_1_A_text_2))+  , ((isoiec_9798_3_7_1_T, ''Text2''), (KnownT isoiec_9798_3_7_1_T_2))+  , ((isoiec_9798_3_7_2_A, ''Text2''), (KnownT isoiec_9798_3_7_2_A_text_2))+  , ((isoiec_9798_3_7_2_T, ''Text2''), (KnownT isoiec_9798_3_7_2_T_2))+  , ((isoiec_9798_3_2_A, ''Text3''), (KnownT isoiec_9798_3_2_A_text_2))+  , ((isoiec_9798_3_2_B, ''Text3''), (KnownT isoiec_9798_3_2_B_2))+  , ((isoiec_9798_3_3_A, ''Text3''), (KnownT isoiec_9798_3_3_A_2))+  , ((isoiec_9798_3_3_B, ''Text3''), (KnownT isoiec_9798_3_3_B_text_2))+  , ((isoiec_9798_3_4_A, ''Text3''), (KnownT isoiec_9798_3_4_A_text_2))+  , ((isoiec_9798_3_4_B, ''Text3''), (KnownT isoiec_9798_3_4_B_2))+  , ((isoiec_9798_3_5_A, ''Text3''), (KnownT isoiec_9798_3_5_A_text_4))+  , ((isoiec_9798_3_5_B, ''Text3''), (KnownT isoiec_9798_3_5_B_4))+  , ((isoiec_9798_3_6_1_A, ''Text3''), (KnownT isoiec_9798_3_6_1_A_2))+  , ((isoiec_9798_3_6_1_B, ''Text3''), (KnownT isoiec_9798_3_6_1_B_text_2))+  , ((isoiec_9798_3_6_2_A, ''Text3''), (KnownT isoiec_9798_3_6_2_A_2))+  , ((isoiec_9798_3_6_2_B, ''Text3''), (KnownT isoiec_9798_3_6_2_B_text_2))+  , ((isoiec_9798_3_7_1_B, ''Text3''), (KnownT isoiec_9798_3_7_1_B_4))+  , ((isoiec_9798_3_7_1_T, ''Text3''), (KnownT isoiec_9798_3_7_1_T_text_3))+  , ((isoiec_9798_3_7_2_A, ''Text3''),+     (KnownT isoiec_9798_3_7_2_A_check_3_in))+  , ((isoiec_9798_3_7_2_B, ''Text3''), (KnownT isoiec_9798_3_7_2_B_4))+  , ((isoiec_9798_3_7_2_T, ''Text3''), (KnownT isoiec_9798_3_7_2_T_text_3))+  , ((isoiec_9798_3_3_A, ''Text4''), (KnownT isoiec_9798_3_3_A_2))+  , ((isoiec_9798_3_3_B, ''Text4''), (KnownT isoiec_9798_3_3_B_text_2))+  , ((isoiec_9798_3_4_A, ''Text4''), (KnownT isoiec_9798_3_4_A_3))+  , ((isoiec_9798_3_4_B, ''Text4''), (KnownT isoiec_9798_3_4_B_text_3))+  , ((isoiec_9798_3_5_A, ''Text4''), (KnownT isoiec_9798_3_5_A_text_4))+  , ((isoiec_9798_3_5_B, ''Text4''), (KnownT isoiec_9798_3_5_B_4))+  , ((isoiec_9798_3_6_1_A, ''Text4''), (KnownT isoiec_9798_3_6_1_A_text_3))+  , ((isoiec_9798_3_6_1_T, ''Text4''), (KnownT isoiec_9798_3_6_1_T_3))+  , ((isoiec_9798_3_6_2_A, ''Text4''), (KnownT isoiec_9798_3_6_2_A_text_3))+  , ((isoiec_9798_3_6_2_T, ''Text4''), (KnownT isoiec_9798_3_6_2_T_3))+  , ((isoiec_9798_3_7_1_A, ''Text4''), (KnownT isoiec_9798_3_7_1_A_3))+  , ((isoiec_9798_3_7_1_T, ''Text4''), (KnownT isoiec_9798_3_7_1_T_text_3))+  , ((isoiec_9798_3_4_A, ''Text5''), (KnownT isoiec_9798_3_4_A_3))+  , ((isoiec_9798_3_4_B, ''Text5''), (KnownT isoiec_9798_3_4_B_text_3))+  , ((isoiec_9798_3_5_A, ''Text5''), (KnownT isoiec_9798_3_5_A_3))+  , ((isoiec_9798_3_5_B, ''Text5''), (KnownT isoiec_9798_3_5_B_text_3))+  , ((isoiec_9798_3_6_1_B, ''Text5''), (KnownT isoiec_9798_3_6_1_B_5))+  , ((isoiec_9798_3_6_1_T, ''Text5''), (KnownT isoiec_9798_3_6_1_T_text_4))+  , ((isoiec_9798_3_6_2_A, ''Text5''),+     (KnownT isoiec_9798_3_6_2_A_check_4_in))+  , ((isoiec_9798_3_6_2_B, ''Text5''), (KnownT isoiec_9798_3_6_2_B_5))+  , ((isoiec_9798_3_6_2_T, ''Text5''), (KnownT isoiec_9798_3_6_2_T_text_4))+  , ((isoiec_9798_3_7_1_A, ''Text5''), (KnownT isoiec_9798_3_7_1_A_3))+  , ((isoiec_9798_3_7_1_T, ''Text5''), (KnownT isoiec_9798_3_7_1_T_text_3))+  , ((isoiec_9798_3_7_2_A, ''Text5''), (KnownT isoiec_9798_3_7_2_A_3))+  , ((isoiec_9798_3_7_2_T, ''Text5''), (KnownT isoiec_9798_3_7_2_T_text_3))+  , ((isoiec_9798_3_5_A, ''Text6''), (KnownT isoiec_9798_3_5_A_3))+  , ((isoiec_9798_3_5_B, ''Text6''), (KnownT isoiec_9798_3_5_B_text_3))+  , ((isoiec_9798_3_6_1_A, ''Text6''), (KnownT isoiec_9798_3_6_1_A_4))+  , ((isoiec_9798_3_6_1_T, ''Text6''), (KnownT isoiec_9798_3_6_1_T_text_4))+  , ((isoiec_9798_3_7_1_A, ''Text6''), (KnownT isoiec_9798_3_7_1_A_text_4))+  , ((isoiec_9798_3_7_1_B, ''Text6''), (KnownT isoiec_9798_3_7_1_B_4))+  , ((isoiec_9798_3_7_2_A, ''Text6''), (KnownT isoiec_9798_3_7_2_A_text_4))+  , ((isoiec_9798_3_7_2_B, ''Text6''), (KnownT isoiec_9798_3_7_2_B_4))+  , ((isoiec_9798_3_6_1_A, ''Text7''), (KnownT isoiec_9798_3_6_1_A_4))+  , ((isoiec_9798_3_6_1_T, ''Text7''), (KnownT isoiec_9798_3_6_1_T_text_4))+  , ((isoiec_9798_3_6_2_A, ''Text7''), (KnownT isoiec_9798_3_6_2_A_4))+  , ((isoiec_9798_3_6_2_T, ''Text7''), (KnownT isoiec_9798_3_6_2_T_text_4))+  , ((isoiec_9798_3_7_1_A, ''Text7''), (KnownT isoiec_9798_3_7_1_A_text_4))+  , ((isoiec_9798_3_7_2_A, ''Text7''), (KnownT isoiec_9798_3_7_2_A_text_4))+  , ((isoiec_9798_3_6_1_A, ''Text8''), (KnownT isoiec_9798_3_6_1_A_text_5))+  , ((isoiec_9798_3_6_1_B, ''Text8''), (KnownT isoiec_9798_3_6_1_B_5))+  , ((isoiec_9798_3_6_2_A, ''Text8''), (KnownT isoiec_9798_3_6_2_A_text_5))+  , ((isoiec_9798_3_6_2_B, ''Text8''), (KnownT isoiec_9798_3_6_2_B_5))+  , ((isoiec_9798_3_7_1_A, ''Text8''), (KnownT isoiec_9798_3_7_1_A_5))+  , ((isoiec_9798_3_7_1_B, ''Text8''), (KnownT isoiec_9798_3_7_1_B_text_5))+  , ((isoiec_9798_3_7_2_A, ''Text8''), (KnownT isoiec_9798_3_7_2_A_5))+  , ((isoiec_9798_3_7_2_B, ''Text8''), (KnownT isoiec_9798_3_7_2_B_text_5))+  , ((isoiec_9798_3_6_1_A, ''Text9''), (KnownT isoiec_9798_3_6_1_A_text_5))+  , ((isoiec_9798_3_6_1_B, ''Text9''), (KnownT isoiec_9798_3_6_1_B_5))+  , ((isoiec_9798_3_6_2_A, ''Text9''), (KnownT isoiec_9798_3_6_2_A_text_5))+  , ((isoiec_9798_3_6_2_B, ''Text9''), (KnownT isoiec_9798_3_6_2_B_5))+  , ((isoiec_9798_3_7_1_A, ''Text9''), (KnownT isoiec_9798_3_7_1_A_5))+  , ((isoiec_9798_3_7_1_B, ''Text9''), (KnownT isoiec_9798_3_7_1_B_4))+  , ((isoiec_9798_3_7_2_A, ''Text9''), (KnownT isoiec_9798_3_7_2_A_5))+  , ((isoiec_9798_3_7_2_B, ''Text9''), (KnownT isoiec_9798_3_7_2_B_4))+  , ((isoiec_9798_3_6_1_A, ''TokenBA''), (KnownT isoiec_9798_3_6_1_A_2))+  , ((isoiec_9798_3_6_2_A, ''TokenBA''), (KnownT isoiec_9798_3_6_2_A_2))+  , ((isoiec_9798_3_6_2_A, ''TokenTA''), (KnownT isoiec_9798_3_6_2_A_4))+  , ((isoiec_9798_3_7_2_A, ''TokenTA''), (KnownT isoiec_9798_3_7_2_A_3))+  , ((isoiec_9798_3_6_1_A, ''TokenTA_for_B''),+     (KnownT isoiec_9798_3_6_1_A_4))+  , ((isoiec_9798_3_7_1_A, ''TokenTA_for_B''),+     (KnownT isoiec_9798_3_7_1_A_3))+  , ((isoiec_9798_3_6_1_B, ''pkA''), (KnownT isoiec_9798_3_6_1_B_5))+  , ((isoiec_9798_3_6_2_A, ''pkA''),+     (KnownT isoiec_9798_3_6_2_A_check_4_in))+  , ((isoiec_9798_3_6_2_B, ''pkA''), (KnownT isoiec_9798_3_6_2_B_5))+  , ((isoiec_9798_3_7_1_B, ''pkA''), (KnownT isoiec_9798_3_7_1_B_4))+  , ((isoiec_9798_3_7_2_A, ''pkA''),+     (KnownT isoiec_9798_3_7_2_A_check_3_in))+  , ((isoiec_9798_3_7_2_B, ''pkA''), (KnownT isoiec_9798_3_7_2_B_4))+  , ((isoiec_9798_3_6_1_A, ''pkB''), (KnownT isoiec_9798_3_6_1_A_4))+  , ((isoiec_9798_3_6_2_A, ''pkB''), (KnownT isoiec_9798_3_6_2_A_4))+  , ((isoiec_9798_3_6_2_B, ''pkB''), (KnownT isoiec_9798_3_6_2_B_5))+  , ((isoiec_9798_3_7_1_A, ''pkB''), (KnownT isoiec_9798_3_7_1_A_3))+  , ((isoiec_9798_3_7_2_A, ''pkB''), (KnownT isoiec_9798_3_7_2_A_3))+  , ((isoiec_9798_3_7_2_B, ''pkB''), (KnownT isoiec_9798_3_7_2_B_4))+  ]"++sublocale isoiec_9798_3_state < isoiec_9798_3_composed_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_3_composed_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_3_composed_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_3_1_A_text_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_1_A_text_1_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_1_B_1_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_1_B_1_TNA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_1_B_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_1_B_1_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_2_A_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_2_A_1_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_2_A_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_2_A_text_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_2_A_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_2_B_2_Ra t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_2_B_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_2_B_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_3_A_text_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_3_A_text_1_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_3_A_2_TNB t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_3_A_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_3_A_2_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_3_B_1_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_3_B_1_TNA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_3_B_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_3_B_1_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_3_B_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_3_B_text_2_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_4_A_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_4_A_1_RB t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_4_A_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_4_A_text_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_4_A_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_4_A_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_4_A_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_4_B_2_RA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_4_B_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_4_B_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_4_B_text_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_4_B_text_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_A_2_RB t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_A_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_A_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_A_3_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_A_text_4_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_A_text_4_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_B_1_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_B_1_RA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_B_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_B_text_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_B_text_3_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_B_4_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_B_4_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_A_2_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_A_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_A_2_TokenBA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_A_4_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_A_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_A_4_TokenTA_for_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_A_4_pkB t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_A_check_4_in_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''check_4'',+               {| LC ''isoiec_9798_3_6_opt_1_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,+                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+               |},+               Enc {| LC ''isoiec_9798_3_6_opt_1_sig_2'', s(AV ''B'' tid0),+                      LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+                   |}+                   ( inv(s(MV ''pkB'' tid0)) )+            |}+            ( LN ''check_nonce_4'' tid0 ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_3_6_1_A_text_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_A_text_5_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_B_1_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_B_1_Ra t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_B_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_B_text_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_B_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_B_5_T t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_B_5_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_B_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_B_5_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_B_5_pkA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_T_3_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_T_3_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_T_3_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_T_3_Rpa t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_T_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_T_text_4_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_T_text_4_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_T_text_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_A_2_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_A_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_A_2_TokenBA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_A_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_A_4_TokenTA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_A_4_pkB t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_A_check_4_in_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''check_4'',+               {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,+                     s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                     s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                  |},+                  Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,+                         s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                         s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                      |}+                      ( SK ( s(AV ''T'' tid0) ) )+               |},+               {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,+                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+               |},+               Enc {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0),+                      LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+                   |}+                   ( inv(s(MV ''pkB'' tid0)) )+            |}+            ( LN ''check_nonce_4'' tid0 ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_3_6_2_A_check_4_in_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''check_4'',+               {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,+                     s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                     s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                  |},+                  Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,+                         s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                         s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                      |}+                      ( SK ( s(AV ''T'' tid0) ) )+               |},+               {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,+                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+               |},+               Enc {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0),+                      LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+                   |}+                   ( inv(s(MV ''pkB'' tid0)) )+            |}+            ( LN ''check_nonce_4'' tid0 ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_3_6_2_A_check_4_in_pkA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''check_4'',+               {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,+                     s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                     s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                  |},+                  Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,+                         s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                         s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                      |}+                      ( SK ( s(AV ''T'' tid0) ) )+               |},+               {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,+                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+               |},+               Enc {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0),+                      LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+                   |}+                   ( inv(s(MV ''pkB'' tid0)) )+            |}+            ( LN ''check_nonce_4'' tid0 ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_3_6_2_A_text_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_A_text_5_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_B_1_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_B_1_Ra t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_B_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_B_text_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_B_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_B_5_Rpa t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_B_5_T t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_B_5_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_B_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_B_5_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_B_5_pkA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_B_5_pkB t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_T_3_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_T_3_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_T_3_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_T_3_Rpa t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_T_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_T_text_4_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_T_text_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_A_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_A_1_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_A_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_A_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_A_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_A_3_TokenTA_for_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_A_3_pkB t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_A_text_4_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_A_text_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_A_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_A_5_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_B_4_Ra t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_B_4_Rpa t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_B_4_T t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_B_4_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_B_4_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_B_4_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_B_4_pkA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_B_text_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_T_2_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_T_2_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_T_2_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_T_2_Rpa t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_T_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_T_text_3_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_T_text_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_T_text_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_A_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_A_1_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_A_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_A_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_A_3_TokenTA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_A_3_pkB t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_A_check_3_in_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''check_4'',+               {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,+                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                  s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+               |},+               Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,+                      s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                      s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+                   |}+                   ( SK ( s(AV ''T'' tid0) ) )+            |}+            ( LN ''check_nonce_4'' tid0 ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_3_7_2_A_check_3_in_pkA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''check_4'',+               {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,+                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                  s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+               |},+               Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,+                      s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                      s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+                   |}+                   ( SK ( s(AV ''T'' tid0) ) )+            |}+            ( LN ''check_nonce_4'' tid0 ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_3_7_2_A_text_4_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_A_text_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_A_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_A_5_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_B_4_Ra t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_B_4_Rpa t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_B_4_T t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_B_4_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_B_4_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_B_4_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_B_4_pkA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_B_4_pkB t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_B_text_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_T_2_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_T_2_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_T_2_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_T_2_Rpa t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_T_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_T_text_3_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_T_text_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_composed_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_3_composed_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_3_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_1_B_non_injective_agreement:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_3_1_B"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_3_1_B_1 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_3_1_A &+        ( tid1, isoiec_9798_3_1_A_1 ) : steps t &+        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,+           s(MV ''Text1'' tid1)+        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),+                s(MV ''Text1'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_3_1_sig_1'', s(MV ''TNA'' tid0),+                          s(AV ''B'' tid0), s(MV ''Text1'' tid0)+                       |}+                       ( SK ( s(MV ''A'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_3_1_A_1_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_2_B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_2_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_2_B_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_2_A &+          ( tid1, isoiec_9798_3_2_A_2 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),+             s(MV ''Text2'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),+                  LN ''Rb'' tid0, s(MV ''Text2'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_2_sig_2'', s(MV ''Ra'' tid0), LN ''Rb'' tid0,+                              s(AV ''B'' tid0), s(MV ''Text2'' tid0)+                           |}+                           ( SK ( s(AV ''A'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_2_A_2_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_3_A_non_injective_agreement:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_3_3_A"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_3_3_A_2 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_3_3_B &+        ( tid1, isoiec_9798_3_3_B_2 ) : steps t &+        {| s(MV ''A'' tid1), s(AV ''B'' tid1), LN ''TNB'' tid1,+           s(MV ''Text3'' tid1)+        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNB'' tid0),+                s(MV ''Text3'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_3_3_sig_2'', s(MV ''TNB'' tid0),+                          s(AV ''A'' tid0), s(MV ''Text3'' tid0)+                       |}+                       ( SK ( s(AV ''B'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_3_3_B_2_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_3_B_non_injective_agreement:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_3_3_B"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_3_3_B_1 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_3_3_A &+        ( tid1, isoiec_9798_3_3_A_1 ) : steps t &+        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,+           s(MV ''Text1'' tid1)+        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),+                s(MV ''Text1'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_3_3_sig_1'', s(MV ''TNA'' tid0),+                          s(AV ''B'' tid0), s(MV ''Text1'' tid0)+                       |}+                       ( SK ( s(MV ''A'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_3_3_A_1_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_4_A_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_4_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_4_A_3 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_4_B &+          ( tid1, isoiec_9798_3_4_B_3 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''RA'' tid1), LN ''RB'' tid1,+             s(MV ''Text2'' tid1), s(MV ''Text4'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''RA'' tid0,+                  s(MV ''RB'' tid0), s(MV ''Text2'' tid0), s(MV ''Text4'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_4_sig_2'', s(MV ''RB'' tid0), LN ''RA'' tid0,+                              s(AV ''A'' tid0), s(MV ''Text4'' tid0)+                           |}+                           ( SK ( s(MV ''B'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_4_B_3_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_3_4_sig_1'', LN ''RA'' tid0, LN ''RB'' tid1,+                                s(AV ''B'' tid1), s(MV ''Text2'' tid1)+                             |}+                             ( SK ( s(AV ''A'' tid0) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_3_4_A_2_enc tid2) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_4_B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_4_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_4_B_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_4_A &+          ( tid1, isoiec_9798_3_4_A_2 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''RA'' tid1, s(MV ''RB'' tid1),+             s(MV ''Text2'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''RA'' tid0),+                  LN ''RB'' tid0, s(MV ''Text2'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_4_sig_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,+                              s(AV ''B'' tid0), s(MV ''Text2'' tid0)+                           |}+                           ( SK ( s(AV ''A'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_4_A_2_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_5_A_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_5_A &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_5_A_3 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_5_B &+          ( tid1, isoiec_9798_3_5_B_3 ) : steps t &+          {| s(MV ''A'' tid1), s(AV ''B'' tid1), s(MV ''RA'' tid1), LN ''RB'' tid1,+             s(MV ''Text5'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''RA'' tid0,+                  s(MV ''RB'' tid0), s(MV ''Text5'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_5_sig_1'', s(MV ''RB'' tid0), LN ''RA'' tid0,+                              s(AV ''A'' tid0), s(MV ''Text5'' tid0)+                           |}+                           ( SK ( s(AV ''B'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_5_B_3_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_5_B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_5_B &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(MV ''A'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_5_B_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_5_A &+          ( tid1, isoiec_9798_3_5_A_4 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''RA'' tid1, s(MV ''RB'' tid1),+             s(MV ''Text3'' tid1), s(MV ''Text5'' tid1)+          |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''RA'' tid0),+                  LN ''RB'' tid0, s(MV ''Text3'' tid0), s(MV ''Text5'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_5_sig_2'', s(MV ''RA'' tid0), LN ''RB'' tid0,+                              s(AV ''B'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( SK ( s(MV ''A'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_5_A_4_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_3_5_sig_1'', LN ''RB'' tid0, LN ''RA'' tid1,+                                s(AV ''A'' tid1), s(MV ''Text5'' tid1)+                             |}+                             ( SK ( s(AV ''B'' tid0) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_3_5_B_3_enc tid2) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_6_1_A_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_6_1_A &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(AV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_6_1_A_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_6_1_B &+          ( tid1, isoiec_9798_3_6_1_B_2 ) : steps t &+          {| s(MV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,+             s(MV ''Text2'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''Ra'' tid0,+                  s(MV ''Rb'' tid0), s(MV ''Text2'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''check_4'',+                              {| LC ''isoiec_9798_3_6_opt_1_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,+                                 s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+                              |},+                              Enc {| LC ''isoiec_9798_3_6_opt_1_sig_2'', s(AV ''B'' tid0),+                                     LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+                                  |}+                                  ( inv(s(MV ''pkB'' tid0)) )+                           |}+                           ( LN ''check_nonce_4'' tid0 ) ")+        case fake note_unified facts = this facts+        thus ?thesis proof(sources! " LN ''check_nonce_4'' tid0 ")+        qed (insert facts, fastforce+)?+      next+        case (isoiec_9798_3_6_1_A_check_4_out_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_3_6_opt_1_sig_2'', s(AV ''B'' tid0),+                                LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+                             |}+                             ( inv(s(MV ''pkB'' tid0)) ) ")+          case fake note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_3_6_opt_1_sig_4_1'', LN ''Rpa'' tid0,+                                  s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text6'' tid0)+                               |}+                               ( SK ( s(AV ''T'' tid0) ) ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest!: ltk_secrecy)+          next+            case (isoiec_9798_3_6_1_T_4_enc tid1) note_unified facts = this facts+            thus ?thesis by (fastforce dest!: ltk_secrecy)+          qed (insert facts, fastforce+)?+        next+          case (isoiec_9798_3_6_1_B_2_enc tid1) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_6_1_B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_6_1_B &+          RLKR(s(MV ''A'' tid0)) ~: reveals t &+          RLKR(s(MV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_6_1_B_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_6_1_A &+          ( tid1, isoiec_9798_3_6_1_A_5 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),+             s(MV ''Text8'' tid1)+          |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),+                  LN ''Rb'' tid0, s(MV ''Text8'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_6_opt_1_sig_4_2'', LN ''Rb'' tid0,+                              s(MV ''A'' tid0), s(MV ''pkA'' tid0), s(MV ''Text5'' tid0)+                           |}+                           ( SK ( s(MV ''T'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_6_1_T_4_enc_1 tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_3_6_opt_1_sig_5'', LN ''Rb'' tid0,+                                s(MV ''Ra'' tid0), s(AV ''B'' tid0), s(MV ''A'' tid0),+                                s(MV ''Text8'' tid0)+                             |}+                             ( SK ( s(MV ''A'' tid0) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_3_6_1_A_5_enc tid2) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_6_1_A_injective_agreement_T:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_6_1_A &+          RLKR(s(AV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_6_1_A_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_6_1_T &+          ( tid1, isoiec_9798_3_6_1_T_4 ) : steps t &+          {| s(MV ''B'' tid1), s(AV ''T'' tid1), s(MV ''Rpa'' tid1),+             PK ( s(MV ''B'' tid1) ), s(MV ''Text6'' tid1)+          |} = {| s(AV ''B'' tid0), s(AV ''T'' tid0), LN ''Rpa'' tid0,+                  s(MV ''pkB'' tid0), s(MV ''Text6'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_6_opt_1_sig_4_1'', LN ''Rpa'' tid0,+                              s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text6'' tid0)+                           |}+                           ( SK ( s(AV ''T'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_6_1_T_4_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_6_1_B_injective_agreement_T:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_6_1_B &+          RLKR(s(MV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_6_1_B_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_6_1_T &+          ( tid1, isoiec_9798_3_6_1_T_4 ) : steps t &+          {| s(MV ''A'' tid1), s(AV ''T'' tid1), s(MV ''Rb'' tid1),+             PK ( s(MV ''A'' tid1) ), s(MV ''Text5'' tid1)+          |} = {| s(MV ''A'' tid0), s(MV ''T'' tid0), LN ''Rb'' tid0,+                  s(MV ''pkA'' tid0), s(MV ''Text5'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_6_opt_1_sig_4_2'', LN ''Rb'' tid0,+                              s(MV ''A'' tid0), s(MV ''pkA'' tid0), s(MV ''Text5'' tid0)+                           |}+                           ( SK ( s(MV ''T'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_6_1_T_4_enc_1 tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_6_2_A_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_6_2_A &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(AV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_6_2_A_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_6_2_B &+          ( tid1, isoiec_9798_3_6_2_B_2 ) : steps t &+          {| s(MV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,+             s(MV ''Text2'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''Ra'' tid0,+                  s(MV ''Rb'' tid0), s(MV ''Text2'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''check_4'',+                              {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,+                                    s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                                    s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                                 |},+                                 Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,+                                        s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                                        s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                                     |}+                                     ( SK ( s(AV ''T'' tid0) ) )+                              |},+                              {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,+                                 s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+                              |},+                              Enc {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0),+                                     LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+                                  |}+                                  ( inv(s(MV ''pkB'' tid0)) )+                           |}+                           ( LN ''check_nonce_4'' tid0 ) ")+        case fake note_unified facts = this facts+        thus ?thesis proof(sources! " LN ''check_nonce_4'' tid0 ")+        qed (insert facts, fastforce+)?+      next+        case (isoiec_9798_3_6_2_A_check_4_out_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0),+                                LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+                             |}+                             ( inv(s(MV ''pkB'' tid0)) ) ")+          case fake note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,+                                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                                  s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                               |}+                               ( SK ( s(AV ''T'' tid0) ) ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest!: ltk_secrecy)+          next+            case (isoiec_9798_3_6_2_T_4_enc tid1) note_unified facts = this facts+            thus ?thesis by (fastforce dest!: ltk_secrecy)+          qed (insert facts, fastforce+)?+        next+          case (isoiec_9798_3_6_2_B_2_enc tid1) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_6_2_B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_6_2_B &+          RLKR(s(MV ''A'' tid0)) ~: reveals t &+          RLKR(s(MV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_6_2_B_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_6_2_A &+          ( tid1, isoiec_9798_3_6_2_A_5 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),+             s(MV ''Text8'' tid1)+          |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),+                  LN ''Rb'' tid0, s(MV ''Text8'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', s(MV ''Rpa'' tid0),+                              LN ''Rb'' tid0, s(MV ''A'' tid0), s(MV ''pkA'' tid0), s(AV ''B'' tid0),+                              s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                           |}+                           ( SK ( s(MV ''T'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_6_2_T_4_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_3_6_opt_2_sig_5'', LN ''Rb'' tid0,+                                s(MV ''Ra'' tid0), s(AV ''B'' tid0), s(MV ''A'' tid0),+                                s(MV ''Text8'' tid0)+                             |}+                             ( SK ( s(MV ''A'' tid0) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_3_6_2_A_5_enc tid2) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_6_2_A_injective_agreement_T:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_6_2_A &+          RLKR(s(AV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_6_2_A_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_6_2_T &+          ( tid1, isoiec_9798_3_6_2_T_4 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''T'' tid1),+             s(MV ''Rpa'' tid1), s(MV ''Rb'' tid1), PK ( s(MV ''A'' tid1) ),+             PK ( s(MV ''B'' tid1) ), s(MV ''Text5'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''T'' tid0),+                  LN ''Rpa'' tid0, s(MV ''Rb'' tid0), s(MV ''pkA'' tid0),+                  s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''check_4'',+                              {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,+                                    s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                                    s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                                 |},+                                 Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,+                                        s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                                        s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                                     |}+                                     ( SK ( s(AV ''T'' tid0) ) )+                              |},+                              {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,+                                 s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+                              |},+                              Enc {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0),+                                     LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+                                  |}+                                  ( inv(s(MV ''pkB'' tid0)) )+                           |}+                           ( LN ''check_nonce_4'' tid0 ) ")+        case fake note_unified facts = this facts+        thus ?thesis proof(sources! " LN ''check_nonce_4'' tid0 ")+        qed (insert facts, fastforce+)?+      next+        case (isoiec_9798_3_6_2_A_check_4_out_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,+                                s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                                s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                             |}+                             ( SK ( s(AV ''T'' tid0) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_3_6_2_T_4_enc tid1) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_6_2_B_injective_agreement_T:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_6_2_B &+          RLKR(s(MV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_6_2_B_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_6_2_T &+          ( tid1, isoiec_9798_3_6_2_T_4 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''T'' tid1),+             s(MV ''Rpa'' tid1), s(MV ''Rb'' tid1), PK ( s(MV ''A'' tid1) ),+             PK ( s(MV ''B'' tid1) ), s(MV ''Text5'' tid1)+          |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''T'' tid0),+                  s(MV ''Rpa'' tid0), LN ''Rb'' tid0, s(MV ''pkA'' tid0),+                  s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', s(MV ''Rpa'' tid0),+                              LN ''Rb'' tid0, s(MV ''A'' tid0), s(MV ''pkA'' tid0), s(AV ''B'' tid0),+                              s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                           |}+                           ( SK ( s(MV ''T'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_6_2_T_4_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_7_1_A_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_7_1_A &+          RLKR(s(AV ''T'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_7_1_A_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_7_1_B &+          ( tid1, isoiec_9798_3_7_1_B_5 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,+             s(MV ''Text8'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''Ra'' tid0,+                  s(MV ''Rb'' tid0), s(MV ''Text8'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_7_opt_1_sig_3_1'', LN ''Rpa'' tid0,+                              s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text4'' tid0)+                           |}+                           ( SK ( s(AV ''T'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_7_1_T_3_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_3_7_opt_1_sig_5'', LN ''Ra'' tid0,+                                s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),+                                s(MV ''Text8'' tid0)+                             |}+                             ( SK ( s(MV ''B'' tid0) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_3_7_1_B_5_enc tid2) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_7_1_B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_7_1_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(MV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_7_1_B_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_7_1_A &+          ( tid1, isoiec_9798_3_7_1_A_4 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),+             s(MV ''Text6'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),+                  LN ''Rb'' tid0, s(MV ''Text6'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_7_opt_1_sig_3_2'', LN ''Rb'' tid0,+                              s(AV ''A'' tid0), s(MV ''pkA'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( SK ( s(MV ''T'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_7_1_T_3_enc_1 tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_3_7_opt_1_sig_4'', LN ''Rb'' tid0,+                                s(MV ''Ra'' tid0), s(AV ''B'' tid0), s(AV ''A'' tid0),+                                s(MV ''Text6'' tid0)+                             |}+                             ( SK ( s(AV ''A'' tid0) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_3_7_1_A_4_enc tid2) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_7_1_A_injective_agreement_T:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_7_1_A &+          RLKR(s(AV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_7_1_A_3 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_7_1_T &+          ( tid1, isoiec_9798_3_7_1_T_3 ) : steps t &+          {| s(MV ''B'' tid1), s(AV ''T'' tid1), s(MV ''Rpa'' tid1),+             PK ( s(MV ''B'' tid1) ), s(MV ''Text4'' tid1)+          |} = {| s(MV ''B'' tid0), s(AV ''T'' tid0), LN ''Rpa'' tid0,+                  s(MV ''pkB'' tid0), s(MV ''Text4'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_7_opt_1_sig_3_1'', LN ''Rpa'' tid0,+                              s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text4'' tid0)+                           |}+                           ( SK ( s(AV ''T'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_7_1_T_3_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_7_1_B_injective_agreement_T:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_7_1_B &+          RLKR(s(MV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_7_1_B_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_7_1_T &+          ( tid1, isoiec_9798_3_7_1_T_3 ) : steps t &+          {| s(MV ''A'' tid1), s(AV ''T'' tid1), s(MV ''Rb'' tid1),+             PK ( s(MV ''A'' tid1) ), s(MV ''Text3'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''T'' tid0), LN ''Rb'' tid0,+                  s(MV ''pkA'' tid0), s(MV ''Text3'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_7_opt_1_sig_3_2'', LN ''Rb'' tid0,+                              s(AV ''A'' tid0), s(MV ''pkA'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( SK ( s(MV ''T'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_7_1_T_3_enc_1 tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_7_2_A_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_7_2_A &+          RLKR(s(AV ''T'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_7_2_A_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_7_2_B &+          ( tid1, isoiec_9798_3_7_2_B_5 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,+             s(MV ''Text8'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''Ra'' tid0,+                  s(MV ''Rb'' tid0), s(MV ''Text8'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''check_4'',+                              {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,+                                 s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                                 s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+                              |},+                              Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,+                                     s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                                     s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+                                  |}+                                  ( SK ( s(AV ''T'' tid0) ) )+                           |}+                           ( LN ''check_nonce_4'' tid0 ) ")+        case fake note_unified facts = this facts+        thus ?thesis proof(sources! " LN ''check_nonce_4'' tid0 ")+        qed (insert facts, fastforce+)?+      next+        case (isoiec_9798_3_7_2_A_check_3_out_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,+                                s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                                s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+                             |}+                             ( SK ( s(AV ''T'' tid0) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_3_7_2_T_3_enc tid1) note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_3_7_opt_2_sig_5'', LN ''Ra'' tid0,+                                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),+                                  s(MV ''Text8'' tid0)+                               |}+                               ( SK ( s(MV ''B'' tid0) ) ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest!: ltk_secrecy)+          next+            case (isoiec_9798_3_7_2_B_5_enc tid2) note_unified facts = this facts+            thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+          qed (insert facts, fastforce+)?+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_7_2_B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_7_2_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(MV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_7_2_B_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_7_2_A &+          ( tid1, isoiec_9798_3_7_2_A_4 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),+             s(MV ''Text6'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),+                  LN ''Rb'' tid0, s(MV ''Text6'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', s(MV ''Rpa'' tid0),+                              LN ''Rb'' tid0, s(AV ''A'' tid0), s(MV ''pkA'' tid0), s(AV ''B'' tid0),+                              s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( SK ( s(MV ''T'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_7_2_T_3_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_3_7_opt_2_sig_4'', LN ''Rb'' tid0,+                                s(MV ''Ra'' tid0), s(AV ''B'' tid0), s(AV ''A'' tid0),+                                s(MV ''Text6'' tid0)+                             |}+                             ( SK ( s(AV ''A'' tid0) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_3_7_2_A_4_enc tid2) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_7_2_A_injective_agreement_T:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_7_2_A &+          RLKR(s(AV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_7_2_A_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_7_2_T &+          ( tid1, isoiec_9798_3_7_2_T_3 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''T'' tid1),+             s(MV ''Rpa'' tid1), s(MV ''Rb'' tid1), PK ( s(MV ''A'' tid1) ),+             PK ( s(MV ''B'' tid1) ), s(MV ''Text3'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''T'' tid0),+                  LN ''Rpa'' tid0, s(MV ''Rb'' tid0), s(MV ''pkA'' tid0),+                  s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''check_4'',+                              {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,+                                 s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                                 s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+                              |},+                              Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,+                                     s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                                     s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+                                  |}+                                  ( SK ( s(AV ''T'' tid0) ) )+                           |}+                           ( LN ''check_nonce_4'' tid0 ) ")+        case fake note_unified facts = this facts+        thus ?thesis proof(sources! " LN ''check_nonce_4'' tid0 ")+        qed (insert facts, fastforce+)?+      next+        case (isoiec_9798_3_7_2_A_check_3_out_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,+                                s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                                s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+                             |}+                             ( SK ( s(AV ''T'' tid0) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_3_7_2_T_3_enc tid1) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_7_2_B_injective_agreement_T:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_7_2_B &+          RLKR(s(MV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_7_2_B_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_7_2_T &+          ( tid1, isoiec_9798_3_7_2_T_3 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''T'' tid1),+             s(MV ''Rpa'' tid1), s(MV ''Rb'' tid1), PK ( s(MV ''A'' tid1) ),+             PK ( s(MV ''B'' tid1) ), s(MV ''Text3'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''T'' tid0),+                  s(MV ''Rpa'' tid0), LN ''Rb'' tid0, s(MV ''pkA'' tid0),+                  s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', s(MV ''Rpa'' tid0),+                              LN ''Rb'' tid0, s(AV ''A'' tid0), s(MV ''pkA'' tid0), s(AV ''B'' tid0),+                              s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( SK ( s(MV ''T'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_7_2_T_3_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj) qed  end
data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-4-bdkey_cert_auto.thy view
@@ -1,6 +1,6 @@ theory "isoiec-9798-4-bdkey_cert_auto" imports-  "../ESPLogic"+  "ESPLogic" begin  role isoiec_9798_4_1_bdkey_A@@ -214,217 +214,217 @@     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_1_bdkey_A_text_1_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_1_bdkey_B_1_A t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_1_bdkey_B_1_TNA t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_1_bdkey_B_1_Text1 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_1_bdkey_B_1_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_bdkey_A_1_B t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_bdkey_A_1_Rb t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_bdkey_A_1_Text1 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_bdkey_A_text_2_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_bdkey_A_text_2_Text3 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_bdkey_B_2_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_bdkey_B_2_Text3 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_bdkey_A_text_1_Text1 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_bdkey_A_text_1_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_bdkey_A_2_TNb t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_bdkey_A_2_Text3 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_bdkey_A_2_Text4 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_bdkey_B_1_A t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_bdkey_B_1_TNa t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_bdkey_B_1_Text1 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_bdkey_B_1_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_bdkey_B_text_2_Text3 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_bdkey_B_text_2_Text4 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_bdkey_A_1_B t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_bdkey_A_1_Rb t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_bdkey_A_1_Text1 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_bdkey_A_text_2_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_bdkey_A_text_2_Text3 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_bdkey_A_3_Text4 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_bdkey_A_3_Text5 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_bdkey_B_2_Ra t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_bdkey_B_2_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_bdkey_B_2_Text3 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_bdkey_B_text_3_Text4 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_bdkey_B_text_3_Text5 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   qed   thus "isoiec_9798_4_bdkey_composed_typing_state t r s" by unfold_locales auto qed@@ -504,41 +504,61 @@                            s(MV ''Text1'' tid0)                         |} ")     case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)+    thus ?thesis by (fastforce dest!: ltk_secrecy)   next     case (isoiec_9798_4_1_bdkey_A_1_hash tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)? qed -lemma (in restricted_isoiec_9798_4_bdkey_state) isoiec_9798_4_2_bdkey_B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_4_2_bdkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_4_2_bdkey_B_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_4_2_bdkey_A &-        ( tid1, isoiec_9798_4_2_bdkey_A_2 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(MV ''Rb'' tid1),-           s(MV ''Text2'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''Rb'' tid0,-                s(MV ''Text2'' tid0)-             |})"+lemma (in restricted_isoiec_9798_4_bdkey_state) isoiec_9798_4_2_bdkey_B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_4_2_bdkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_4_2_bdkey_B_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_4_2_bdkey_A &+          ( tid1, isoiec_9798_4_2_bdkey_A_2 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(MV ''Rb'' tid1),+             s(MV ''Text2'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''Rb'' tid0,+                  s(MV ''Text2'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs") proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) |},-                           LC ''isoiec_9798_4_2_ccf_2'', LN ''Rb'' tid0, s(AV ''B'' tid0),-                           s(MV ''Text2'' tid0)-                        |} ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_4_2_bdkey_A_2_hash tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) |},+                               LC ''isoiec_9798_4_2_ccf_2'', LN ''Rb'' tid0, s(AV ''B'' tid0),+                               s(MV ''Text2'' tid0)+                            |} ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_4_2_bdkey_A_2_hash tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj) qed  lemma (in restricted_isoiec_9798_4_bdkey_state) isoiec_9798_4_3_bdkey_A_non_injective_agreement:@@ -564,11 +584,11 @@                            s(MV ''Text3'' tid0)                         |} ")     case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)+    thus ?thesis by (fastforce dest!: ltk_secrecy)   next     case (isoiec_9798_4_3_bdkey_B_2_hash tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)? qed  lemma (in restricted_isoiec_9798_4_bdkey_state) isoiec_9798_4_3_bdkey_B_non_injective_agreement:@@ -594,100 +614,140 @@                            s(MV ''Text1'' tid0)                         |} ")     case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)+    thus ?thesis by (fastforce dest!: ltk_secrecy)   next     case (isoiec_9798_4_3_bdkey_A_1_hash tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)? qed -lemma (in restricted_isoiec_9798_4_bdkey_state) isoiec_9798_4_4_bdkey_A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_4_4_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_4_4_bdkey_A_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_4_4_bdkey_B &-        ( tid1, isoiec_9798_4_4_bdkey_B_3 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,-           s(MV ''Text2'' tid1), s(MV ''Text4'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''Ra'' tid0,-                s(MV ''Rb'' tid0), s(MV ''Text2'' tid0), s(MV ''Text4'' tid0)-             |})"+lemma (in restricted_isoiec_9798_4_bdkey_state) isoiec_9798_4_4_bdkey_A_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_4_4_bdkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_4_4_bdkey_A_3 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_4_4_bdkey_B &+          ( tid1, isoiec_9798_4_4_bdkey_B_3 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,+             s(MV ''Text2'' tid1), s(MV ''Text4'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''Ra'' tid0,+                  s(MV ''Rb'' tid0), s(MV ''Text2'' tid0), s(MV ''Text4'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs") proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) ) |},-                           LC ''isoiec_9798_4_4_ccf_3'', s(MV ''Rb'' tid0), LN ''Ra'' tid0,-                           s(MV ''Text4'' tid0)-                        |} ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_4_4_bdkey_B_3_hash tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''A'' tid1) )-               ( s(AV ''B'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts       thus ?thesis proof(sources! "-                       Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid1) ) |},-                               LC ''isoiec_9798_4_4_ccf_2'', LN ''Ra'' tid0, LN ''Rb'' tid1,-                               s(AV ''B'' tid1), s(MV ''Text2'' tid1)+                       Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) ) |},+                               LC ''isoiec_9798_4_4_ccf_3'', s(MV ''Rb'' tid0), LN ''Ra'' tid0,+                               s(MV ''Text4'' tid0)                             |} ")         case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest!: ltk_secrecy)+        thus ?thesis by (fastforce dest!: ltk_secrecy)       next-        case (isoiec_9798_4_4_bdkey_A_2_hash tid2) note_unified facts = this facts-        thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-      qed (insert facts, fastsimp+)?-    next-      case swapped note_unified facts = this facts+        case (isoiec_9798_4_4_bdkey_B_3_hash tid1) note_unified facts = this facts+        hence "Kbd ( s(AV ''A'' tid1) )+                   ( s(AV ''B'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) )"+          by simp note facts = this facts+        thus ?thesis proof(cases rule: Kbd_cases)+          case noswap note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid1) ) |},+                                   LC ''isoiec_9798_4_4_ccf_2'', LN ''Ra'' tid0, LN ''Rb'' tid1,+                                   s(AV ''B'' tid1), s(MV ''Text2'' tid1)+                                |} ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest!: ltk_secrecy)+          next+            case (isoiec_9798_4_4_bdkey_A_2_hash tid2) note_unified facts = this facts+            thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+          qed (insert facts, fastforce+)?+        next+          case swapped note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(AV ''A'' tid1) ) |},+                                   LC ''isoiec_9798_4_4_ccf_2'', LN ''Ra'' tid0, LN ''Rb'' tid1,+                                   s(AV ''A'' tid0), s(MV ''Text2'' tid1)+                                |} ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest!: ltk_secrecy)+          next+            case (isoiec_9798_4_4_bdkey_A_2_hash tid2) note_unified facts = this facts+            thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+          qed (insert facts, fastforce+)?+        qed (fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_4_bdkey_state) isoiec_9798_4_4_bdkey_B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_4_4_bdkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_4_4_bdkey_B_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_4_4_bdkey_A &+          ( tid1, isoiec_9798_4_4_bdkey_A_2 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),+             s(MV ''Text2'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),+                  LN ''Rb'' tid0, s(MV ''Text2'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts       thus ?thesis proof(sources! "-                       Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(AV ''A'' tid1) ) |},-                               LC ''isoiec_9798_4_4_ccf_2'', LN ''Ra'' tid0, LN ''Rb'' tid1,-                               s(AV ''A'' tid0), s(MV ''Text2'' tid1)+                       Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) |},+                               LC ''isoiec_9798_4_4_ccf_2'', s(MV ''Ra'' tid0), LN ''Rb'' tid0,+                               s(AV ''B'' tid0), s(MV ''Text2'' tid0)                             |} ")         case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest!: ltk_secrecy)+        thus ?thesis by (fastforce dest!: ltk_secrecy)       next-        case (isoiec_9798_4_4_bdkey_A_2_hash tid2) note_unified facts = this facts-        thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-      qed (insert facts, fastsimp+)?-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_4_bdkey_state) isoiec_9798_4_4_bdkey_B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_4_4_bdkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_4_4_bdkey_B_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_4_4_bdkey_A &-        ( tid1, isoiec_9798_4_4_bdkey_A_2 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),-           s(MV ''Text2'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),-                LN ''Rb'' tid0, s(MV ''Text2'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) |},-                           LC ''isoiec_9798_4_4_ccf_2'', s(MV ''Ra'' tid0), LN ''Rb'' tid0,-                           s(AV ''B'' tid0), s(MV ''Text2'' tid0)-                        |} ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_4_4_bdkey_A_2_hash tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?+        case (isoiec_9798_4_4_bdkey_A_2_hash tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj) qed  end
data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-4-udkey_cert_auto.thy view
@@ -1,6 +1,6 @@ theory "isoiec-9798-4-udkey_cert_auto" imports-  "../ESPLogic"+  "ESPLogic" begin  role isoiec_9798_4_1_udkey_A@@ -212,217 +212,217 @@     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_1_udkey_A_text_1_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_1_udkey_B_1_A t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_1_udkey_B_1_TNA t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_1_udkey_B_1_Text1 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_1_udkey_B_1_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_udkey_A_1_B t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_udkey_A_1_Rb t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_udkey_A_1_Text1 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_udkey_A_text_2_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_udkey_A_text_2_Text3 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_udkey_B_2_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_udkey_B_2_Text3 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_udkey_A_text_1_Text1 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_udkey_A_text_1_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_udkey_A_2_TNb t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_udkey_A_2_Text3 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_udkey_A_2_Text4 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_udkey_B_1_A t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_udkey_B_1_TNa t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_udkey_B_1_Text1 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_udkey_B_1_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_udkey_B_text_2_Text3 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_udkey_B_text_2_Text4 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_udkey_A_1_B t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_udkey_A_1_Rb t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_udkey_A_1_Text1 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_udkey_A_text_2_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_udkey_A_text_2_Text3 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_udkey_A_3_Text4 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_udkey_A_3_Text5 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_udkey_B_2_Ra t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_udkey_B_2_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_udkey_B_2_Text3 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_udkey_B_text_3_Text4 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_udkey_B_text_3_Text5 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   qed   thus "isoiec_9798_4_udkey_composed_typing_state t r s" by unfold_locales auto qed@@ -501,40 +501,60 @@                            LC ''isoiec_9798_4_1_ccf_1'', s(MV ''TNA'' tid0), s(MV ''Text1'' tid0)                         |} ")     case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)+    thus ?thesis by (fastforce dest!: ltk_secrecy)   next     case (isoiec_9798_4_1_udkey_A_1_hash tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)? qed -lemma (in restricted_isoiec_9798_4_udkey_state) isoiec_9798_4_2_udkey_B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_4_2_udkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_4_2_udkey_B_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_4_2_udkey_A &-        ( tid1, isoiec_9798_4_2_udkey_A_2 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(MV ''Rb'' tid1),-           s(MV ''Text2'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''Rb'' tid0,-                s(MV ''Text2'' tid0)-             |})"+lemma (in restricted_isoiec_9798_4_udkey_state) isoiec_9798_4_2_udkey_B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_4_2_udkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_4_2_udkey_B_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_4_2_udkey_A &+          ( tid1, isoiec_9798_4_2_udkey_A_2 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(MV ''Rb'' tid1),+             s(MV ''Text2'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''Rb'' tid0,+                  s(MV ''Text2'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs") proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Hash {| {| LC ''CCF'', K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) |},-                           LC ''isoiec_9798_4_2_ccf_2'', LN ''Rb'' tid0, s(MV ''Text2'' tid0)-                        |} ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_4_2_udkey_A_2_hash tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Hash {| {| LC ''CCF'', K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) |},+                               LC ''isoiec_9798_4_2_ccf_2'', LN ''Rb'' tid0, s(MV ''Text2'' tid0)+                            |} ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_4_2_udkey_A_2_hash tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj) qed  lemma (in restricted_isoiec_9798_4_udkey_state) isoiec_9798_4_3_udkey_A_non_injective_agreement:@@ -559,11 +579,11 @@                            LC ''isoiec_9798_4_3_ccf_2'', s(MV ''TNb'' tid0), s(MV ''Text3'' tid0)                         |} ")     case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)+    thus ?thesis by (fastforce dest!: ltk_secrecy)   next     case (isoiec_9798_4_3_udkey_B_2_hash tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)? qed  lemma (in restricted_isoiec_9798_4_udkey_state) isoiec_9798_4_3_udkey_B_non_injective_agreement:@@ -588,81 +608,121 @@                            LC ''isoiec_9798_4_3_ccf_1'', s(MV ''TNa'' tid0), s(MV ''Text1'' tid0)                         |} ")     case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)+    thus ?thesis by (fastforce dest!: ltk_secrecy)   next     case (isoiec_9798_4_3_udkey_A_1_hash tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)? qed -lemma (in restricted_isoiec_9798_4_udkey_state) isoiec_9798_4_4_udkey_A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_4_4_udkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_4_4_udkey_A_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_4_4_udkey_B &-        ( tid1, isoiec_9798_4_4_udkey_B_3 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,-           s(MV ''Text2'' tid1), s(MV ''Text4'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''Ra'' tid0,-                s(MV ''Rb'' tid0), s(MV ''Text2'' tid0), s(MV ''Text4'' tid0)-             |})"+lemma (in restricted_isoiec_9798_4_udkey_state) isoiec_9798_4_4_udkey_A_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_4_4_udkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_4_4_udkey_A_3 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_4_4_udkey_B &+          ( tid1, isoiec_9798_4_4_udkey_B_3 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,+             s(MV ''Text2'' tid1), s(MV ''Text4'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''Ra'' tid0,+                  s(MV ''Rb'' tid0), s(MV ''Text2'' tid0), s(MV ''Text4'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs") proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Hash {| {| LC ''CCF'', K ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) ) |},-                           LC ''isoiec_9798_4_4_ccf_3'', s(MV ''Rb'' tid0), LN ''Ra'' tid0,-                           s(MV ''Text4'' tid0)-                        |} ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_4_4_udkey_B_3_hash tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Hash {| {| LC ''CCF'', K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid1) ) |},-                             LC ''isoiec_9798_4_4_ccf_2'', LN ''Ra'' tid0, LN ''Rb'' tid1,-                             s(MV ''Text2'' tid1)-                          |} ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest!: ltk_secrecy)-    next-      case (isoiec_9798_4_4_udkey_A_2_hash tid2) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Hash {| {| LC ''CCF'', K ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) ) |},+                               LC ''isoiec_9798_4_4_ccf_3'', s(MV ''Rb'' tid0), LN ''Ra'' tid0,+                               s(MV ''Text4'' tid0)+                            |} ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_4_4_udkey_B_3_hash tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Hash {| {| LC ''CCF'', K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid1) ) |},+                                 LC ''isoiec_9798_4_4_ccf_2'', LN ''Ra'' tid0, LN ''Rb'' tid1,+                                 s(MV ''Text2'' tid1)+                              |} ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_4_4_udkey_A_2_hash tid2) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj) qed -lemma (in restricted_isoiec_9798_4_udkey_state) isoiec_9798_4_4_udkey_B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_4_4_udkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_4_4_udkey_B_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_4_4_udkey_A &-        ( tid1, isoiec_9798_4_4_udkey_A_2 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),-           s(MV ''Text2'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),-                LN ''Rb'' tid0, s(MV ''Text2'' tid0)-             |})"+lemma (in restricted_isoiec_9798_4_udkey_state) isoiec_9798_4_4_udkey_B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_4_4_udkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_4_4_udkey_B_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_4_4_udkey_A &+          ( tid1, isoiec_9798_4_4_udkey_A_2 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),+             s(MV ''Text2'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),+                  LN ''Rb'' tid0, s(MV ''Text2'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs") proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Hash {| {| LC ''CCF'', K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) |},-                           LC ''isoiec_9798_4_4_ccf_2'', s(MV ''Ra'' tid0), LN ''Rb'' tid0,-                           s(MV ''Text2'' tid0)-                        |} ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_4_4_udkey_A_2_hash tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Hash {| {| LC ''CCF'', K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) |},+                               LC ''isoiec_9798_4_4_ccf_2'', s(MV ''Ra'' tid0), LN ''Rb'' tid0,+                               s(MV ''Text2'' tid0)+                            |} ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_4_4_udkey_A_2_hash tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj) qed  end
data/examples/iso9798/isabelle-proofs/isoiec-9798-2-bdkey_cert_auto.thy view
@@ -1,3702 +1,4002 @@ theory "isoiec-9798-2-bdkey_cert_auto" imports-  "../ESPLogic"-begin--role isoiec_9798_2_1_bdkey_A-where "isoiec_9798_2_1_bdkey_A =-  [ Send ''leak_A'' ( sN ''TNA'' )-  , Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>-  , Send ''1'' <| sAV ''A'', sAV ''B'', sMV ''Text2'',-                  PEnc <| sC ''isoiec_9798_2_1_enc_1'', sN ''TNA'', sAV ''B'',-                          sMV ''Text1''-                       |>-                       ( sKbd (AVar ''A'') (AVar ''B'') )-               |>-  ]"--role isoiec_9798_2_1_bdkey_B-where "isoiec_9798_2_1_bdkey_B =-  [ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Text2'',-                  PEnc <| sC ''isoiec_9798_2_1_enc_1'', sMV ''TNA'', sAV ''B'',-                          sMV ''Text1''-                       |>-                       ( sKbd (MVar ''A'') (AVar ''B'') )-               |>-  ]"--protocol isoiec_9798_2_1_bdkey-where "isoiec_9798_2_1_bdkey =-{ isoiec_9798_2_1_bdkey_A, isoiec_9798_2_1_bdkey_B }"--locale restricted_isoiec_9798_2_1_bdkey_state = isoiec_9798_2_1_bdkey_state--type_invariant isoiec_9798_2_1_bdkey_msc_typing for isoiec_9798_2_1_bdkey-where "isoiec_9798_2_1_bdkey_msc_typing = mk_typing-  [ ((isoiec_9798_2_1_bdkey_B, ''A''), (KnownT isoiec_9798_2_1_bdkey_B_1))-  , ((isoiec_9798_2_1_bdkey_B, ''TNA''),-     (SumT (KnownT isoiec_9798_2_1_bdkey_B_1) (NonceT isoiec_9798_2_1_bdkey_A ''TNA'')))-  , ((isoiec_9798_2_1_bdkey_A, ''Text1''),-     (KnownT isoiec_9798_2_1_bdkey_A_text_1))-  , ((isoiec_9798_2_1_bdkey_B, ''Text1''),-     (KnownT isoiec_9798_2_1_bdkey_B_1))-  , ((isoiec_9798_2_1_bdkey_A, ''Text2''),-     (KnownT isoiec_9798_2_1_bdkey_A_text_1))-  , ((isoiec_9798_2_1_bdkey_B, ''Text2''),-     (KnownT isoiec_9798_2_1_bdkey_B_1))-  ]"--sublocale isoiec_9798_2_1_bdkey_state < isoiec_9798_2_1_bdkey_msc_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_2_1_bdkey_msc_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_2_1_bdkey_msc_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_2_1_bdkey_A_text_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_1_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_1_bdkey_A_text_1_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_1_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_1_bdkey_B_1_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_1_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_1_bdkey_B_1_TNA t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_1_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_1_enc_1'', s(MV ''TNA'' tid0),-               s(AV ''B'' tid0), s(MV ''Text1'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_1_bdkey_B_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_1_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_1_enc_1'', s(MV ''TNA'' tid0),-               s(AV ''B'' tid0), s(MV ''Text1'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_1_bdkey_B_1_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_1_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_2_1_bdkey_msc_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_2_1_bdkey_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end--lemma (in restricted_isoiec_9798_2_1_bdkey_state) B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_1_bdkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_1_bdkey_B_1 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_1_bdkey_A &-        ( tid1, isoiec_9798_2_1_bdkey_A_1 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,-           s(MV ''Text1'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),-                s(MV ''Text1'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_1_enc_1'', s(MV ''TNA'' tid0),-                          s(AV ''B'' tid0), s(MV ''Text1'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_1_bdkey_A_1_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--role isoiec_9798_2_2_bdkey_A-where "isoiec_9798_2_2_bdkey_A =-  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''RB'', sMV ''Text1'' |>-  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>-  , Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'',-                  PEnc <| sC ''isoiec_9798_2_2_enc_2'', sMV ''RB'', sMV ''B'',-                          sMV ''Text2''-                       |>-                       ( sKbd (MVar ''B'') (AVar ''A'') )-               |>-  ]"--role isoiec_9798_2_2_bdkey_B-where "isoiec_9798_2_2_bdkey_B =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''RB'', sMV ''Text1'' |>-  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'',-                  PEnc <| sC ''isoiec_9798_2_2_enc_2'', sN ''RB'', sAV ''B'', sMV ''Text2''-                       |>-                       ( sKbd (AVar ''B'') (AVar ''A'') )-               |>-  ]"--protocol isoiec_9798_2_2_bdkey-where "isoiec_9798_2_2_bdkey =-{ isoiec_9798_2_2_bdkey_A, isoiec_9798_2_2_bdkey_B }"--locale restricted_isoiec_9798_2_2_bdkey_state = isoiec_9798_2_2_bdkey_state--type_invariant isoiec_9798_2_2_bdkey_msc_typing for isoiec_9798_2_2_bdkey-where "isoiec_9798_2_2_bdkey_msc_typing = mk_typing-  [ ((isoiec_9798_2_2_bdkey_A, ''B''), (KnownT isoiec_9798_2_2_bdkey_A_1))-  , ((isoiec_9798_2_2_bdkey_A, ''RB''), (KnownT isoiec_9798_2_2_bdkey_A_1))-  , ((isoiec_9798_2_2_bdkey_A, ''Text1''),-     (KnownT isoiec_9798_2_2_bdkey_A_1))-  , ((isoiec_9798_2_2_bdkey_B, ''Text1''),-     (KnownT isoiec_9798_2_2_bdkey_B_text_1))-  , ((isoiec_9798_2_2_bdkey_A, ''Text2''),-     (KnownT isoiec_9798_2_2_bdkey_A_text_2))-  , ((isoiec_9798_2_2_bdkey_B, ''Text2''),-     (KnownT isoiec_9798_2_2_bdkey_B_2))-  , ((isoiec_9798_2_2_bdkey_A, ''Text3''),-     (KnownT isoiec_9798_2_2_bdkey_A_text_2))-  , ((isoiec_9798_2_2_bdkey_B, ''Text3''),-     (KnownT isoiec_9798_2_2_bdkey_B_2))-  ]"--sublocale isoiec_9798_2_2_bdkey_state < isoiec_9798_2_2_bdkey_msc_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_2_2_bdkey_msc_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_2_2_bdkey_msc_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_2_2_bdkey_A_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_2_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_2_bdkey_A_1_RB t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_2_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_2_bdkey_A_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_2_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_2_bdkey_A_text_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_2_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_2_bdkey_A_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_2_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_2_bdkey_B_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_2_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_2_enc_2'', LN ''RB'' tid0, s(AV ''B'' tid0),-               s(MV ''Text2'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_2_bdkey_B_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_2_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_2_2_bdkey_msc_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_2_2_bdkey_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end--lemma (in restricted_isoiec_9798_2_2_bdkey_state) B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_2_bdkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_2_bdkey_B_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_2_bdkey_A &-        ( tid1, isoiec_9798_2_2_bdkey_A_2 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(MV ''RB'' tid1),-           s(MV ''Text2'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''RB'' tid0,-                s(MV ''Text2'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_2_enc_2'', LN ''RB'' tid0, s(AV ''B'' tid0),-                          s(MV ''Text2'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_2_bdkey_A_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--role isoiec_9798_2_3_bdkey_A-where "isoiec_9798_2_3_bdkey_A =-  [ Send ''leak_A'' ( sN ''TNA'' )-  , Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>-  , Send ''1'' <| sAV ''A'', sAV ''B'', sMV ''Text2'',-                  PEnc <| sC ''isoiec_9798_2_3_enc_1'', sN ''TNA'', sAV ''B'',-                          sMV ''Text1''-                       |>-                       ( sKbd (AVar ''A'') (AVar ''B'') )-               |>-  , Recv ''2'' <| sAV ''B'', sAV ''A'', sMV ''Text4'',-                  PEnc <| sC ''isoiec_9798_2_3_enc_2'', sMV ''TNB'', sAV ''A'',-                          sMV ''Text3''-                       |>-                       ( sKbd (AVar ''B'') (AVar ''A'') )-               |>-  ]"--role isoiec_9798_2_3_bdkey_B-where "isoiec_9798_2_3_bdkey_B =-  [ Send ''leak_B'' ( sN ''TNB'' )-  , Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Text2'',-                  PEnc <| sC ''isoiec_9798_2_3_enc_1'', sMV ''TNA'', sAV ''B'',-                          sMV ''Text1''-                       |>-                       ( sKbd (MVar ''A'') (AVar ''B'') )-               |>-  , Recv ''text_2'' <| sMV ''Text3'', sMV ''Text4'' |>-  , Send ''2'' <| sAV ''B'', sMV ''A'', sMV ''Text4'',-                  PEnc <| sC ''isoiec_9798_2_3_enc_2'', sN ''TNB'', sMV ''A'',-                          sMV ''Text3''-                       |>-                       ( sKbd (AVar ''B'') (MVar ''A'') )-               |>-  ]"--protocol isoiec_9798_2_3_bdkey-where "isoiec_9798_2_3_bdkey =-{ isoiec_9798_2_3_bdkey_A, isoiec_9798_2_3_bdkey_B }"--locale restricted_isoiec_9798_2_3_bdkey_state = isoiec_9798_2_3_bdkey_state--type_invariant isoiec_9798_2_3_bdkey_msc_typing for isoiec_9798_2_3_bdkey-where "isoiec_9798_2_3_bdkey_msc_typing = mk_typing-  [ ((isoiec_9798_2_3_bdkey_B, ''A''), (KnownT isoiec_9798_2_3_bdkey_B_1))-  , ((isoiec_9798_2_3_bdkey_B, ''TNA''),-     (SumT (KnownT isoiec_9798_2_3_bdkey_B_1) (NonceT isoiec_9798_2_3_bdkey_A ''TNA'')))-  , ((isoiec_9798_2_3_bdkey_A, ''TNB''),-     (SumT (KnownT isoiec_9798_2_3_bdkey_A_2) (NonceT isoiec_9798_2_3_bdkey_B ''TNB'')))-  , ((isoiec_9798_2_3_bdkey_A, ''Text1''),-     (KnownT isoiec_9798_2_3_bdkey_A_text_1))-  , ((isoiec_9798_2_3_bdkey_B, ''Text1''),-     (KnownT isoiec_9798_2_3_bdkey_B_1))-  , ((isoiec_9798_2_3_bdkey_A, ''Text2''),-     (KnownT isoiec_9798_2_3_bdkey_A_text_1))-  , ((isoiec_9798_2_3_bdkey_B, ''Text2''),-     (KnownT isoiec_9798_2_3_bdkey_B_1))-  , ((isoiec_9798_2_3_bdkey_A, ''Text3''),-     (KnownT isoiec_9798_2_3_bdkey_A_2))-  , ((isoiec_9798_2_3_bdkey_B, ''Text3''),-     (KnownT isoiec_9798_2_3_bdkey_B_text_2))-  , ((isoiec_9798_2_3_bdkey_A, ''Text4''),-     (KnownT isoiec_9798_2_3_bdkey_A_2))-  , ((isoiec_9798_2_3_bdkey_B, ''Text4''),-     (KnownT isoiec_9798_2_3_bdkey_B_text_2))-  ]"--sublocale isoiec_9798_2_3_bdkey_state < isoiec_9798_2_3_bdkey_msc_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_2_3_bdkey_msc_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_2_3_bdkey_msc_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_2_3_bdkey_A_text_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_bdkey_A_text_1_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_bdkey_A_2_TNB t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_3_enc_2'', s(MV ''TNB'' tid0),-               s(AV ''A'' tid0), s(MV ''Text3'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_3_bdkey_A_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_3_enc_2'', s(MV ''TNB'' tid0),-               s(AV ''A'' tid0), s(MV ''Text3'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_3_bdkey_A_2_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_bdkey_B_1_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_bdkey_B_1_TNA t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_3_enc_1'', s(MV ''TNA'' tid0),-               s(AV ''B'' tid0), s(MV ''Text1'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_3_bdkey_B_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_3_enc_1'', s(MV ''TNA'' tid0),-               s(AV ''B'' tid0), s(MV ''Text1'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_3_bdkey_B_1_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_bdkey_B_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_bdkey_B_text_2_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_2_3_bdkey_msc_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_2_3_bdkey_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end--lemma (in restricted_isoiec_9798_2_3_bdkey_state) A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_3_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_3_bdkey_A_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_3_bdkey_B &-        ( tid1, isoiec_9798_2_3_bdkey_B_2 ) : steps t &-        {| s(MV ''A'' tid1), s(AV ''B'' tid1), LN ''TNB'' tid1,-           s(MV ''Text3'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNB'' tid0),-                s(MV ''Text3'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_3_enc_2'', s(MV ''TNB'' tid0),-                          s(AV ''A'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_3_bdkey_B_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_3_bdkey_state) B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_3_bdkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_3_bdkey_B_1 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_3_bdkey_A &-        ( tid1, isoiec_9798_2_3_bdkey_A_1 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,-           s(MV ''Text1'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),-                s(MV ''Text1'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_3_enc_1'', s(MV ''TNA'' tid0),-                          s(AV ''B'' tid0), s(MV ''Text1'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_3_bdkey_A_1_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--role isoiec_9798_2_4_bdkey_A-where "isoiec_9798_2_4_bdkey_A =-  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''RB'', sMV ''Text1'' |>-  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>-  , Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'',-                  PEnc <| sC ''isoiec_9798_2_4_enc_1'', sN ''RA'', sMV ''RB'', sMV ''B'',-                          sMV ''Text2''-                       |>-                       ( sKbd (AVar ''A'') (MVar ''B'') )-               |>-  , Recv ''3'' <| sMV ''B'', sAV ''A'', sMV ''Text5'',-                  PEnc <| sC ''isoiec_9798_2_4_enc_2'', sMV ''RB'', sN ''RA'',-                          sMV ''Text4''-                       |>-                       ( sKbd (AVar ''A'') (MVar ''B'') )-               |>-  ]"--role isoiec_9798_2_4_bdkey_B-where "isoiec_9798_2_4_bdkey_B =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''RB'', sMV ''Text1'' |>-  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'',-                  PEnc <| sC ''isoiec_9798_2_4_enc_1'', sMV ''RA'', sN ''RB'', sAV ''B'',-                          sMV ''Text2''-                       |>-                       ( sKbd (AVar ''A'') (AVar ''B'') )-               |>-  , Recv ''text_3'' <| sMV ''Text4'', sMV ''Text5'' |>-  , Send ''3'' <| sAV ''B'', sAV ''A'', sMV ''Text5'',-                  PEnc <| sC ''isoiec_9798_2_4_enc_2'', sN ''RB'', sMV ''RA'',-                          sMV ''Text4''-                       |>-                       ( sKbd (AVar ''A'') (AVar ''B'') )-               |>-  ]"--protocol isoiec_9798_2_4_bdkey-where "isoiec_9798_2_4_bdkey =-{ isoiec_9798_2_4_bdkey_A, isoiec_9798_2_4_bdkey_B }"--locale restricted_isoiec_9798_2_4_bdkey_state = isoiec_9798_2_4_bdkey_state--type_invariant isoiec_9798_2_4_bdkey_msc_typing for isoiec_9798_2_4_bdkey-where "isoiec_9798_2_4_bdkey_msc_typing = mk_typing-  [ ((isoiec_9798_2_4_bdkey_A, ''B''), (KnownT isoiec_9798_2_4_bdkey_A_1))-  , ((isoiec_9798_2_4_bdkey_B, ''RA''),-     (SumT (KnownT isoiec_9798_2_4_bdkey_B_2) (NonceT isoiec_9798_2_4_bdkey_A ''RA'')))-  , ((isoiec_9798_2_4_bdkey_A, ''RB''), (KnownT isoiec_9798_2_4_bdkey_A_1))-  , ((isoiec_9798_2_4_bdkey_A, ''Text1''),-     (KnownT isoiec_9798_2_4_bdkey_A_1))-  , ((isoiec_9798_2_4_bdkey_B, ''Text1''),-     (KnownT isoiec_9798_2_4_bdkey_B_text_1))-  , ((isoiec_9798_2_4_bdkey_A, ''Text2''),-     (KnownT isoiec_9798_2_4_bdkey_A_text_2))-  , ((isoiec_9798_2_4_bdkey_B, ''Text2''),-     (KnownT isoiec_9798_2_4_bdkey_B_2))-  , ((isoiec_9798_2_4_bdkey_A, ''Text3''),-     (KnownT isoiec_9798_2_4_bdkey_A_text_2))-  , ((isoiec_9798_2_4_bdkey_B, ''Text3''),-     (KnownT isoiec_9798_2_4_bdkey_B_2))-  , ((isoiec_9798_2_4_bdkey_A, ''Text4''),-     (KnownT isoiec_9798_2_4_bdkey_A_3))-  , ((isoiec_9798_2_4_bdkey_B, ''Text4''),-     (KnownT isoiec_9798_2_4_bdkey_B_text_3))-  , ((isoiec_9798_2_4_bdkey_A, ''Text5''),-     (KnownT isoiec_9798_2_4_bdkey_A_3))-  , ((isoiec_9798_2_4_bdkey_B, ''Text5''),-     (KnownT isoiec_9798_2_4_bdkey_B_text_3))-  ]"--sublocale isoiec_9798_2_4_bdkey_state < isoiec_9798_2_4_bdkey_msc_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_2_4_bdkey_msc_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_2_4_bdkey_msc_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_2_4_bdkey_A_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_bdkey_A_1_RB t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_bdkey_A_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_bdkey_A_text_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_bdkey_A_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_bdkey_A_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_4_enc_2'', s(MV ''RB'' tid0), LN ''RA'' tid0,-               s(MV ''Text4'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_4_bdkey_A_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_bdkey_B_2_RA t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_4_enc_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,-               s(AV ''B'' tid0), s(MV ''Text2'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_4_bdkey_B_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_4_enc_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,-               s(AV ''B'' tid0), s(MV ''Text2'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_4_bdkey_B_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_bdkey_B_text_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_bdkey_B_text_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_2_4_bdkey_msc_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_2_4_bdkey_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end--lemma (in restricted_isoiec_9798_2_4_bdkey_state) A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_4_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_4_bdkey_A_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_4_bdkey_B &-        ( tid1, isoiec_9798_2_4_bdkey_B_3 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''RA'' tid1), LN ''RB'' tid1,-           s(MV ''Text2'' tid1), s(MV ''Text4'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''RA'' tid0,-                s(MV ''RB'' tid0), s(MV ''Text2'' tid0), s(MV ''Text4'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_4_enc_2'', s(MV ''RB'' tid0), LN ''RA'' tid0,-                          s(MV ''Text4'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_4_bdkey_B_3_enc tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''A'' tid1) )-               ( s(AV ''B'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_4_enc_1'', LN ''RA'' tid0, LN ''RB'' tid1,-                              s(AV ''B'' tid1), s(MV ''Text2'' tid1)-                           |}-                           ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid1) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest!: ltk_secrecy)-      next-        case (isoiec_9798_2_4_bdkey_A_2_enc tid2) note_unified facts = this facts-        thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-      qed (insert facts, fastsimp+)?-    next-      case swapped note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_4_enc_1'', LN ''RA'' tid0, LN ''RB'' tid1,-                              s(AV ''A'' tid0), s(MV ''Text2'' tid1)-                           |}-                           ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''A'' tid1) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest!: ltk_secrecy)-      next-        case (isoiec_9798_2_4_bdkey_A_2_enc tid2) note_unified facts = this facts-        thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-      qed (insert facts, fastsimp+)?-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_4_bdkey_state) B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_4_bdkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_4_bdkey_B_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_4_bdkey_A &-        ( tid1, isoiec_9798_2_4_bdkey_A_2 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''RA'' tid1, s(MV ''RB'' tid1),-           s(MV ''Text2'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''RA'' tid0),-                LN ''RB'' tid0, s(MV ''Text2'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_4_enc_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,-                          s(AV ''B'' tid0), s(MV ''Text2'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_4_bdkey_A_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--role isoiec_9798_2_5_bdkey_A-where "isoiec_9798_2_5_bdkey_A =-  [ Send ''leak_A'' <| sN ''TVPa'', sN ''TNa'' |>-  , Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''A'', sAV ''P'', sN ''TVPa'', sAV ''B'',-                  sMV ''Text1''-               |>-  , Recv ''2'' <| sAV ''P'', sAV ''A'', sMV ''Text4'',-                  PEnc <| sC ''isoiec_9798_2_5_enc_2_1'', sN ''TVPa'', sMV ''Kab'',-                          sAV ''A'', sAV ''B'', sMV ''Text3''-                       |>-                       ( sKbd (AVar ''A'') (AVar ''P'') ),-                  sMV ''TokenPA_for_B''-               |>-  , Recv ''text_3'' <| sMV ''Text5'', sMV ''Text6'' |>-  , Send ''3'' <| sAV ''A'', sAV ''B'', sMV ''Text6'', sAV ''P'',-                  sMV ''TokenPA_for_B'',-                  PEnc <| sC ''isoiec_9798_2_5_enc_3'', sN ''TNa'', sAV ''B'',-                          sMV ''Text5''-                       |>-                       ( sMV ''Kab'' )-               |>-  , Recv ''4'' <| sAV ''B'', sAV ''A'', sMV ''Text8'',-                  PEnc <| sC ''isoiec_9798_2_5_enc_4'', sMV ''TNb'', sAV ''A'',-                          sMV ''Text7''-                       |>-                       ( sMV ''Kab'' )-               |>-  ]"--role isoiec_9798_2_5_bdkey_B-where "isoiec_9798_2_5_bdkey_B =-  [ Send ''leak_B'' ( sN ''TNb'' )-  , Recv ''3'' <| sMV ''A'', sAV ''B'', sMV ''Text6'', sMV ''P'',-                  PEnc <| sC ''isoiec_9798_2_5_enc_2_2'', sMV ''TNp'', sMV ''Kab'',-                          sMV ''A'', sAV ''B'', sMV ''Text2''-                       |>-                       ( sKbd (AVar ''B'') (MVar ''P'') ),-                  PEnc <| sC ''isoiec_9798_2_5_enc_3'', sMV ''TNa'', sAV ''B'',-                          sMV ''Text5''-                       |>-                       ( sMV ''Kab'' )-               |>-  , Recv ''text_4'' <| sMV ''Text7'', sMV ''Text8'' |>-  , Send ''4'' <| sAV ''B'', sMV ''A'', sMV ''Text8'',-                  PEnc <| sC ''isoiec_9798_2_5_enc_4'', sN ''TNb'', sMV ''A'',-                          sMV ''Text7''-                       |>-                       ( sMV ''Kab'' )-               |>-  ]"--role isoiec_9798_2_5_bdkey_P-where "isoiec_9798_2_5_bdkey_P =-  [ Send ''leak_P'' ( sN ''TNp'' )-  , Recv ''1'' <| sMV ''A'', sAV ''P'', sMV ''TVPa'', sMV ''B'',-                  sMV ''Text1''-               |>-  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'', sMV ''Text4'' |>-  , Send ''2'' <| sAV ''P'', sMV ''A'', sMV ''Text4'',-                  PEnc <| sC ''isoiec_9798_2_5_enc_2_1'', sMV ''TVPa'', sN ''Kab'',-                          sMV ''A'', sMV ''B'', sMV ''Text3''-                       |>-                       ( sKbd (MVar ''A'') (AVar ''P'') ),-                  PEnc <| sC ''isoiec_9798_2_5_enc_2_2'', sN ''TNp'', sN ''Kab'',-                          sMV ''A'', sMV ''B'', sMV ''Text2''-                       |>-                       ( sKbd (MVar ''B'') (AVar ''P'') )-               |>-  ]"--protocol isoiec_9798_2_5_bdkey-where "isoiec_9798_2_5_bdkey =-{ isoiec_9798_2_5_bdkey_A, isoiec_9798_2_5_bdkey_B,-  isoiec_9798_2_5_bdkey_P-}"--locale restricted_isoiec_9798_2_5_bdkey_state = isoiec_9798_2_5_bdkey_state--type_invariant isoiec_9798_2_5_bdkey_msc_typing for isoiec_9798_2_5_bdkey-where "isoiec_9798_2_5_bdkey_msc_typing = mk_typing-  [ ((isoiec_9798_2_5_bdkey_B, ''A''), (KnownT isoiec_9798_2_5_bdkey_B_3))-  , ((isoiec_9798_2_5_bdkey_P, ''A''), (KnownT isoiec_9798_2_5_bdkey_P_1))-  , ((isoiec_9798_2_5_bdkey_P, ''B''), (KnownT isoiec_9798_2_5_bdkey_P_1))-  , ((isoiec_9798_2_5_bdkey_A, ''Kab''),-     (SumT (KnownT isoiec_9798_2_5_bdkey_A_2) (NonceT isoiec_9798_2_5_bdkey_P ''Kab'')))-  , ((isoiec_9798_2_5_bdkey_B, ''Kab''),-     (SumT (KnownT isoiec_9798_2_5_bdkey_B_3) (NonceT isoiec_9798_2_5_bdkey_P ''Kab'')))-  , ((isoiec_9798_2_5_bdkey_B, ''P''), (KnownT isoiec_9798_2_5_bdkey_B_3))-  , ((isoiec_9798_2_5_bdkey_B, ''TNa''),-     (SumT (KnownT isoiec_9798_2_5_bdkey_B_3) (NonceT isoiec_9798_2_5_bdkey_A ''TNa'')))-  , ((isoiec_9798_2_5_bdkey_A, ''TNb''),-     (SumT (KnownT isoiec_9798_2_5_bdkey_A_4) (NonceT isoiec_9798_2_5_bdkey_B ''TNb'')))-  , ((isoiec_9798_2_5_bdkey_B, ''TNp''),-     (SumT (KnownT isoiec_9798_2_5_bdkey_B_3) (NonceT isoiec_9798_2_5_bdkey_P ''TNp'')))-  , ((isoiec_9798_2_5_bdkey_P, ''TVPa''),-     (KnownT isoiec_9798_2_5_bdkey_P_1))-  , ((isoiec_9798_2_5_bdkey_A, ''Text1''),-     (KnownT isoiec_9798_2_5_bdkey_A_text_1))-  , ((isoiec_9798_2_5_bdkey_P, ''Text1''),-     (KnownT isoiec_9798_2_5_bdkey_P_1))-  , ((isoiec_9798_2_5_bdkey_B, ''Text2''),-     (KnownT isoiec_9798_2_5_bdkey_B_3))-  , ((isoiec_9798_2_5_bdkey_P, ''Text2''),-     (KnownT isoiec_9798_2_5_bdkey_P_text_2))-  , ((isoiec_9798_2_5_bdkey_A, ''Text3''),-     (KnownT isoiec_9798_2_5_bdkey_A_2))-  , ((isoiec_9798_2_5_bdkey_P, ''Text3''),-     (KnownT isoiec_9798_2_5_bdkey_P_text_2))-  , ((isoiec_9798_2_5_bdkey_A, ''Text4''),-     (KnownT isoiec_9798_2_5_bdkey_A_2))-  , ((isoiec_9798_2_5_bdkey_P, ''Text4''),-     (KnownT isoiec_9798_2_5_bdkey_P_text_2))-  , ((isoiec_9798_2_5_bdkey_A, ''Text5''),-     (KnownT isoiec_9798_2_5_bdkey_A_text_3))-  , ((isoiec_9798_2_5_bdkey_B, ''Text5''),-     (KnownT isoiec_9798_2_5_bdkey_B_3))-  , ((isoiec_9798_2_5_bdkey_A, ''Text6''),-     (KnownT isoiec_9798_2_5_bdkey_A_text_3))-  , ((isoiec_9798_2_5_bdkey_B, ''Text6''),-     (KnownT isoiec_9798_2_5_bdkey_B_3))-  , ((isoiec_9798_2_5_bdkey_A, ''Text7''),-     (KnownT isoiec_9798_2_5_bdkey_A_4))-  , ((isoiec_9798_2_5_bdkey_B, ''Text7''),-     (KnownT isoiec_9798_2_5_bdkey_B_text_4))-  , ((isoiec_9798_2_5_bdkey_A, ''Text8''),-     (KnownT isoiec_9798_2_5_bdkey_A_4))-  , ((isoiec_9798_2_5_bdkey_B, ''Text8''),-     (KnownT isoiec_9798_2_5_bdkey_B_text_4))-  , ((isoiec_9798_2_5_bdkey_A, ''TokenPA_for_B''),-     (KnownT isoiec_9798_2_5_bdkey_A_2))-  ]"--sublocale isoiec_9798_2_5_bdkey_state < isoiec_9798_2_5_bdkey_msc_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_2_5_bdkey_msc_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_2_5_bdkey_msc_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_2_5_bdkey_A_2_Kab t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,-               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),-               s(MV ''Text3'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_bdkey_A_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,-               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),-               s(MV ''Text3'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_bdkey_A_2_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_A_2_TokenPA_for_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_A_text_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_A_text_3_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_A_4_TNb t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_4'', s(MV ''TNb'' tid0),-               s(AV ''A'' tid0), s(MV ''Text7'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_bdkey_A_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_4'', s(MV ''TNb'' tid0),-               s(AV ''A'' tid0), s(MV ''Text7'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_bdkey_A_4_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_B_3_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_B_3_Kab t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),-               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(AV ''B'' tid0),-               s(MV ''Text2'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_bdkey_B_3_P t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_B_3_TNa t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid0),-               s(AV ''B'' tid0), s(MV ''Text5'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_bdkey_B_3_TNp t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),-               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(AV ''B'' tid0),-               s(MV ''Text2'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_bdkey_B_3_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),-               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(AV ''B'' tid0),-               s(MV ''Text2'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_bdkey_B_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid0),-               s(AV ''B'' tid0), s(MV ''Text5'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_bdkey_B_3_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_B_text_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_B_text_4_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_P_1_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_P_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_P_1_TVPa t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_P_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_P_text_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_P_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_bdkey_P_text_2_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_2_5_bdkey_msc_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_2_5_bdkey_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end--lemma (in restricted_isoiec_9798_2_5_bdkey_state) P_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_bdkey_P"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "LN ''Kab'' tid0 : knows t"-  shows "False"-using facts proof(sources! " LN ''Kab'' tid0 ")-  case isoiec_9798_2_5_bdkey_P_2_Kab note_unified facts = this facts-  thus ?thesis by (fastsimp dest!: ltk_secrecy)-next-  case isoiec_9798_2_5_bdkey_P_2_Kab_1 note_unified facts = this facts-  thus ?thesis by (fastsimp dest!: ltk_secrecy)-qed (insert facts, fastsimp+)?--lemma (in restricted_isoiec_9798_2_5_bdkey_state) A_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_bdkey_A_2 ) : steps t"-    "s(MV ''Kab'' tid0) : knows t"-  shows "False"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),-                          s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_bdkey_P_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_5_bdkey_state) B_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_bdkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_bdkey_B_3 ) : steps t"-    "s(MV ''Kab'' tid0) : knows t"-  shows "False"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),-                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(AV ''B'' tid0),-                          s(MV ''Text2'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_bdkey_P_2_enc_1 tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_5_bdkey_state) A_non_injective_agreement_B:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_bdkey_A_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_5_bdkey_B &-        ( tid1, isoiec_9798_2_5_bdkey_B_4 ) : steps t &-        {| s(MV ''A'' tid1), s(AV ''B'' tid1), s(MV ''P'' tid1),-           s(MV ''Kab'' tid1), s(MV ''TNa'' tid1), s(MV ''Text5'' tid1),-           LN ''TNb'' tid1, s(MV ''Text7'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''P'' tid0),-                s(MV ''Kab'' tid0), LN ''TNa'' tid0, s(MV ''Text5'' tid0),-                s(MV ''TNb'' tid0), s(MV ''Text7'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),-                          s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_bdkey_P_2_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_2_5_enc_4'', s(MV ''TNb'' tid0),-                            s(AV ''A'' tid0), s(MV ''Text7'' tid0)-                         |}-                         ( LN ''Kab'' tid1 ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-    next-      case (isoiec_9798_2_5_bdkey_B_4_enc tid2) note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid2),-                              LN ''Kab'' tid1, s(AV ''A'' tid0), s(AV ''B'' tid2), s(MV ''Text2'' tid2)-                           |}-                           ( Kbd ( s(AV ''B'' tid2) ) ( s(MV ''P'' tid2) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-      next-        case (isoiec_9798_2_5_bdkey_P_2_enc_1 tid3) note_unified facts = this facts-        thus ?thesis proof(sources! "-                         Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid2),-                                s(AV ''B'' tid0), s(MV ''Text5'' tid2)-                             |}-                             ( LN ''Kab'' tid1 ) ")-          case fake note_unified facts = this facts-          thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-        next-          case (isoiec_9798_2_5_bdkey_A_3_enc tid3) note_unified facts = this facts-          thus ?thesis proof(sources! "-                           Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid3, LN ''Kab'' tid1,-                                  s(AV ''A'' tid3), s(AV ''B'' tid0), s(MV ''Text3'' tid3)-                               |}-                               ( Kbd ( s(AV ''A'' tid3) ) ( s(AV ''P'' tid3) ) ) ")-            case fake note_unified facts = this facts-            thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-          next-            case (isoiec_9798_2_5_bdkey_P_2_enc tid4) note_unified facts = this facts-            thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-          qed (insert facts, fastsimp+)?-        qed (insert facts, fastsimp+)?-      qed (insert facts, fastsimp+)?-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_5_bdkey_state) B_non_injective_agreement_A:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_bdkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_bdkey_B_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_5_bdkey_A &-        ( tid1, isoiec_9798_2_5_bdkey_A_3 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(AV ''P'' tid1),-           s(MV ''Kab'' tid1), LN ''TNa'' tid1, s(MV ''Text5'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),-                s(MV ''Kab'' tid0), s(MV ''TNa'' tid0), s(MV ''Text5'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),-                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(AV ''B'' tid0),-                          s(MV ''Text2'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_bdkey_P_2_enc_1 tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid0),-                            s(AV ''B'' tid0), s(MV ''Text5'' tid0)-                         |}-                         ( LN ''Kab'' tid1 ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-    next-      case (isoiec_9798_2_5_bdkey_A_3_enc tid2) note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid2, LN ''Kab'' tid1,-                              s(AV ''A'' tid2), s(AV ''B'' tid0), s(MV ''Text3'' tid2)-                           |}-                           ( Kbd ( s(AV ''A'' tid2) ) ( s(AV ''P'' tid2) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-      next-        case (isoiec_9798_2_5_bdkey_P_2_enc tid3) note_unified facts = this facts-        thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-      qed (insert facts, fastsimp+)?-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_5_bdkey_state) A_non_injective_agreement_P:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_bdkey_A_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_5_bdkey_P &-        ( tid1, isoiec_9798_2_5_bdkey_P_2 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1), LN ''Kab'' tid1,-           s(MV ''TVPa'' tid1), s(MV ''Text3'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''P'' tid0),-                s(MV ''Kab'' tid0), LN ''TVPa'' tid0, s(MV ''Text3'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),-                          s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_bdkey_P_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_5_bdkey_state) B_non_injective_agreement_P:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_bdkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_bdkey_B_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_5_bdkey_P &-        ( tid1, isoiec_9798_2_5_bdkey_P_2 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1), LN ''Kab'' tid1,-           LN ''TNp'' tid1, s(MV ''Text2'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),-                s(MV ''Kab'' tid0), s(MV ''TNp'' tid0), s(MV ''Text2'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),-                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(AV ''B'' tid0),-                          s(MV ''Text2'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_bdkey_P_2_enc_1 tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--role isoiec_9798_2_6_bdkey_A-where "isoiec_9798_2_6_bdkey_A =-  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>-  , Recv ''text_2'' ( sMV ''Text2'' )-  , Send ''2'' <| sAV ''A'', sAV ''P'', sN ''Ra'', sMV ''Rb'', sMV ''B'',-                  sMV ''Text2''-               |>-  , Recv ''3'' <| sAV ''P'', sAV ''A'', sMV ''Text5'',-                  PEnc <| sC ''isoiec_9798_2_6_enc_3_1'', sN ''Ra'', sMV ''Kab'',-                          sAV ''A'', sMV ''B'', sMV ''Text4''-                       |>-                       ( sKbd (AVar ''A'') (AVar ''P'') ),-                  sMV ''TokenPA_for_B''-               |>-  , Recv ''text_4'' <| sMV ''Text6'', sMV ''Text7'' |>-  , Send ''4'' <| sAV ''A'', sMV ''B'', sMV ''Text7'', sAV ''P'',-                  sMV ''TokenPA_for_B'',-                  PEnc <| sC ''isoiec_9798_2_6_enc_4'', sN ''Rpa'', sMV ''Rb'',-                          sMV ''Text6''-                       |>-                       ( sMV ''Kab'' )-               |>-  , Recv ''5'' <| sMV ''B'', sAV ''A'', sMV ''Text9'',-                  PEnc <| sC ''isoiec_9798_2_6_enc_5'', sMV ''Rb'', sN ''Rpa'',-                          sMV ''Text8''-                       |>-                       ( sMV ''Kab'' )-               |>-  ]"--role isoiec_9798_2_6_bdkey_B-where "isoiec_9798_2_6_bdkey_B =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>-  , Recv ''4'' <| sAV ''A'', sAV ''B'', sMV ''Text7'', sMV ''P'',-                  PEnc <| sC ''isoiec_9798_2_6_enc_3_2'', sN ''Rb'', sMV ''Kab'',-                          sAV ''A'', sAV ''B'', sMV ''Text3''-                       |>-                       ( sKbd (AVar ''B'') (MVar ''P'') ),-                  PEnc <| sC ''isoiec_9798_2_6_enc_4'', sMV ''Rpa'', sN ''Rb'',-                          sMV ''Text6''-                       |>-                       ( sMV ''Kab'' )-               |>-  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>-  , Send ''5'' <| sAV ''B'', sAV ''A'', sMV ''Text9'',-                  PEnc <| sC ''isoiec_9798_2_6_enc_5'', sN ''Rb'', sMV ''Rpa'',-                          sMV ''Text8''-                       |>-                       ( sMV ''Kab'' )-               |>-  ]"--role isoiec_9798_2_6_bdkey_P-where "isoiec_9798_2_6_bdkey_P =-  [ Recv ''2'' <| sMV ''A'', sAV ''P'', sMV ''Ra'', sMV ''Rb'', sMV ''B'',-                  sMV ''Text2''-               |>-  , Recv ''text_3'' <| sMV ''Text3'', sMV ''Text4'', sMV ''Text5'' |>-  , Send ''3'' <| sAV ''P'', sMV ''A'', sMV ''Text5'',-                  PEnc <| sC ''isoiec_9798_2_6_enc_3_1'', sMV ''Ra'', sN ''Kab'',-                          sMV ''A'', sMV ''B'', sMV ''Text4''-                       |>-                       ( sKbd (MVar ''A'') (AVar ''P'') ),-                  PEnc <| sC ''isoiec_9798_2_6_enc_3_2'', sMV ''Rb'', sN ''Kab'',-                          sMV ''A'', sMV ''B'', sMV ''Text3''-                       |>-                       ( sKbd (MVar ''B'') (AVar ''P'') )-               |>-  ]"--protocol isoiec_9798_2_6_bdkey-where "isoiec_9798_2_6_bdkey =-{ isoiec_9798_2_6_bdkey_A, isoiec_9798_2_6_bdkey_B,-  isoiec_9798_2_6_bdkey_P-}"--locale restricted_isoiec_9798_2_6_bdkey_state = isoiec_9798_2_6_bdkey_state--type_invariant isoiec_9798_2_6_bdkey_msc_typing for isoiec_9798_2_6_bdkey-where "isoiec_9798_2_6_bdkey_msc_typing = mk_typing-  [ ((isoiec_9798_2_6_bdkey_P, ''A''), (KnownT isoiec_9798_2_6_bdkey_P_2))-  , ((isoiec_9798_2_6_bdkey_A, ''B''), (KnownT isoiec_9798_2_6_bdkey_A_1))-  , ((isoiec_9798_2_6_bdkey_P, ''B''), (KnownT isoiec_9798_2_6_bdkey_P_2))-  , ((isoiec_9798_2_6_bdkey_A, ''Kab''),-     (SumT (KnownT isoiec_9798_2_6_bdkey_A_3) (NonceT isoiec_9798_2_6_bdkey_P ''Kab'')))-  , ((isoiec_9798_2_6_bdkey_B, ''Kab''),-     (SumT (KnownT isoiec_9798_2_6_bdkey_B_4) (NonceT isoiec_9798_2_6_bdkey_P ''Kab'')))-  , ((isoiec_9798_2_6_bdkey_B, ''P''), (KnownT isoiec_9798_2_6_bdkey_B_4))-  , ((isoiec_9798_2_6_bdkey_P, ''Ra''), (KnownT isoiec_9798_2_6_bdkey_P_2))-  , ((isoiec_9798_2_6_bdkey_A, ''Rb''), (KnownT isoiec_9798_2_6_bdkey_A_1))-  , ((isoiec_9798_2_6_bdkey_P, ''Rb''), (KnownT isoiec_9798_2_6_bdkey_P_2))-  , ((isoiec_9798_2_6_bdkey_B, ''Rpa''),-     (SumT (KnownT isoiec_9798_2_6_bdkey_B_4) (NonceT isoiec_9798_2_6_bdkey_A ''Rpa'')))-  , ((isoiec_9798_2_6_bdkey_A, ''Text1''),-     (KnownT isoiec_9798_2_6_bdkey_A_1))-  , ((isoiec_9798_2_6_bdkey_B, ''Text1''),-     (KnownT isoiec_9798_2_6_bdkey_B_text_1))-  , ((isoiec_9798_2_6_bdkey_A, ''Text2''),-     (KnownT isoiec_9798_2_6_bdkey_A_text_2))-  , ((isoiec_9798_2_6_bdkey_P, ''Text2''),-     (KnownT isoiec_9798_2_6_bdkey_P_2))-  , ((isoiec_9798_2_6_bdkey_B, ''Text3''),-     (KnownT isoiec_9798_2_6_bdkey_B_4))-  , ((isoiec_9798_2_6_bdkey_P, ''Text3''),-     (KnownT isoiec_9798_2_6_bdkey_P_text_3))-  , ((isoiec_9798_2_6_bdkey_A, ''Text4''),-     (KnownT isoiec_9798_2_6_bdkey_A_3))-  , ((isoiec_9798_2_6_bdkey_P, ''Text4''),-     (KnownT isoiec_9798_2_6_bdkey_P_text_3))-  , ((isoiec_9798_2_6_bdkey_A, ''Text5''),-     (KnownT isoiec_9798_2_6_bdkey_A_3))-  , ((isoiec_9798_2_6_bdkey_P, ''Text5''),-     (KnownT isoiec_9798_2_6_bdkey_P_text_3))-  , ((isoiec_9798_2_6_bdkey_A, ''Text6''),-     (KnownT isoiec_9798_2_6_bdkey_A_text_4))-  , ((isoiec_9798_2_6_bdkey_B, ''Text6''),-     (KnownT isoiec_9798_2_6_bdkey_B_4))-  , ((isoiec_9798_2_6_bdkey_A, ''Text7''),-     (KnownT isoiec_9798_2_6_bdkey_A_text_4))-  , ((isoiec_9798_2_6_bdkey_B, ''Text7''),-     (KnownT isoiec_9798_2_6_bdkey_B_4))-  , ((isoiec_9798_2_6_bdkey_A, ''Text8''),-     (KnownT isoiec_9798_2_6_bdkey_A_5))-  , ((isoiec_9798_2_6_bdkey_B, ''Text8''),-     (KnownT isoiec_9798_2_6_bdkey_B_text_5))-  , ((isoiec_9798_2_6_bdkey_A, ''Text9''),-     (KnownT isoiec_9798_2_6_bdkey_A_5))-  , ((isoiec_9798_2_6_bdkey_B, ''Text9''),-     (KnownT isoiec_9798_2_6_bdkey_B_text_5))-  , ((isoiec_9798_2_6_bdkey_A, ''TokenPA_for_B''),-     (KnownT isoiec_9798_2_6_bdkey_A_3))-  ]"--sublocale isoiec_9798_2_6_bdkey_state < isoiec_9798_2_6_bdkey_msc_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_2_6_bdkey_msc_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_2_6_bdkey_msc_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_2_6_bdkey_A_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_A_1_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_A_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_A_3_Kab t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,-               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),-               s(MV ''Text4'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_bdkey_A_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,-               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),-               s(MV ''Text4'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_bdkey_A_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_A_3_TokenPA_for_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_A_text_4_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_A_text_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_A_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_5'', s(MV ''Rb'' tid0), LN ''Rpa'' tid0,-               s(MV ''Text8'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_bdkey_A_5_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_B_4_Kab t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,-               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),-               s(MV ''Text3'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_bdkey_B_4_P t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_B_4_Rpa t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_4'', s(MV ''Rpa'' tid0), LN ''Rb'' tid0,-               s(MV ''Text6'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_bdkey_B_4_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,-               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),-               s(MV ''Text3'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_bdkey_B_4_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_4'', s(MV ''Rpa'' tid0), LN ''Rb'' tid0,-               s(MV ''Text6'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_bdkey_B_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_B_text_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_B_text_5_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_P_2_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_P_2_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_P_2_Ra t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_P_2_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_P_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_P_text_3_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_P_text_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_bdkey_P_text_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_2_6_bdkey_msc_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_2_6_bdkey_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end--lemma (in restricted_isoiec_9798_2_6_bdkey_state) P_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_bdkey_P"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "LN ''Kab'' tid0 : knows t"-  shows "False"-using facts proof(sources! " LN ''Kab'' tid0 ")-  case isoiec_9798_2_6_bdkey_P_3_Kab note_unified facts = this facts-  thus ?thesis by (fastsimp dest!: ltk_secrecy)-next-  case isoiec_9798_2_6_bdkey_P_3_Kab_1 note_unified facts = this facts-  thus ?thesis by (fastsimp dest!: ltk_secrecy)-qed (insert facts, fastsimp+)?--lemma (in restricted_isoiec_9798_2_6_bdkey_state) A_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_bdkey_A_3 ) : steps t"-    "s(MV ''Kab'' tid0) : knows t"-  shows "False"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),-                          s(MV ''Text4'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_bdkey_P_3_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_6_bdkey_state) B_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_bdkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_bdkey_B_4 ) : steps t"-    "s(MV ''Kab'' tid0) : knows t"-  shows "False"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),-                          s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_bdkey_P_3_enc_1 tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_6_bdkey_state) A_non_injective_agreement_B:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_bdkey_A_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_6_bdkey_B &-        ( tid1, isoiec_9798_2_6_bdkey_B_5 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''P'' tid1),-           s(MV ''Kab'' tid1), s(MV ''Rpa'' tid1), LN ''Rb'' tid1,-           s(MV ''Text6'' tid1), s(MV ''Text8'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''P'' tid0),-                s(MV ''Kab'' tid0), LN ''Rpa'' tid0, s(MV ''Rb'' tid0),-                s(MV ''Text6'' tid0), s(MV ''Text8'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),-                          s(MV ''Text4'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_bdkey_P_3_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_2_6_enc_5'', s(MV ''Rb'' tid0), LN ''Rpa'' tid0,-                            s(MV ''Text8'' tid0)-                         |}-                         ( LN ''Kab'' tid1 ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-    next-      case (isoiec_9798_2_6_bdkey_B_5_enc tid2) note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid2, LN ''Kab'' tid1,-                              s(AV ''A'' tid2), s(AV ''B'' tid2), s(MV ''Text3'' tid2)-                           |}-                           ( Kbd ( s(AV ''B'' tid2) ) ( s(MV ''P'' tid2) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-      next-        case (isoiec_9798_2_6_bdkey_P_3_enc_1 tid3) note_unified facts = this facts-        thus ?thesis proof(sources! "-                         Enc {| LC ''isoiec_9798_2_6_enc_4'', LN ''Rpa'' tid0, LN ''Rb'' tid2,-                                s(MV ''Text6'' tid2)-                             |}-                             ( LN ''Kab'' tid1 ) ")-          case fake note_unified facts = this facts-          thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-        next-          case (isoiec_9798_2_6_bdkey_A_4_enc tid3) note_unified facts = this facts-          thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-        qed (insert facts, fastsimp+)?-      qed (insert facts, fastsimp+)?-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_6_bdkey_state) B_non_injective_agreement_A:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_bdkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_bdkey_B_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_6_bdkey_A &-        ( tid1, isoiec_9798_2_6_bdkey_A_4 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),-           s(MV ''Kab'' tid1), LN ''Rpa'' tid1, s(MV ''Rb'' tid1),-           s(MV ''Text6'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),-                s(MV ''Kab'' tid0), s(MV ''Rpa'' tid0), LN ''Rb'' tid0,-                s(MV ''Text6'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),-                          s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_bdkey_P_3_enc_1 tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_2_6_enc_4'', s(MV ''Rpa'' tid0), LN ''Rb'' tid0,-                            s(MV ''Text6'' tid0)-                         |}-                         ( LN ''Kab'' tid1 ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-    next-      case (isoiec_9798_2_6_bdkey_A_4_enc tid2) note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid2, LN ''Kab'' tid1,-                              s(AV ''A'' tid2), s(MV ''B'' tid2), s(MV ''Text4'' tid2)-                           |}-                           ( Kbd ( s(AV ''A'' tid2) ) ( s(AV ''P'' tid2) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-      next-        case (isoiec_9798_2_6_bdkey_P_3_enc tid3) note_unified facts = this facts-        thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-      qed (insert facts, fastsimp+)?-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_6_bdkey_state) A_non_injective_agreement_P:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_bdkey_A_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_6_bdkey_P &-        ( tid1, isoiec_9798_2_6_bdkey_P_3 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),-           s(MV ''Ra'' tid1), LN ''Kab'' tid1, s(MV ''Text4'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''P'' tid0),-                LN ''Ra'' tid0, s(MV ''Kab'' tid0), s(MV ''Text4'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),-                          s(MV ''Text4'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_bdkey_P_3_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_6_bdkey_state) B_non_injective_agreement_P:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_bdkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_bdkey_B_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_6_bdkey_P &-        ( tid1, isoiec_9798_2_6_bdkey_P_3 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),-           s(MV ''Rb'' tid1), LN ''Kab'' tid1, s(MV ''Text3'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),-                LN ''Rb'' tid0, s(MV ''Kab'' tid0), s(MV ''Text3'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),-                          s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_bdkey_P_3_enc_1 tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--role isoiec_9798_2_5_special_TTP_bdkey_A-where "isoiec_9798_2_5_special_TTP_bdkey_A =-  [ Send ''leak_A'' <| sN ''TVPa'', sN ''TNa'' |>-  , Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''A'', sAV ''P'', sN ''TVPa'', sAV ''B'',-                  sMV ''Text1''-               |>-  , Recv ''2'' <| sAV ''P'', sAV ''A'', sMV ''Text4'',-                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_2_1'', sN ''TVPa'',-                          sMV ''Kab'', sAV ''B'', sMV ''Text3''-                       |>-                       ( sKbd (AVar ''A'') (AVar ''P'') ),-                  sMV ''TokenPA_for_B''-               |>-  , Recv ''text_3'' <| sMV ''Text5'', sMV ''Text6'' |>-  , Send ''3'' <| sAV ''A'', sAV ''B'', sMV ''Text6'', sAV ''P'',-                  sMV ''TokenPA_for_B'',-                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_3'', sN ''TNa'', sAV ''B'',-                          sMV ''Text5''-                       |>-                       ( sMV ''Kab'' )-               |>-  , Recv ''4'' <| sAV ''B'', sAV ''A'', sMV ''Text8'',-                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_4'', sMV ''TNb'', sAV ''A'',-                          sMV ''Text7''-                       |>-                       ( sMV ''Kab'' )-               |>-  ]"--role isoiec_9798_2_5_special_TTP_bdkey_B-where "isoiec_9798_2_5_special_TTP_bdkey_B =-  [ Send ''leak_B'' ( sN ''TNb'' )-  , Recv ''3'' <| sMV ''A'', sAV ''B'', sMV ''Text6'', sMV ''P'',-                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_2_2'', sMV ''TNp'',-                          sMV ''Kab'', sMV ''A'', sMV ''Text2''-                       |>-                       ( sKbd (AVar ''B'') (MVar ''P'') ),-                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_3'', sMV ''TNa'', sAV ''B'',-                          sMV ''Text5''-                       |>-                       ( sMV ''Kab'' )-               |>-  , Recv ''text_4'' <| sMV ''Text7'', sMV ''Text8'' |>-  , Send ''4'' <| sAV ''B'', sMV ''A'', sMV ''Text8'',-                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_4'', sN ''TNb'', sMV ''A'',-                          sMV ''Text7''-                       |>-                       ( sMV ''Kab'' )-               |>-  ]"--role isoiec_9798_2_5_special_TTP_bdkey_P-where "isoiec_9798_2_5_special_TTP_bdkey_P =-  [ Send ''leak_P'' ( sN ''TNp'' )-  , Recv ''1'' <| sMV ''A'', sAV ''P'', sMV ''TVPa'', sMV ''B'',-                  sMV ''Text1''-               |>-  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'', sMV ''Text4'' |>-  , Send ''2'' <| sAV ''P'', sMV ''A'', sMV ''Text4'',-                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_2_1'', sMV ''TVPa'',-                          sN ''Kab'', sMV ''B'', sMV ''Text3''-                       |>-                       ( sKbd (MVar ''A'') (AVar ''P'') ),-                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_2_2'', sN ''TNp'',-                          sN ''Kab'', sMV ''A'', sMV ''Text2''-                       |>-                       ( sKbd (MVar ''B'') (AVar ''P'') )-               |>-  ]"--protocol isoiec_9798_2_5_special_TTP_bdkey-where "isoiec_9798_2_5_special_TTP_bdkey =-{ isoiec_9798_2_5_special_TTP_bdkey_A,-  isoiec_9798_2_5_special_TTP_bdkey_B, isoiec_9798_2_5_special_TTP_bdkey_P-}"--locale restricted_isoiec_9798_2_5_special_TTP_bdkey_state = isoiec_9798_2_5_special_TTP_bdkey_state +-  assumes different_actors_A_P:-    "!! tid0 tid1.-       [| roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_A;-         roleMap r tid1 = Some isoiec_9798_2_5_special_TTP_bdkey_P;-         s(AV ''P'' tid1) = s(AV ''A'' tid0)-       |] ==> False"--type_invariant isoiec_9798_2_5_special_TTP_bdkey_msc_typing for isoiec_9798_2_5_special_TTP_bdkey-where "isoiec_9798_2_5_special_TTP_bdkey_msc_typing = mk_typing-  [ ((isoiec_9798_2_5_special_TTP_bdkey_B, ''A''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3))-  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''A''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_1))-  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''B''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_1))-  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Kab''),-     (SumT (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_2) (NonceT isoiec_9798_2_5_special_TTP_bdkey_P ''Kab'')))-  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''Kab''),-     (SumT (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3) (NonceT isoiec_9798_2_5_special_TTP_bdkey_P ''Kab'')))-  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''P''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3))-  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''TNa''),-     (SumT (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3) (NonceT isoiec_9798_2_5_special_TTP_bdkey_A ''TNa'')))-  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''TNb''),-     (SumT (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_4) (NonceT isoiec_9798_2_5_special_TTP_bdkey_B ''TNb'')))-  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''TNp''),-     (SumT (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3) (NonceT isoiec_9798_2_5_special_TTP_bdkey_P ''TNp'')))-  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''TVPa''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_1))-  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text1''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_text_1))-  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''Text1''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_1))-  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''Text2''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3))-  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''Text2''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_text_2))-  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text3''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_2))-  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''Text3''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_text_2))-  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text4''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_2))-  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''Text4''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_text_2))-  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text5''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_text_3))-  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''Text5''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3))-  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text6''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_text_3))-  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''Text6''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3))-  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text7''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_4))-  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''Text7''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_text_4))-  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text8''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_4))-  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''Text8''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_text_4))-  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''TokenPA_for_B''),-     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_2))-  ]"--sublocale isoiec_9798_2_5_special_TTP_bdkey_state < isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_2_5_special_TTP_bdkey_msc_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_2_5_special_TTP_bdkey_msc_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_2_5_special_TTP_bdkey_A_2_Kab t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid0,-               s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_A_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid0,-               s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_A_2_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_A_2_TokenPA_for_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_A_text_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_A_text_3_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_A_4_TNb t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_4'', s(MV ''TNb'' tid0),-               s(AV ''A'' tid0), s(MV ''Text7'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_A_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_4'', s(MV ''TNb'' tid0),-               s(AV ''A'' tid0), s(MV ''Text7'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_A_4_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_Kab t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid0),-               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_P t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_TNa t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_3'', s(MV ''TNa'' tid0),-               s(AV ''B'' tid0), s(MV ''Text5'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_TNp t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid0),-               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid0),-               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_3'', s(MV ''TNa'' tid0),-               s(AV ''B'' tid0), s(MV ''Text5'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_B_text_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_B_text_4_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_P_1_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_P_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_P_1_TVPa t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_P_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_P_text_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_P_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_P_text_2_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_2_5_special_TTP_bdkey_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end---lemma (in restricted_isoiec_9798_2_5_special_TTP_bdkey_state) P_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_P"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "LN ''Kab'' tid0 : knows t"-  shows "False"-using facts proof(sources! " LN ''Kab'' tid0 ")-  case isoiec_9798_2_5_special_TTP_bdkey_P_2_Kab note_unified facts = this facts-  thus ?thesis by (fastsimp dest!: ltk_secrecy)-next-  case isoiec_9798_2_5_special_TTP_bdkey_P_2_Kab_1 note_unified facts = this facts-  thus ?thesis by (fastsimp dest!: ltk_secrecy)-qed (insert facts, fastsimp+)?--lemma (in restricted_isoiec_9798_2_5_special_TTP_bdkey_state) A_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_special_TTP_bdkey_A_2 ) : steps t"-    "s(MV ''Kab'' tid0) : knows t"-  shows "False"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''P'' tid1) )-               ( s(MV ''A'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts-      thus ?thesis by (fastsimp dest: different_actors_A_P intro: event_predOrdI)-    next-      case swapped note_unified facts = this facts-      thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_5_special_TTP_bdkey_state) B_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_special_TTP_bdkey_B_3 ) : steps t"-    "s(MV ''Kab'' tid0) : knows t"-  shows "False"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid0),-                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc_1 tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''P'' tid1) )-               ( s(MV ''B'' tid1) ) = Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts-      thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-    next-      case swapped note_unified facts = this facts-      thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_5_special_TTP_bdkey_state) A_non_injective_agreement_B:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_special_TTP_bdkey_A_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_5_special_TTP_bdkey_B &-        ( tid1, isoiec_9798_2_5_special_TTP_bdkey_B_4 ) : steps t &-        {| s(MV ''A'' tid1), s(AV ''B'' tid1), s(MV ''P'' tid1),-           s(MV ''Kab'' tid1), s(MV ''TNa'' tid1), s(MV ''Text5'' tid1),-           LN ''TNb'' tid1, s(MV ''Text7'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''P'' tid0),-                s(MV ''Kab'' tid0), LN ''TNa'' tid0, s(MV ''Text5'' tid0),-                s(MV ''TNb'' tid0), s(MV ''Text7'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''P'' tid1) )-               ( s(MV ''A'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts-      thus ?thesis by (fastsimp dest: different_actors_A_P intro: event_predOrdI)-    next-      case swapped note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_4'', s(MV ''TNb'' tid0),-                              s(AV ''A'' tid0), s(MV ''Text7'' tid0)-                           |}-                           ( LN ''Kab'' tid1 ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-      next-        case (isoiec_9798_2_5_special_TTP_bdkey_B_4_enc tid2) note_unified facts = this facts-        thus ?thesis proof(sources! "-                         Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_3'', s(MV ''TNa'' tid2),-                                s(AV ''B'' tid2), s(MV ''Text5'' tid2)-                             |}-                             ( LN ''Kab'' tid1 ) ")-          case fake note_unified facts = this facts-          thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-        next-          case (isoiec_9798_2_5_special_TTP_bdkey_A_3_enc tid3) note_unified facts = this facts-          thus ?thesis proof(sources! "-                           Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid3,-                                  LN ''Kab'' tid1, s(AV ''B'' tid2), s(MV ''Text3'' tid3)-                               |}-                               ( Kbd ( s(AV ''A'' tid3) ) ( s(AV ''P'' tid3) ) ) ")-            case fake note_unified facts = this facts-            thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-          next-            case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc tid4) note_unified facts = this facts-            thus ?thesis proof(sources! "-                             Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid2),-                                    LN ''Kab'' tid1, s(AV ''A'' tid0), s(MV ''Text2'' tid2)-                                 |}-                                 ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid2) ) ) ")-              case fake note_unified facts = this facts-              thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-            next-              case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc_1 tid3) note_unified facts = this facts-              thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-            qed (insert facts, fastsimp+)?-          qed (insert facts, fastsimp+)?-        qed (insert facts, fastsimp+)?-      qed (insert facts, fastsimp+)?-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_5_special_TTP_bdkey_state) B_non_injective_agreement_A:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_special_TTP_bdkey_B_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_5_special_TTP_bdkey_A &-        ( tid1, isoiec_9798_2_5_special_TTP_bdkey_A_3 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(AV ''P'' tid1),-           s(MV ''Kab'' tid1), LN ''TNa'' tid1, s(MV ''Text5'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),-                s(MV ''Kab'' tid0), s(MV ''TNa'' tid0), s(MV ''Text5'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_3'', s(MV ''TNa'' tid0),-                          s(AV ''B'' tid0), s(MV ''Text5'' tid0)-                       |}-                       ( s(MV ''Kab'' tid0) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest: B_secret_Kab intro: event_predOrdI)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_A_3_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid1,-                            s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid1)-                         |}-                         ( Kbd ( s(AV ''A'' tid1) ) ( s(AV ''P'' tid1) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest: B_secret_Kab intro: event_predOrdI)-    next-      case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc tid2) note_unified facts = this facts-      hence "Kbd ( s(AV ''P'' tid2) )-                 ( s(MV ''A'' tid2) ) = Kbd ( s(AV ''A'' tid1) ) ( s(AV ''P'' tid1) )"-        by simp note facts = this facts-      thus ?thesis proof(cases rule: Kbd_cases)-        case noswap note_unified facts = this facts-        thus ?thesis by (fastsimp dest: different_actors_A_P intro: event_predOrdI)-      next-        case swapped note_unified facts = this facts-        thus ?thesis proof(sources! "-                         Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid0),-                                LN ''Kab'' tid2, s(MV ''A'' tid0), s(MV ''Text2'' tid0)-                             |}-                             ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-          case fake note_unified facts = this facts-          thus ?thesis by (fastsimp dest!: ltk_secrecy)-        next-          case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc_1 tid3) note_unified facts = this facts-          thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-        qed (insert facts, fastsimp+)?-      qed (fastsimp+)?-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_5_special_TTP_bdkey_state) A_non_injective_agreement_P:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_special_TTP_bdkey_A_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_5_special_TTP_bdkey_P &-        ( tid1, isoiec_9798_2_5_special_TTP_bdkey_P_2 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1), LN ''Kab'' tid1,-           s(MV ''TVPa'' tid1), s(MV ''Text3'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''P'' tid0),-                s(MV ''Kab'' tid0), LN ''TVPa'' tid0, s(MV ''Text3'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''P'' tid1) )-               ( s(MV ''A'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts-      thus ?thesis by (fastsimp dest: different_actors_A_P intro: event_predOrdI)-    next-      case swapped note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_5_special_TTP_bdkey_state) B_non_injective_agreement_P:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_special_TTP_bdkey_B_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_5_special_TTP_bdkey_P &-        ( tid1, isoiec_9798_2_5_special_TTP_bdkey_P_2 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1), LN ''Kab'' tid1,-           LN ''TNp'' tid1, s(MV ''Text2'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),-                s(MV ''Kab'' tid0), s(MV ''TNp'' tid0), s(MV ''Text2'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid0),-                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc_1 tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''P'' tid1) )-               ( s(MV ''B'' tid1) ) = Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_3'', s(MV ''TNa'' tid0),-                              s(AV ''B'' tid0), s(MV ''Text5'' tid0)-                           |}-                           ( LN ''Kab'' tid1 ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-      next-        case (isoiec_9798_2_5_special_TTP_bdkey_A_3_enc tid2) note_unified facts = this facts-        thus ?thesis proof(sources! "-                         Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid2,-                                LN ''Kab'' tid1, s(AV ''B'' tid0), s(MV ''Text3'' tid2)-                             |}-                             ( Kbd ( s(AV ''A'' tid2) ) ( s(AV ''P'' tid2) ) ) ")-          case fake note_unified facts = this facts-          thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-        next-          case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc tid3) note_unified facts = this facts-          thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-        qed (insert facts, fastsimp+)?-      qed (insert facts, fastsimp+)?-    next-      case swapped note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--role isoiec_9798_2_6_special_TTP_bdkey_A-where "isoiec_9798_2_6_special_TTP_bdkey_A =-  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>-  , Recv ''text_2'' ( sMV ''Text2'' )-  , Send ''2'' <| sAV ''A'', sAV ''P'', sN ''Ra'', sMV ''Rb'', sMV ''B'',-                  sMV ''Text2''-               |>-  , Recv ''3'' <| sAV ''P'', sAV ''A'', sMV ''Text5'',-                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_3_1'', sN ''Ra'',-                          sMV ''Kab'', sMV ''B'', sMV ''Text4''-                       |>-                       ( sKbd (AVar ''A'') (AVar ''P'') ),-                  sMV ''TokenPA_for_B''-               |>-  , Recv ''text_4'' <| sMV ''Text6'', sMV ''Text7'' |>-  , Send ''4'' <| sAV ''A'', sMV ''B'', sMV ''Text7'', sAV ''P'',-                  sMV ''TokenPA_for_B'',-                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_4'', sN ''Rpa'', sMV ''Rb'',-                          sMV ''Text6''-                       |>-                       ( sMV ''Kab'' )-               |>-  , Recv ''5'' <| sMV ''B'', sAV ''A'', sMV ''Text9'',-                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_5'', sMV ''Rb'', sN ''Rpa'',-                          sMV ''Text8''-                       |>-                       ( sMV ''Kab'' )-               |>-  ]"--role isoiec_9798_2_6_special_TTP_bdkey_B-where "isoiec_9798_2_6_special_TTP_bdkey_B =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>-  , Recv ''4'' <| sAV ''A'', sAV ''B'', sMV ''Text7'', sMV ''P'',-                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_3_2'', sN ''Rb'',-                          sMV ''Kab'', sAV ''A'', sMV ''Text3''-                       |>-                       ( sKbd (AVar ''B'') (MVar ''P'') ),-                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_4'', sMV ''Rpa'', sN ''Rb'',-                          sMV ''Text6''-                       |>-                       ( sMV ''Kab'' )-               |>-  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>-  , Send ''5'' <| sAV ''B'', sAV ''A'', sMV ''Text9'',-                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_5'', sN ''Rb'', sMV ''Rpa'',-                          sMV ''Text8''-                       |>-                       ( sMV ''Kab'' )-               |>-  ]"--role isoiec_9798_2_6_special_TTP_bdkey_P-where "isoiec_9798_2_6_special_TTP_bdkey_P =-  [ Recv ''2'' <| sMV ''A'', sAV ''P'', sMV ''Ra'', sMV ''Rb'', sMV ''B'',-                  sMV ''Text2''-               |>-  , Recv ''text_3'' <| sMV ''Text3'', sMV ''Text4'', sMV ''Text5'' |>-  , Send ''3'' <| sAV ''P'', sMV ''A'', sMV ''Text5'',-                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_3_1'', sMV ''Ra'',-                          sN ''Kab'', sMV ''B'', sMV ''Text4''-                       |>-                       ( sKbd (MVar ''A'') (AVar ''P'') ),-                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_3_2'', sMV ''Rb'',-                          sN ''Kab'', sMV ''A'', sMV ''Text3''-                       |>-                       ( sKbd (MVar ''B'') (AVar ''P'') )-               |>-  ]"--protocol isoiec_9798_2_6_special_TTP_bdkey-where "isoiec_9798_2_6_special_TTP_bdkey =-{ isoiec_9798_2_6_special_TTP_bdkey_A,-  isoiec_9798_2_6_special_TTP_bdkey_B, isoiec_9798_2_6_special_TTP_bdkey_P-}"--locale restricted_isoiec_9798_2_6_special_TTP_bdkey_state = isoiec_9798_2_6_special_TTP_bdkey_state +-  assumes different_actors_A_P:-    "!! tid0 tid1.-       [| roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_A;-         roleMap r tid1 = Some isoiec_9798_2_6_special_TTP_bdkey_P;-         s(AV ''P'' tid1) = s(AV ''A'' tid0)-       |] ==> False"-  assumes different_actors_B_P:-    "!! tid0 tid1.-       [| roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_B;-         roleMap r tid1 = Some isoiec_9798_2_6_special_TTP_bdkey_P;-         s(AV ''P'' tid1) = s(AV ''B'' tid0)-       |] ==> False"--type_invariant isoiec_9798_2_6_special_TTP_bdkey_msc_typing for isoiec_9798_2_6_special_TTP_bdkey-where "isoiec_9798_2_6_special_TTP_bdkey_msc_typing = mk_typing-  [ ((isoiec_9798_2_6_special_TTP_bdkey_P, ''A''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_2))-  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''B''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_1))-  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''B''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_2))-  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Kab''),-     (SumT (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_3) (NonceT isoiec_9798_2_6_special_TTP_bdkey_P ''Kab'')))-  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Kab''),-     (SumT (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_4) (NonceT isoiec_9798_2_6_special_TTP_bdkey_P ''Kab'')))-  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''P''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_4))-  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''Ra''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_2))-  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Rb''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_1))-  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''Rb''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_2))-  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Rpa''),-     (SumT (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_4) (NonceT isoiec_9798_2_6_special_TTP_bdkey_A ''Rpa'')))-  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text1''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_1))-  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Text1''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_text_1))-  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text2''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_text_2))-  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''Text2''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_2))-  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Text3''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_4))-  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''Text3''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_text_3))-  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text4''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_3))-  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''Text4''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_text_3))-  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text5''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_3))-  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''Text5''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_text_3))-  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text6''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_text_4))-  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Text6''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_4))-  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text7''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_text_4))-  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Text7''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_4))-  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text8''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_5))-  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Text8''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_text_5))-  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text9''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_5))-  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Text9''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_text_5))-  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''TokenPA_for_B''),-     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_3))-  ]"--sublocale isoiec_9798_2_6_special_TTP_bdkey_state < isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_2_6_special_TTP_bdkey_msc_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_2_6_special_TTP_bdkey_msc_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_2_6_special_TTP_bdkey_A_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_A_1_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_A_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_A_3_Kab t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_1'', LN ''Ra'' tid0,-               s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_A_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_1'', LN ''Ra'' tid0,-               s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)-            |}-            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_A_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_A_3_TokenPA_for_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_A_text_4_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_A_text_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_A_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_5'', s(MV ''Rb'' tid0),-               LN ''Rpa'' tid0, s(MV ''Text8'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_A_5_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Kab t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_2'', LN ''Rb'' tid0,-               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_B_4_P t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Rpa t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_4'', s(MV ''Rpa'' tid0),-               LN ''Rb'' tid0, s(MV ''Text6'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_2'', LN ''Rb'' tid0,-               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)-            |}-            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_4'', s(MV ''Rpa'' tid0),-               LN ''Rb'' tid0, s(MV ''Text6'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_B_text_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_B_text_5_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_2_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_2_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_2_Ra t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_2_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_text_3_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_text_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_text_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_2_6_special_TTP_bdkey_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end----lemma (in restricted_isoiec_9798_2_6_special_TTP_bdkey_state) P_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_P"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "LN ''Kab'' tid0 : knows t"-  shows "False"-using facts proof(sources! " LN ''Kab'' tid0 ")-  case isoiec_9798_2_6_special_TTP_bdkey_P_3_Kab note_unified facts = this facts-  thus ?thesis by (fastsimp dest!: ltk_secrecy)-next-  case isoiec_9798_2_6_special_TTP_bdkey_P_3_Kab_1 note_unified facts = this facts-  thus ?thesis by (fastsimp dest!: ltk_secrecy)-qed (insert facts, fastsimp+)?--lemma (in restricted_isoiec_9798_2_6_special_TTP_bdkey_state) A_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_special_TTP_bdkey_A_3 ) : steps t"-    "s(MV ''Kab'' tid0) : knows t"-  shows "False"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_1'', LN ''Ra'' tid0,-                          s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''P'' tid1) )-               ( s(MV ''A'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts-      thus ?thesis by (fastsimp dest: different_actors_A_P intro: event_predOrdI)-    next-      case swapped note_unified facts = this facts-      thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_6_special_TTP_bdkey_state) B_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_special_TTP_bdkey_B_4 ) : steps t"-    "s(MV ''Kab'' tid0) : knows t"-  shows "False"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_2'', LN ''Rb'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc_1 tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''P'' tid1) )-               ( s(MV ''B'' tid1) ) = Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts-      thus ?thesis by (fastsimp dest: different_actors_B_P intro: event_predOrdI)-    next-      case swapped note_unified facts = this facts-      thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_6_special_TTP_bdkey_state) A_non_injective_agreement_B:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_special_TTP_bdkey_A_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_6_special_TTP_bdkey_B &-        ( tid1, isoiec_9798_2_6_special_TTP_bdkey_B_5 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''P'' tid1),-           s(MV ''Kab'' tid1), s(MV ''Rpa'' tid1), LN ''Rb'' tid1,-           s(MV ''Text6'' tid1), s(MV ''Text8'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''P'' tid0),-                s(MV ''Kab'' tid0), LN ''Rpa'' tid0, s(MV ''Rb'' tid0),-                s(MV ''Text6'' tid0), s(MV ''Text8'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_1'', LN ''Ra'' tid0,-                          s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''P'' tid1) )-               ( s(MV ''A'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts-      thus ?thesis by (fastsimp dest: different_actors_A_P intro: event_predOrdI)-    next-      case swapped note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_5'', s(MV ''Rb'' tid0),-                              LN ''Rpa'' tid0, s(MV ''Text8'' tid0)-                           |}-                           ( LN ''Kab'' tid1 ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-      next-        case (isoiec_9798_2_6_special_TTP_bdkey_B_5_enc tid2) note_unified facts = this facts-        thus ?thesis proof(sources! "-                         Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_2'', LN ''Rb'' tid2,-                                LN ''Kab'' tid1, s(AV ''A'' tid2), s(MV ''Text3'' tid2)-                             |}-                             ( Kbd ( s(AV ''B'' tid2) ) ( s(MV ''P'' tid2) ) ) ")-          case fake note_unified facts = this facts-          thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-        next-          case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc_1 tid3) note_unified facts = this facts-          hence "Kbd ( s(AV ''P'' tid0) )-                     ( s(MV ''B'' tid0) ) = Kbd ( s(AV ''B'' tid2) ) ( s(MV ''P'' tid2) )"-            by simp note facts = this facts-          thus ?thesis proof(cases rule: Kbd_cases)-            case noswap note_unified facts = this facts-            thus ?thesis by (fastsimp dest: different_actors_B_P intro: event_predOrdI)-          next-            case swapped note_unified facts = this facts-            thus ?thesis proof(sources! "-                             Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_4'', LN ''Rpa'' tid0,-                                    LN ''Rb'' tid2, s(MV ''Text6'' tid2)-                                 |}-                                 ( LN ''Kab'' tid1 ) ")-              case fake note_unified facts = this facts-              thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-            next-              case (isoiec_9798_2_6_special_TTP_bdkey_A_4_enc tid3) note_unified facts = this facts-              thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-            qed (insert facts, fastsimp+)?-          qed (fastsimp+)?-        qed (insert facts, fastsimp+)?-      qed (insert facts, fastsimp+)?-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_6_special_TTP_bdkey_state) B_non_injective_agreement_A:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_special_TTP_bdkey_B_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_6_special_TTP_bdkey_A &-        ( tid1, isoiec_9798_2_6_special_TTP_bdkey_A_4 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),-           s(MV ''Kab'' tid1), LN ''Rpa'' tid1, s(MV ''Rb'' tid1),-           s(MV ''Text6'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),-                s(MV ''Kab'' tid0), s(MV ''Rpa'' tid0), LN ''Rb'' tid0,-                s(MV ''Text6'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_2'', LN ''Rb'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc_1 tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''P'' tid1) )-               ( s(MV ''B'' tid1) ) = Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts-      thus ?thesis by (fastsimp dest: different_actors_B_P intro: event_predOrdI)-    next-      case swapped note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_4'', s(MV ''Rpa'' tid0),-                              LN ''Rb'' tid0, s(MV ''Text6'' tid0)-                           |}-                           ( LN ''Kab'' tid1 ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-      next-        case (isoiec_9798_2_6_special_TTP_bdkey_A_4_enc tid2) note_unified facts = this facts-        thus ?thesis proof(sources! "-                         Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_1'', LN ''Ra'' tid2,-                                LN ''Kab'' tid1, s(MV ''B'' tid2), s(MV ''Text4'' tid2)-                             |}-                             ( Kbd ( s(AV ''A'' tid2) ) ( s(AV ''P'' tid2) ) ) ")-          case fake note_unified facts = this facts-          thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-        next-          case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc tid3) note_unified facts = this facts-          hence "Kbd ( s(AV ''A'' tid2) )-                     ( s(AV ''P'' tid2) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid1) )"-            by simp note facts = this facts-          thus ?thesis proof(cases rule: Kbd_cases)-            case noswap note_unified facts = this facts-            thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-          next-            case swapped note_unified facts = this facts-            thus ?thesis by (fastsimp dest: different_actors_A_P intro: event_predOrdI)-          qed (fastsimp+)?-        qed (insert facts, fastsimp+)?-      qed (insert facts, fastsimp+)?-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_6_special_TTP_bdkey_state) A_non_injective_agreement_P:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_special_TTP_bdkey_A_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_6_special_TTP_bdkey_P &-        ( tid1, isoiec_9798_2_6_special_TTP_bdkey_P_3 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),-           s(MV ''Ra'' tid1), LN ''Kab'' tid1, s(MV ''Text4'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''P'' tid0),-                LN ''Ra'' tid0, s(MV ''Kab'' tid0), s(MV ''Text4'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_1'', LN ''Ra'' tid0,-                          s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)-                       |}-                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''P'' tid1) )-               ( s(MV ''A'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts-      thus ?thesis by (fastsimp dest: different_actors_A_P intro: event_predOrdI)-    next-      case swapped note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_6_special_TTP_bdkey_state) B_non_injective_agreement_P:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_special_TTP_bdkey_B_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_6_special_TTP_bdkey_P &-        ( tid1, isoiec_9798_2_6_special_TTP_bdkey_P_3 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),-           s(MV ''Rb'' tid1), LN ''Kab'' tid1, s(MV ''Text3'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),-                LN ''Rb'' tid0, s(MV ''Kab'' tid0), s(MV ''Text3'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_2'', LN ''Rb'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc_1 tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''P'' tid1) )-               ( s(MV ''B'' tid1) ) = Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts-      thus ?thesis by (fastsimp dest: different_actors_B_P intro: event_predOrdI)-    next-      case swapped note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?+  "ESPLogic"+begin++role isoiec_9798_2_1_bdkey_A+where "isoiec_9798_2_1_bdkey_A =+  [ Send ''leak_A'' ( sN ''TNA'' )+  , Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>+  , Send ''1'' <| sAV ''A'', sAV ''B'', sMV ''Text2'',+                  PEnc <| sC ''isoiec_9798_2_1_enc_1'', sN ''TNA'', sAV ''B'',+                          sMV ''Text1''+                       |>+                       ( sKbd (AVar ''A'') (AVar ''B'') )+               |>+  ]"++role isoiec_9798_2_1_bdkey_B+where "isoiec_9798_2_1_bdkey_B =+  [ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Text2'',+                  PEnc <| sC ''isoiec_9798_2_1_enc_1'', sMV ''TNA'', sAV ''B'',+                          sMV ''Text1''+                       |>+                       ( sKbd (MVar ''A'') (AVar ''B'') )+               |>+  ]"++protocol isoiec_9798_2_1_bdkey+where "isoiec_9798_2_1_bdkey =+{ isoiec_9798_2_1_bdkey_A, isoiec_9798_2_1_bdkey_B }"++locale restricted_isoiec_9798_2_1_bdkey_state = isoiec_9798_2_1_bdkey_state++type_invariant isoiec_9798_2_1_bdkey_msc_typing for isoiec_9798_2_1_bdkey+where "isoiec_9798_2_1_bdkey_msc_typing = mk_typing+  [ ((isoiec_9798_2_1_bdkey_B, ''A''), (KnownT isoiec_9798_2_1_bdkey_B_1))+  , ((isoiec_9798_2_1_bdkey_B, ''TNA''),+     (SumT (KnownT isoiec_9798_2_1_bdkey_B_1) (NonceT isoiec_9798_2_1_bdkey_A ''TNA'')))+  , ((isoiec_9798_2_1_bdkey_A, ''Text1''),+     (KnownT isoiec_9798_2_1_bdkey_A_text_1))+  , ((isoiec_9798_2_1_bdkey_B, ''Text1''),+     (KnownT isoiec_9798_2_1_bdkey_B_1))+  , ((isoiec_9798_2_1_bdkey_A, ''Text2''),+     (KnownT isoiec_9798_2_1_bdkey_A_text_1))+  , ((isoiec_9798_2_1_bdkey_B, ''Text2''),+     (KnownT isoiec_9798_2_1_bdkey_B_1))+  ]"++sublocale isoiec_9798_2_1_bdkey_state < isoiec_9798_2_1_bdkey_msc_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_2_1_bdkey_msc_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_2_1_bdkey_msc_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_2_1_bdkey_A_text_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_1_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_1_bdkey_A_text_1_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_1_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_1_bdkey_B_1_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_1_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_1_bdkey_B_1_TNA t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_1_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_1_enc_1'', s(MV ''TNA'' tid0),+               s(AV ''B'' tid0), s(MV ''Text1'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_1_bdkey_B_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_1_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_1_enc_1'', s(MV ''TNA'' tid0),+               s(AV ''B'' tid0), s(MV ''Text1'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_1_bdkey_B_1_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_1_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_2_1_bdkey_msc_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_2_1_bdkey_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++lemma (in restricted_isoiec_9798_2_1_bdkey_state) B_non_injective_agreement:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_1_bdkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_1_bdkey_B_1 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_2_1_bdkey_A &+        ( tid1, isoiec_9798_2_1_bdkey_A_1 ) : steps t &+        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,+           s(MV ''Text1'' tid1)+        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),+                s(MV ''Text1'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_1_enc_1'', s(MV ''TNA'' tid0),+                          s(AV ''B'' tid0), s(MV ''Text1'' tid0)+                       |}+                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_1_bdkey_A_1_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)?+qed++role isoiec_9798_2_2_bdkey_A+where "isoiec_9798_2_2_bdkey_A =+  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''RB'', sMV ''Text1'' |>+  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>+  , Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'',+                  PEnc <| sC ''isoiec_9798_2_2_enc_2'', sMV ''RB'', sMV ''B'',+                          sMV ''Text2''+                       |>+                       ( sKbd (MVar ''B'') (AVar ''A'') )+               |>+  ]"++role isoiec_9798_2_2_bdkey_B+where "isoiec_9798_2_2_bdkey_B =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''RB'', sMV ''Text1'' |>+  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'',+                  PEnc <| sC ''isoiec_9798_2_2_enc_2'', sN ''RB'', sAV ''B'', sMV ''Text2''+                       |>+                       ( sKbd (AVar ''B'') (AVar ''A'') )+               |>+  ]"++protocol isoiec_9798_2_2_bdkey+where "isoiec_9798_2_2_bdkey =+{ isoiec_9798_2_2_bdkey_A, isoiec_9798_2_2_bdkey_B }"++locale restricted_isoiec_9798_2_2_bdkey_state = isoiec_9798_2_2_bdkey_state++type_invariant isoiec_9798_2_2_bdkey_msc_typing for isoiec_9798_2_2_bdkey+where "isoiec_9798_2_2_bdkey_msc_typing = mk_typing+  [ ((isoiec_9798_2_2_bdkey_A, ''B''), (KnownT isoiec_9798_2_2_bdkey_A_1))+  , ((isoiec_9798_2_2_bdkey_A, ''RB''), (KnownT isoiec_9798_2_2_bdkey_A_1))+  , ((isoiec_9798_2_2_bdkey_A, ''Text1''),+     (KnownT isoiec_9798_2_2_bdkey_A_1))+  , ((isoiec_9798_2_2_bdkey_B, ''Text1''),+     (KnownT isoiec_9798_2_2_bdkey_B_text_1))+  , ((isoiec_9798_2_2_bdkey_A, ''Text2''),+     (KnownT isoiec_9798_2_2_bdkey_A_text_2))+  , ((isoiec_9798_2_2_bdkey_B, ''Text2''),+     (KnownT isoiec_9798_2_2_bdkey_B_2))+  , ((isoiec_9798_2_2_bdkey_A, ''Text3''),+     (KnownT isoiec_9798_2_2_bdkey_A_text_2))+  , ((isoiec_9798_2_2_bdkey_B, ''Text3''),+     (KnownT isoiec_9798_2_2_bdkey_B_2))+  ]"++sublocale isoiec_9798_2_2_bdkey_state < isoiec_9798_2_2_bdkey_msc_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_2_2_bdkey_msc_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_2_2_bdkey_msc_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_2_2_bdkey_A_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_2_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_2_bdkey_A_1_RB t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_2_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_2_bdkey_A_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_2_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_2_bdkey_A_text_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_2_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_2_bdkey_A_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_2_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_2_bdkey_B_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_2_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_2_enc_2'', LN ''RB'' tid0, s(AV ''B'' tid0),+               s(MV ''Text2'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_2_bdkey_B_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_2_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_2_2_bdkey_msc_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_2_2_bdkey_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++lemma (in restricted_isoiec_9798_2_2_bdkey_state) B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_2_bdkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_2_bdkey_B_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_2_bdkey_A &+          ( tid1, isoiec_9798_2_2_bdkey_A_2 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(MV ''RB'' tid1),+             s(MV ''Text2'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''RB'' tid0,+                  s(MV ''Text2'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_2_enc_2'', LN ''RB'' tid0, s(AV ''B'' tid0),+                              s(MV ''Text2'' tid0)+                           |}+                           ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_2_bdkey_A_2_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++role isoiec_9798_2_3_bdkey_A+where "isoiec_9798_2_3_bdkey_A =+  [ Send ''leak_A'' ( sN ''TNA'' )+  , Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>+  , Send ''1'' <| sAV ''A'', sAV ''B'', sMV ''Text2'',+                  PEnc <| sC ''isoiec_9798_2_3_enc_1'', sN ''TNA'', sAV ''B'',+                          sMV ''Text1''+                       |>+                       ( sKbd (AVar ''A'') (AVar ''B'') )+               |>+  , Recv ''2'' <| sAV ''B'', sAV ''A'', sMV ''Text4'',+                  PEnc <| sC ''isoiec_9798_2_3_enc_2'', sMV ''TNB'', sAV ''A'',+                          sMV ''Text3''+                       |>+                       ( sKbd (AVar ''B'') (AVar ''A'') )+               |>+  ]"++role isoiec_9798_2_3_bdkey_B+where "isoiec_9798_2_3_bdkey_B =+  [ Send ''leak_B'' ( sN ''TNB'' )+  , Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Text2'',+                  PEnc <| sC ''isoiec_9798_2_3_enc_1'', sMV ''TNA'', sAV ''B'',+                          sMV ''Text1''+                       |>+                       ( sKbd (MVar ''A'') (AVar ''B'') )+               |>+  , Recv ''text_2'' <| sMV ''Text3'', sMV ''Text4'' |>+  , Send ''2'' <| sAV ''B'', sMV ''A'', sMV ''Text4'',+                  PEnc <| sC ''isoiec_9798_2_3_enc_2'', sN ''TNB'', sMV ''A'',+                          sMV ''Text3''+                       |>+                       ( sKbd (AVar ''B'') (MVar ''A'') )+               |>+  ]"++protocol isoiec_9798_2_3_bdkey+where "isoiec_9798_2_3_bdkey =+{ isoiec_9798_2_3_bdkey_A, isoiec_9798_2_3_bdkey_B }"++locale restricted_isoiec_9798_2_3_bdkey_state = isoiec_9798_2_3_bdkey_state++type_invariant isoiec_9798_2_3_bdkey_msc_typing for isoiec_9798_2_3_bdkey+where "isoiec_9798_2_3_bdkey_msc_typing = mk_typing+  [ ((isoiec_9798_2_3_bdkey_B, ''A''), (KnownT isoiec_9798_2_3_bdkey_B_1))+  , ((isoiec_9798_2_3_bdkey_B, ''TNA''),+     (SumT (KnownT isoiec_9798_2_3_bdkey_B_1) (NonceT isoiec_9798_2_3_bdkey_A ''TNA'')))+  , ((isoiec_9798_2_3_bdkey_A, ''TNB''),+     (SumT (KnownT isoiec_9798_2_3_bdkey_A_2) (NonceT isoiec_9798_2_3_bdkey_B ''TNB'')))+  , ((isoiec_9798_2_3_bdkey_A, ''Text1''),+     (KnownT isoiec_9798_2_3_bdkey_A_text_1))+  , ((isoiec_9798_2_3_bdkey_B, ''Text1''),+     (KnownT isoiec_9798_2_3_bdkey_B_1))+  , ((isoiec_9798_2_3_bdkey_A, ''Text2''),+     (KnownT isoiec_9798_2_3_bdkey_A_text_1))+  , ((isoiec_9798_2_3_bdkey_B, ''Text2''),+     (KnownT isoiec_9798_2_3_bdkey_B_1))+  , ((isoiec_9798_2_3_bdkey_A, ''Text3''),+     (KnownT isoiec_9798_2_3_bdkey_A_2))+  , ((isoiec_9798_2_3_bdkey_B, ''Text3''),+     (KnownT isoiec_9798_2_3_bdkey_B_text_2))+  , ((isoiec_9798_2_3_bdkey_A, ''Text4''),+     (KnownT isoiec_9798_2_3_bdkey_A_2))+  , ((isoiec_9798_2_3_bdkey_B, ''Text4''),+     (KnownT isoiec_9798_2_3_bdkey_B_text_2))+  ]"++sublocale isoiec_9798_2_3_bdkey_state < isoiec_9798_2_3_bdkey_msc_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_2_3_bdkey_msc_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_2_3_bdkey_msc_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_2_3_bdkey_A_text_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_bdkey_A_text_1_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_bdkey_A_2_TNB t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_3_enc_2'', s(MV ''TNB'' tid0),+               s(AV ''A'' tid0), s(MV ''Text3'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_3_bdkey_A_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_3_enc_2'', s(MV ''TNB'' tid0),+               s(AV ''A'' tid0), s(MV ''Text3'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_3_bdkey_A_2_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_bdkey_B_1_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_bdkey_B_1_TNA t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_3_enc_1'', s(MV ''TNA'' tid0),+               s(AV ''B'' tid0), s(MV ''Text1'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_3_bdkey_B_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_3_enc_1'', s(MV ''TNA'' tid0),+               s(AV ''B'' tid0), s(MV ''Text1'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_3_bdkey_B_1_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_bdkey_B_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_bdkey_B_text_2_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_2_3_bdkey_msc_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_2_3_bdkey_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++lemma (in restricted_isoiec_9798_2_3_bdkey_state) A_non_injective_agreement:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_3_bdkey_A"+    "RLKR(s(AV ''A'' tid0)) ~: reveals t"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_3_bdkey_A_2 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_2_3_bdkey_B &+        ( tid1, isoiec_9798_2_3_bdkey_B_2 ) : steps t &+        {| s(MV ''A'' tid1), s(AV ''B'' tid1), LN ''TNB'' tid1,+           s(MV ''Text3'' tid1)+        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNB'' tid0),+                s(MV ''Text3'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_3_enc_2'', s(MV ''TNB'' tid0),+                          s(AV ''A'' tid0), s(MV ''Text3'' tid0)+                       |}+                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_3_bdkey_B_2_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_3_bdkey_state) B_non_injective_agreement:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_3_bdkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_3_bdkey_B_1 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_2_3_bdkey_A &+        ( tid1, isoiec_9798_2_3_bdkey_A_1 ) : steps t &+        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,+           s(MV ''Text1'' tid1)+        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),+                s(MV ''Text1'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_3_enc_1'', s(MV ''TNA'' tid0),+                          s(AV ''B'' tid0), s(MV ''Text1'' tid0)+                       |}+                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_3_bdkey_A_1_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)?+qed++role isoiec_9798_2_4_bdkey_A+where "isoiec_9798_2_4_bdkey_A =+  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''RB'', sMV ''Text1'' |>+  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>+  , Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'',+                  PEnc <| sC ''isoiec_9798_2_4_enc_1'', sN ''RA'', sMV ''RB'', sMV ''B'',+                          sMV ''Text2''+                       |>+                       ( sKbd (AVar ''A'') (MVar ''B'') )+               |>+  , Recv ''3'' <| sMV ''B'', sAV ''A'', sMV ''Text5'',+                  PEnc <| sC ''isoiec_9798_2_4_enc_2'', sMV ''RB'', sN ''RA'',+                          sMV ''Text4''+                       |>+                       ( sKbd (AVar ''A'') (MVar ''B'') )+               |>+  ]"++role isoiec_9798_2_4_bdkey_B+where "isoiec_9798_2_4_bdkey_B =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''RB'', sMV ''Text1'' |>+  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'',+                  PEnc <| sC ''isoiec_9798_2_4_enc_1'', sMV ''RA'', sN ''RB'', sAV ''B'',+                          sMV ''Text2''+                       |>+                       ( sKbd (AVar ''A'') (AVar ''B'') )+               |>+  , Recv ''text_3'' <| sMV ''Text4'', sMV ''Text5'' |>+  , Send ''3'' <| sAV ''B'', sAV ''A'', sMV ''Text5'',+                  PEnc <| sC ''isoiec_9798_2_4_enc_2'', sN ''RB'', sMV ''RA'',+                          sMV ''Text4''+                       |>+                       ( sKbd (AVar ''A'') (AVar ''B'') )+               |>+  ]"++protocol isoiec_9798_2_4_bdkey+where "isoiec_9798_2_4_bdkey =+{ isoiec_9798_2_4_bdkey_A, isoiec_9798_2_4_bdkey_B }"++locale restricted_isoiec_9798_2_4_bdkey_state = isoiec_9798_2_4_bdkey_state++type_invariant isoiec_9798_2_4_bdkey_msc_typing for isoiec_9798_2_4_bdkey+where "isoiec_9798_2_4_bdkey_msc_typing = mk_typing+  [ ((isoiec_9798_2_4_bdkey_A, ''B''), (KnownT isoiec_9798_2_4_bdkey_A_1))+  , ((isoiec_9798_2_4_bdkey_B, ''RA''),+     (SumT (KnownT isoiec_9798_2_4_bdkey_B_2) (NonceT isoiec_9798_2_4_bdkey_A ''RA'')))+  , ((isoiec_9798_2_4_bdkey_A, ''RB''), (KnownT isoiec_9798_2_4_bdkey_A_1))+  , ((isoiec_9798_2_4_bdkey_A, ''Text1''),+     (KnownT isoiec_9798_2_4_bdkey_A_1))+  , ((isoiec_9798_2_4_bdkey_B, ''Text1''),+     (KnownT isoiec_9798_2_4_bdkey_B_text_1))+  , ((isoiec_9798_2_4_bdkey_A, ''Text2''),+     (KnownT isoiec_9798_2_4_bdkey_A_text_2))+  , ((isoiec_9798_2_4_bdkey_B, ''Text2''),+     (KnownT isoiec_9798_2_4_bdkey_B_2))+  , ((isoiec_9798_2_4_bdkey_A, ''Text3''),+     (KnownT isoiec_9798_2_4_bdkey_A_text_2))+  , ((isoiec_9798_2_4_bdkey_B, ''Text3''),+     (KnownT isoiec_9798_2_4_bdkey_B_2))+  , ((isoiec_9798_2_4_bdkey_A, ''Text4''),+     (KnownT isoiec_9798_2_4_bdkey_A_3))+  , ((isoiec_9798_2_4_bdkey_B, ''Text4''),+     (KnownT isoiec_9798_2_4_bdkey_B_text_3))+  , ((isoiec_9798_2_4_bdkey_A, ''Text5''),+     (KnownT isoiec_9798_2_4_bdkey_A_3))+  , ((isoiec_9798_2_4_bdkey_B, ''Text5''),+     (KnownT isoiec_9798_2_4_bdkey_B_text_3))+  ]"++sublocale isoiec_9798_2_4_bdkey_state < isoiec_9798_2_4_bdkey_msc_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_2_4_bdkey_msc_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_2_4_bdkey_msc_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_2_4_bdkey_A_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_bdkey_A_1_RB t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_bdkey_A_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_bdkey_A_text_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_bdkey_A_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_bdkey_A_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_4_enc_2'', s(MV ''RB'' tid0), LN ''RA'' tid0,+               s(MV ''Text4'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_4_bdkey_A_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_bdkey_B_2_RA t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_4_enc_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,+               s(AV ''B'' tid0), s(MV ''Text2'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_4_bdkey_B_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_4_enc_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,+               s(AV ''B'' tid0), s(MV ''Text2'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_4_bdkey_B_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_bdkey_B_text_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_bdkey_B_text_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_2_4_bdkey_msc_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_2_4_bdkey_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++lemma (in restricted_isoiec_9798_2_4_bdkey_state) A_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_4_bdkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_4_bdkey_A_3 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_4_bdkey_B &+          ( tid1, isoiec_9798_2_4_bdkey_B_3 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''RA'' tid1), LN ''RB'' tid1,+             s(MV ''Text2'' tid1), s(MV ''Text4'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''RA'' tid0,+                  s(MV ''RB'' tid0), s(MV ''Text2'' tid0), s(MV ''Text4'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_4_enc_2'', s(MV ''RB'' tid0), LN ''RA'' tid0,+                              s(MV ''Text4'' tid0)+                           |}+                           ( Kbd ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_4_bdkey_B_3_enc tid1) note_unified facts = this facts+        hence "Kbd ( s(AV ''A'' tid1) )+                   ( s(AV ''B'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) )"+          by simp note facts = this facts+        thus ?thesis proof(cases rule: Kbd_cases)+          case noswap note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_2_4_enc_1'', LN ''RA'' tid0, LN ''RB'' tid1,+                                  s(AV ''B'' tid1), s(MV ''Text2'' tid1)+                               |}+                               ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid1) ) ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest!: ltk_secrecy)+          next+            case (isoiec_9798_2_4_bdkey_A_2_enc tid2) note_unified facts = this facts+            thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+          qed (insert facts, fastforce+)?+        next+          case swapped note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_2_4_enc_1'', LN ''RA'' tid0, LN ''RB'' tid1,+                                  s(AV ''A'' tid0), s(MV ''Text2'' tid1)+                               |}+                               ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''A'' tid1) ) ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest!: ltk_secrecy)+          next+            case (isoiec_9798_2_4_bdkey_A_2_enc tid2) note_unified facts = this facts+            thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+          qed (insert facts, fastforce+)?+        qed (fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_4_bdkey_state) B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_4_bdkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_4_bdkey_B_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_4_bdkey_A &+          ( tid1, isoiec_9798_2_4_bdkey_A_2 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''RA'' tid1, s(MV ''RB'' tid1),+             s(MV ''Text2'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''RA'' tid0),+                  LN ''RB'' tid0, s(MV ''Text2'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_4_enc_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,+                              s(AV ''B'' tid0), s(MV ''Text2'' tid0)+                           |}+                           ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_4_bdkey_A_2_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++role isoiec_9798_2_5_bdkey_A+where "isoiec_9798_2_5_bdkey_A =+  [ Send ''leak_A'' <| sN ''TVPa'', sN ''TNa'' |>+  , Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''A'', sAV ''P'', sN ''TVPa'', sAV ''B'',+                  sMV ''Text1''+               |>+  , Recv ''2'' <| sAV ''P'', sAV ''A'', sMV ''Text4'',+                  PEnc <| sC ''isoiec_9798_2_5_enc_2_1'', sN ''TVPa'', sMV ''Kab'',+                          sAV ''A'', sAV ''B'', sMV ''Text3''+                       |>+                       ( sKbd (AVar ''A'') (AVar ''P'') ),+                  sMV ''TokenPA_for_B''+               |>+  , Recv ''text_3'' <| sMV ''Text5'', sMV ''Text6'' |>+  , Send ''3'' <| sAV ''A'', sAV ''B'', sMV ''Text6'', sAV ''P'',+                  sMV ''TokenPA_for_B'',+                  PEnc <| sC ''isoiec_9798_2_5_enc_3'', sN ''TNa'', sAV ''B'',+                          sMV ''Text5''+                       |>+                       ( sMV ''Kab'' )+               |>+  , Recv ''4'' <| sAV ''B'', sAV ''A'', sMV ''Text8'',+                  PEnc <| sC ''isoiec_9798_2_5_enc_4'', sMV ''TNb'', sAV ''A'',+                          sMV ''Text7''+                       |>+                       ( sMV ''Kab'' )+               |>+  ]"++role isoiec_9798_2_5_bdkey_B+where "isoiec_9798_2_5_bdkey_B =+  [ Send ''leak_B'' ( sN ''TNb'' )+  , Recv ''3'' <| sMV ''A'', sAV ''B'', sMV ''Text6'', sMV ''P'',+                  PEnc <| sC ''isoiec_9798_2_5_enc_2_2'', sMV ''TNp'', sMV ''Kab'',+                          sMV ''A'', sAV ''B'', sMV ''Text2''+                       |>+                       ( sKbd (AVar ''B'') (MVar ''P'') ),+                  PEnc <| sC ''isoiec_9798_2_5_enc_3'', sMV ''TNa'', sAV ''B'',+                          sMV ''Text5''+                       |>+                       ( sMV ''Kab'' )+               |>+  , Recv ''text_4'' <| sMV ''Text7'', sMV ''Text8'' |>+  , Send ''4'' <| sAV ''B'', sMV ''A'', sMV ''Text8'',+                  PEnc <| sC ''isoiec_9798_2_5_enc_4'', sN ''TNb'', sMV ''A'',+                          sMV ''Text7''+                       |>+                       ( sMV ''Kab'' )+               |>+  ]"++role isoiec_9798_2_5_bdkey_P+where "isoiec_9798_2_5_bdkey_P =+  [ Send ''leak_P'' ( sN ''TNp'' )+  , Recv ''1'' <| sMV ''A'', sAV ''P'', sMV ''TVPa'', sMV ''B'',+                  sMV ''Text1''+               |>+  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'', sMV ''Text4'' |>+  , Send ''2'' <| sAV ''P'', sMV ''A'', sMV ''Text4'',+                  PEnc <| sC ''isoiec_9798_2_5_enc_2_1'', sMV ''TVPa'', sN ''Kab'',+                          sMV ''A'', sMV ''B'', sMV ''Text3''+                       |>+                       ( sKbd (MVar ''A'') (AVar ''P'') ),+                  PEnc <| sC ''isoiec_9798_2_5_enc_2_2'', sN ''TNp'', sN ''Kab'',+                          sMV ''A'', sMV ''B'', sMV ''Text2''+                       |>+                       ( sKbd (MVar ''B'') (AVar ''P'') )+               |>+  ]"++protocol isoiec_9798_2_5_bdkey+where "isoiec_9798_2_5_bdkey =+{ isoiec_9798_2_5_bdkey_A, isoiec_9798_2_5_bdkey_B,+  isoiec_9798_2_5_bdkey_P+}"++locale restricted_isoiec_9798_2_5_bdkey_state = isoiec_9798_2_5_bdkey_state++type_invariant isoiec_9798_2_5_bdkey_msc_typing for isoiec_9798_2_5_bdkey+where "isoiec_9798_2_5_bdkey_msc_typing = mk_typing+  [ ((isoiec_9798_2_5_bdkey_B, ''A''), (KnownT isoiec_9798_2_5_bdkey_B_3))+  , ((isoiec_9798_2_5_bdkey_P, ''A''), (KnownT isoiec_9798_2_5_bdkey_P_1))+  , ((isoiec_9798_2_5_bdkey_P, ''B''), (KnownT isoiec_9798_2_5_bdkey_P_1))+  , ((isoiec_9798_2_5_bdkey_A, ''Kab''),+     (SumT (KnownT isoiec_9798_2_5_bdkey_A_2) (NonceT isoiec_9798_2_5_bdkey_P ''Kab'')))+  , ((isoiec_9798_2_5_bdkey_B, ''Kab''),+     (SumT (KnownT isoiec_9798_2_5_bdkey_B_3) (NonceT isoiec_9798_2_5_bdkey_P ''Kab'')))+  , ((isoiec_9798_2_5_bdkey_B, ''P''), (KnownT isoiec_9798_2_5_bdkey_B_3))+  , ((isoiec_9798_2_5_bdkey_B, ''TNa''),+     (SumT (KnownT isoiec_9798_2_5_bdkey_B_3) (NonceT isoiec_9798_2_5_bdkey_A ''TNa'')))+  , ((isoiec_9798_2_5_bdkey_A, ''TNb''),+     (SumT (KnownT isoiec_9798_2_5_bdkey_A_4) (NonceT isoiec_9798_2_5_bdkey_B ''TNb'')))+  , ((isoiec_9798_2_5_bdkey_B, ''TNp''),+     (SumT (KnownT isoiec_9798_2_5_bdkey_B_3) (NonceT isoiec_9798_2_5_bdkey_P ''TNp'')))+  , ((isoiec_9798_2_5_bdkey_P, ''TVPa''),+     (KnownT isoiec_9798_2_5_bdkey_P_1))+  , ((isoiec_9798_2_5_bdkey_A, ''Text1''),+     (KnownT isoiec_9798_2_5_bdkey_A_text_1))+  , ((isoiec_9798_2_5_bdkey_P, ''Text1''),+     (KnownT isoiec_9798_2_5_bdkey_P_1))+  , ((isoiec_9798_2_5_bdkey_B, ''Text2''),+     (KnownT isoiec_9798_2_5_bdkey_B_3))+  , ((isoiec_9798_2_5_bdkey_P, ''Text2''),+     (KnownT isoiec_9798_2_5_bdkey_P_text_2))+  , ((isoiec_9798_2_5_bdkey_A, ''Text3''),+     (KnownT isoiec_9798_2_5_bdkey_A_2))+  , ((isoiec_9798_2_5_bdkey_P, ''Text3''),+     (KnownT isoiec_9798_2_5_bdkey_P_text_2))+  , ((isoiec_9798_2_5_bdkey_A, ''Text4''),+     (KnownT isoiec_9798_2_5_bdkey_A_2))+  , ((isoiec_9798_2_5_bdkey_P, ''Text4''),+     (KnownT isoiec_9798_2_5_bdkey_P_text_2))+  , ((isoiec_9798_2_5_bdkey_A, ''Text5''),+     (KnownT isoiec_9798_2_5_bdkey_A_text_3))+  , ((isoiec_9798_2_5_bdkey_B, ''Text5''),+     (KnownT isoiec_9798_2_5_bdkey_B_3))+  , ((isoiec_9798_2_5_bdkey_A, ''Text6''),+     (KnownT isoiec_9798_2_5_bdkey_A_text_3))+  , ((isoiec_9798_2_5_bdkey_B, ''Text6''),+     (KnownT isoiec_9798_2_5_bdkey_B_3))+  , ((isoiec_9798_2_5_bdkey_A, ''Text7''),+     (KnownT isoiec_9798_2_5_bdkey_A_4))+  , ((isoiec_9798_2_5_bdkey_B, ''Text7''),+     (KnownT isoiec_9798_2_5_bdkey_B_text_4))+  , ((isoiec_9798_2_5_bdkey_A, ''Text8''),+     (KnownT isoiec_9798_2_5_bdkey_A_4))+  , ((isoiec_9798_2_5_bdkey_B, ''Text8''),+     (KnownT isoiec_9798_2_5_bdkey_B_text_4))+  , ((isoiec_9798_2_5_bdkey_A, ''TokenPA_for_B''),+     (KnownT isoiec_9798_2_5_bdkey_A_2))+  ]"++sublocale isoiec_9798_2_5_bdkey_state < isoiec_9798_2_5_bdkey_msc_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_2_5_bdkey_msc_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_2_5_bdkey_msc_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_2_5_bdkey_A_2_Kab t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,+               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),+               s(MV ''Text3'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_bdkey_A_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,+               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),+               s(MV ''Text3'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_bdkey_A_2_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_A_2_TokenPA_for_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_A_text_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_A_text_3_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_A_4_TNb t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_4'', s(MV ''TNb'' tid0),+               s(AV ''A'' tid0), s(MV ''Text7'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_bdkey_A_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_4'', s(MV ''TNb'' tid0),+               s(AV ''A'' tid0), s(MV ''Text7'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_bdkey_A_4_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_B_3_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_B_3_Kab t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),+               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(AV ''B'' tid0),+               s(MV ''Text2'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_bdkey_B_3_P t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_B_3_TNa t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid0),+               s(AV ''B'' tid0), s(MV ''Text5'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_bdkey_B_3_TNp t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),+               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(AV ''B'' tid0),+               s(MV ''Text2'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_bdkey_B_3_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),+               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(AV ''B'' tid0),+               s(MV ''Text2'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_bdkey_B_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid0),+               s(AV ''B'' tid0), s(MV ''Text5'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_bdkey_B_3_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_B_text_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_B_text_4_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_P_1_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_P_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_P_1_TVPa t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_P_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_P_text_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_P_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_bdkey_P_text_2_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_2_5_bdkey_msc_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_2_5_bdkey_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++lemma (in restricted_isoiec_9798_2_5_bdkey_state) P_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_bdkey_P"+    "RLKR(s(AV ''P'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''B'' tid0)) ~: reveals t"+    "LN ''Kab'' tid0 : knows t"+  shows "False"+using facts proof(sources! " LN ''Kab'' tid0 ")+  case isoiec_9798_2_5_bdkey_P_2_Kab note_unified facts = this facts+  thus ?thesis by (fastforce dest!: ltk_secrecy)+next+  case isoiec_9798_2_5_bdkey_P_2_Kab_1 note_unified facts = this facts+  thus ?thesis by (fastforce dest!: ltk_secrecy)+qed (insert facts, fastforce+)?++lemma (in restricted_isoiec_9798_2_5_bdkey_state) A_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_bdkey_A"+    "RLKR(s(AV ''A'' tid0)) ~: reveals t"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(AV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_5_bdkey_A_2 ) : steps t"+    "s(MV ''Kab'' tid0) : knows t"+  shows "False"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,+                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),+                          s(MV ''Text3'' tid0)+                       |}+                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_5_bdkey_P_2_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_5_bdkey_state) B_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_bdkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_5_bdkey_B_3 ) : steps t"+    "s(MV ''Kab'' tid0) : knows t"+  shows "False"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),+                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(AV ''B'' tid0),+                          s(MV ''Text2'' tid0)+                       |}+                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_5_bdkey_P_2_enc_1 tid1) note_unified facts = this facts+    thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_5_bdkey_state) A_injective_agreement_B:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_5_bdkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(AV ''P'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_5_bdkey_A_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_5_bdkey_B &+          ( tid1, isoiec_9798_2_5_bdkey_B_4 ) : steps t &+          {| s(MV ''A'' tid1), s(AV ''B'' tid1), s(MV ''P'' tid1),+             s(MV ''Kab'' tid1), s(MV ''TNa'' tid1), s(MV ''Text5'' tid1),+             LN ''TNb'' tid1, s(MV ''Text7'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''P'' tid0),+                  s(MV ''Kab'' tid0), LN ''TNa'' tid0, s(MV ''Text5'' tid0),+                  s(MV ''TNb'' tid0), s(MV ''Text7'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),+                              s(MV ''Text3'' tid0)+                           |}+                           ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_5_bdkey_P_2_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_2_5_enc_4'', s(MV ''TNb'' tid0),+                                s(AV ''A'' tid0), s(MV ''Text7'' tid0)+                             |}+                             ( LN ''Kab'' tid1 ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+        next+          case (isoiec_9798_2_5_bdkey_B_4_enc tid2) note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid2),+                                  LN ''Kab'' tid1, s(AV ''A'' tid0), s(AV ''B'' tid2), s(MV ''Text2'' tid2)+                               |}+                               ( Kbd ( s(AV ''B'' tid2) ) ( s(MV ''P'' tid2) ) ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+          next+            case (isoiec_9798_2_5_bdkey_P_2_enc_1 tid3) note_unified facts = this facts+            thus ?thesis proof(sources! "+                             Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid2),+                                    s(AV ''B'' tid0), s(MV ''Text5'' tid2)+                                 |}+                                 ( LN ''Kab'' tid1 ) ")+              case fake note_unified facts = this facts+              thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+            next+              case (isoiec_9798_2_5_bdkey_A_3_enc tid3) note_unified facts = this facts+              thus ?thesis proof(sources! "+                               Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid3, LN ''Kab'' tid1,+                                      s(AV ''A'' tid3), s(AV ''B'' tid0), s(MV ''Text3'' tid3)+                                   |}+                                   ( Kbd ( s(AV ''A'' tid3) ) ( s(AV ''P'' tid3) ) ) ")+                case fake note_unified facts = this facts+                thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+              next+                case (isoiec_9798_2_5_bdkey_P_2_enc tid4) note_unified facts = this facts+                thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+              qed (insert facts, fastforce+)?+            qed (insert facts, fastforce+)?+          qed (insert facts, fastforce+)?+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_5_bdkey_state) B_non_injective_agreement_A:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_bdkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_5_bdkey_B_3 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_2_5_bdkey_A &+        ( tid1, isoiec_9798_2_5_bdkey_A_3 ) : steps t &+        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(AV ''P'' tid1),+           s(MV ''Kab'' tid1), LN ''TNa'' tid1, s(MV ''Text5'' tid1)+        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),+                s(MV ''Kab'' tid0), s(MV ''TNa'' tid0), s(MV ''Text5'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),+                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(AV ''B'' tid0),+                          s(MV ''Text2'' tid0)+                       |}+                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_5_bdkey_P_2_enc_1 tid1) note_unified facts = this facts+    thus ?thesis proof(sources! "+                     Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid0),+                            s(AV ''B'' tid0), s(MV ''Text5'' tid0)+                         |}+                         ( LN ''Kab'' tid1 ) ")+      case fake note_unified facts = this facts+      thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+    next+      case (isoiec_9798_2_5_bdkey_A_3_enc tid2) note_unified facts = this facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid2, LN ''Kab'' tid1,+                              s(AV ''A'' tid2), s(AV ''B'' tid0), s(MV ''Text3'' tid2)+                           |}+                           ( Kbd ( s(AV ''A'' tid2) ) ( s(AV ''P'' tid2) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+      next+        case (isoiec_9798_2_5_bdkey_P_2_enc tid3) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed (insert facts, fastforce+)?+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_5_bdkey_state) A_injective_agreement_P:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_5_bdkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(AV ''P'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_5_bdkey_A_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_5_bdkey_P &+          ( tid1, isoiec_9798_2_5_bdkey_P_2 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1), LN ''Kab'' tid1,+             s(MV ''TVPa'' tid1), s(MV ''Text3'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''P'' tid0),+                  s(MV ''Kab'' tid0), LN ''TVPa'' tid0, s(MV ''Text3'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),+                              s(MV ''Text3'' tid0)+                           |}+                           ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_5_bdkey_P_2_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_5_bdkey_state) B_non_injective_agreement_P:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_bdkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_5_bdkey_B_3 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_2_5_bdkey_P &+        ( tid1, isoiec_9798_2_5_bdkey_P_2 ) : steps t &+        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1), LN ''Kab'' tid1,+           LN ''TNp'' tid1, s(MV ''Text2'' tid1)+        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),+                s(MV ''Kab'' tid0), s(MV ''TNp'' tid0), s(MV ''Text2'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),+                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(AV ''B'' tid0),+                          s(MV ''Text2'' tid0)+                       |}+                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_5_bdkey_P_2_enc_1 tid1) note_unified facts = this facts+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)?+qed++role isoiec_9798_2_6_bdkey_A+where "isoiec_9798_2_6_bdkey_A =+  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>+  , Recv ''text_2'' ( sMV ''Text2'' )+  , Send ''2'' <| sAV ''A'', sAV ''P'', sN ''Ra'', sMV ''Rb'', sMV ''B'',+                  sMV ''Text2''+               |>+  , Recv ''3'' <| sAV ''P'', sAV ''A'', sMV ''Text5'',+                  PEnc <| sC ''isoiec_9798_2_6_enc_3_1'', sN ''Ra'', sMV ''Kab'',+                          sAV ''A'', sMV ''B'', sMV ''Text4''+                       |>+                       ( sKbd (AVar ''A'') (AVar ''P'') ),+                  sMV ''TokenPA_for_B''+               |>+  , Recv ''text_4'' <| sMV ''Text6'', sMV ''Text7'' |>+  , Send ''4'' <| sAV ''A'', sMV ''B'', sMV ''Text7'', sAV ''P'',+                  sMV ''TokenPA_for_B'',+                  PEnc <| sC ''isoiec_9798_2_6_enc_4'', sN ''Rpa'', sMV ''Rb'',+                          sMV ''Text6''+                       |>+                       ( sMV ''Kab'' )+               |>+  , Recv ''5'' <| sMV ''B'', sAV ''A'', sMV ''Text9'',+                  PEnc <| sC ''isoiec_9798_2_6_enc_5'', sMV ''Rb'', sN ''Rpa'',+                          sMV ''Text8''+                       |>+                       ( sMV ''Kab'' )+               |>+  ]"++role isoiec_9798_2_6_bdkey_B+where "isoiec_9798_2_6_bdkey_B =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>+  , Recv ''4'' <| sAV ''A'', sAV ''B'', sMV ''Text7'', sMV ''P'',+                  PEnc <| sC ''isoiec_9798_2_6_enc_3_2'', sN ''Rb'', sMV ''Kab'',+                          sAV ''A'', sAV ''B'', sMV ''Text3''+                       |>+                       ( sKbd (AVar ''B'') (MVar ''P'') ),+                  PEnc <| sC ''isoiec_9798_2_6_enc_4'', sMV ''Rpa'', sN ''Rb'',+                          sMV ''Text6''+                       |>+                       ( sMV ''Kab'' )+               |>+  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>+  , Send ''5'' <| sAV ''B'', sAV ''A'', sMV ''Text9'',+                  PEnc <| sC ''isoiec_9798_2_6_enc_5'', sN ''Rb'', sMV ''Rpa'',+                          sMV ''Text8''+                       |>+                       ( sMV ''Kab'' )+               |>+  ]"++role isoiec_9798_2_6_bdkey_P+where "isoiec_9798_2_6_bdkey_P =+  [ Recv ''2'' <| sMV ''A'', sAV ''P'', sMV ''Ra'', sMV ''Rb'', sMV ''B'',+                  sMV ''Text2''+               |>+  , Recv ''text_3'' <| sMV ''Text3'', sMV ''Text4'', sMV ''Text5'' |>+  , Send ''3'' <| sAV ''P'', sMV ''A'', sMV ''Text5'',+                  PEnc <| sC ''isoiec_9798_2_6_enc_3_1'', sMV ''Ra'', sN ''Kab'',+                          sMV ''A'', sMV ''B'', sMV ''Text4''+                       |>+                       ( sKbd (MVar ''A'') (AVar ''P'') ),+                  PEnc <| sC ''isoiec_9798_2_6_enc_3_2'', sMV ''Rb'', sN ''Kab'',+                          sMV ''A'', sMV ''B'', sMV ''Text3''+                       |>+                       ( sKbd (MVar ''B'') (AVar ''P'') )+               |>+  ]"++protocol isoiec_9798_2_6_bdkey+where "isoiec_9798_2_6_bdkey =+{ isoiec_9798_2_6_bdkey_A, isoiec_9798_2_6_bdkey_B,+  isoiec_9798_2_6_bdkey_P+}"++locale restricted_isoiec_9798_2_6_bdkey_state = isoiec_9798_2_6_bdkey_state++type_invariant isoiec_9798_2_6_bdkey_msc_typing for isoiec_9798_2_6_bdkey+where "isoiec_9798_2_6_bdkey_msc_typing = mk_typing+  [ ((isoiec_9798_2_6_bdkey_P, ''A''), (KnownT isoiec_9798_2_6_bdkey_P_2))+  , ((isoiec_9798_2_6_bdkey_A, ''B''), (KnownT isoiec_9798_2_6_bdkey_A_1))+  , ((isoiec_9798_2_6_bdkey_P, ''B''), (KnownT isoiec_9798_2_6_bdkey_P_2))+  , ((isoiec_9798_2_6_bdkey_A, ''Kab''),+     (SumT (KnownT isoiec_9798_2_6_bdkey_A_3) (NonceT isoiec_9798_2_6_bdkey_P ''Kab'')))+  , ((isoiec_9798_2_6_bdkey_B, ''Kab''),+     (SumT (KnownT isoiec_9798_2_6_bdkey_B_4) (NonceT isoiec_9798_2_6_bdkey_P ''Kab'')))+  , ((isoiec_9798_2_6_bdkey_B, ''P''), (KnownT isoiec_9798_2_6_bdkey_B_4))+  , ((isoiec_9798_2_6_bdkey_P, ''Ra''), (KnownT isoiec_9798_2_6_bdkey_P_2))+  , ((isoiec_9798_2_6_bdkey_A, ''Rb''), (KnownT isoiec_9798_2_6_bdkey_A_1))+  , ((isoiec_9798_2_6_bdkey_P, ''Rb''), (KnownT isoiec_9798_2_6_bdkey_P_2))+  , ((isoiec_9798_2_6_bdkey_B, ''Rpa''),+     (SumT (KnownT isoiec_9798_2_6_bdkey_B_4) (NonceT isoiec_9798_2_6_bdkey_A ''Rpa'')))+  , ((isoiec_9798_2_6_bdkey_A, ''Text1''),+     (KnownT isoiec_9798_2_6_bdkey_A_1))+  , ((isoiec_9798_2_6_bdkey_B, ''Text1''),+     (KnownT isoiec_9798_2_6_bdkey_B_text_1))+  , ((isoiec_9798_2_6_bdkey_A, ''Text2''),+     (KnownT isoiec_9798_2_6_bdkey_A_text_2))+  , ((isoiec_9798_2_6_bdkey_P, ''Text2''),+     (KnownT isoiec_9798_2_6_bdkey_P_2))+  , ((isoiec_9798_2_6_bdkey_B, ''Text3''),+     (KnownT isoiec_9798_2_6_bdkey_B_4))+  , ((isoiec_9798_2_6_bdkey_P, ''Text3''),+     (KnownT isoiec_9798_2_6_bdkey_P_text_3))+  , ((isoiec_9798_2_6_bdkey_A, ''Text4''),+     (KnownT isoiec_9798_2_6_bdkey_A_3))+  , ((isoiec_9798_2_6_bdkey_P, ''Text4''),+     (KnownT isoiec_9798_2_6_bdkey_P_text_3))+  , ((isoiec_9798_2_6_bdkey_A, ''Text5''),+     (KnownT isoiec_9798_2_6_bdkey_A_3))+  , ((isoiec_9798_2_6_bdkey_P, ''Text5''),+     (KnownT isoiec_9798_2_6_bdkey_P_text_3))+  , ((isoiec_9798_2_6_bdkey_A, ''Text6''),+     (KnownT isoiec_9798_2_6_bdkey_A_text_4))+  , ((isoiec_9798_2_6_bdkey_B, ''Text6''),+     (KnownT isoiec_9798_2_6_bdkey_B_4))+  , ((isoiec_9798_2_6_bdkey_A, ''Text7''),+     (KnownT isoiec_9798_2_6_bdkey_A_text_4))+  , ((isoiec_9798_2_6_bdkey_B, ''Text7''),+     (KnownT isoiec_9798_2_6_bdkey_B_4))+  , ((isoiec_9798_2_6_bdkey_A, ''Text8''),+     (KnownT isoiec_9798_2_6_bdkey_A_5))+  , ((isoiec_9798_2_6_bdkey_B, ''Text8''),+     (KnownT isoiec_9798_2_6_bdkey_B_text_5))+  , ((isoiec_9798_2_6_bdkey_A, ''Text9''),+     (KnownT isoiec_9798_2_6_bdkey_A_5))+  , ((isoiec_9798_2_6_bdkey_B, ''Text9''),+     (KnownT isoiec_9798_2_6_bdkey_B_text_5))+  , ((isoiec_9798_2_6_bdkey_A, ''TokenPA_for_B''),+     (KnownT isoiec_9798_2_6_bdkey_A_3))+  ]"++sublocale isoiec_9798_2_6_bdkey_state < isoiec_9798_2_6_bdkey_msc_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_2_6_bdkey_msc_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_2_6_bdkey_msc_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_2_6_bdkey_A_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_A_1_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_A_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_A_3_Kab t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,+               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),+               s(MV ''Text4'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_bdkey_A_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,+               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),+               s(MV ''Text4'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_bdkey_A_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_A_3_TokenPA_for_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_A_text_4_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_A_text_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_A_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_5'', s(MV ''Rb'' tid0), LN ''Rpa'' tid0,+               s(MV ''Text8'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_bdkey_A_5_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_B_4_Kab t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,+               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),+               s(MV ''Text3'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_bdkey_B_4_P t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_B_4_Rpa t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_4'', s(MV ''Rpa'' tid0), LN ''Rb'' tid0,+               s(MV ''Text6'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_bdkey_B_4_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,+               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),+               s(MV ''Text3'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_bdkey_B_4_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_4'', s(MV ''Rpa'' tid0), LN ''Rb'' tid0,+               s(MV ''Text6'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_bdkey_B_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_B_text_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_B_text_5_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_P_2_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_P_2_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_P_2_Ra t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_P_2_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_P_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_P_text_3_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_P_text_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_bdkey_P_text_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_2_6_bdkey_msc_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_2_6_bdkey_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++lemma (in restricted_isoiec_9798_2_6_bdkey_state) P_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_6_bdkey_P"+    "RLKR(s(AV ''P'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''B'' tid0)) ~: reveals t"+    "LN ''Kab'' tid0 : knows t"+  shows "False"+using facts proof(sources! " LN ''Kab'' tid0 ")+  case isoiec_9798_2_6_bdkey_P_3_Kab note_unified facts = this facts+  thus ?thesis by (fastforce dest!: ltk_secrecy)+next+  case isoiec_9798_2_6_bdkey_P_3_Kab_1 note_unified facts = this facts+  thus ?thesis by (fastforce dest!: ltk_secrecy)+qed (insert facts, fastforce+)?++lemma (in restricted_isoiec_9798_2_6_bdkey_state) A_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_6_bdkey_A"+    "RLKR(s(AV ''A'' tid0)) ~: reveals t"+    "RLKR(s(AV ''P'' tid0)) ~: reveals t"+    "RLKR(s(MV ''B'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_6_bdkey_A_3 ) : steps t"+    "s(MV ''Kab'' tid0) : knows t"+  shows "False"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,+                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),+                          s(MV ''Text4'' tid0)+                       |}+                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_6_bdkey_P_3_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_6_bdkey_state) B_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_6_bdkey_B"+    "RLKR(s(AV ''A'' tid0)) ~: reveals t"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_6_bdkey_B_4 ) : steps t"+    "s(MV ''Kab'' tid0) : knows t"+  shows "False"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,+                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),+                          s(MV ''Text3'' tid0)+                       |}+                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_6_bdkey_P_3_enc_1 tid1) note_unified facts = this facts+    thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_6_bdkey_state) A_injective_agreement_B:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_6_bdkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''P'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_6_bdkey_A_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_6_bdkey_B &+          ( tid1, isoiec_9798_2_6_bdkey_B_5 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''P'' tid1),+             s(MV ''Kab'' tid1), s(MV ''Rpa'' tid1), LN ''Rb'' tid1,+             s(MV ''Text6'' tid1), s(MV ''Text8'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''P'' tid0),+                  s(MV ''Kab'' tid0), LN ''Rpa'' tid0, s(MV ''Rb'' tid0),+                  s(MV ''Text6'' tid0), s(MV ''Text8'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),+                              s(MV ''Text4'' tid0)+                           |}+                           ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_6_bdkey_P_3_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_2_6_enc_5'', s(MV ''Rb'' tid0), LN ''Rpa'' tid0,+                                s(MV ''Text8'' tid0)+                             |}+                             ( LN ''Kab'' tid1 ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+        next+          case (isoiec_9798_2_6_bdkey_B_5_enc tid2) note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid2, LN ''Kab'' tid1,+                                  s(AV ''A'' tid2), s(AV ''B'' tid2), s(MV ''Text3'' tid2)+                               |}+                               ( Kbd ( s(AV ''B'' tid2) ) ( s(MV ''P'' tid2) ) ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+          next+            case (isoiec_9798_2_6_bdkey_P_3_enc_1 tid3) note_unified facts = this facts+            thus ?thesis proof(sources! "+                             Enc {| LC ''isoiec_9798_2_6_enc_4'', LN ''Rpa'' tid0, LN ''Rb'' tid2,+                                    s(MV ''Text6'' tid2)+                                 |}+                                 ( LN ''Kab'' tid1 ) ")+              case fake note_unified facts = this facts+              thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+            next+              case (isoiec_9798_2_6_bdkey_A_4_enc tid3) note_unified facts = this facts+              thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+            qed (insert facts, fastforce+)?+          qed (insert facts, fastforce+)?+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_6_bdkey_state) B_injective_agreement_A:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_6_bdkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(MV ''P'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_6_bdkey_B_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_6_bdkey_A &+          ( tid1, isoiec_9798_2_6_bdkey_A_4 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),+             s(MV ''Kab'' tid1), LN ''Rpa'' tid1, s(MV ''Rb'' tid1),+             s(MV ''Text6'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),+                  s(MV ''Kab'' tid0), s(MV ''Rpa'' tid0), LN ''Rb'' tid0,+                  s(MV ''Text6'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),+                              s(MV ''Text3'' tid0)+                           |}+                           ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_6_bdkey_P_3_enc_1 tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_2_6_enc_4'', s(MV ''Rpa'' tid0), LN ''Rb'' tid0,+                                s(MV ''Text6'' tid0)+                             |}+                             ( LN ''Kab'' tid1 ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+        next+          case (isoiec_9798_2_6_bdkey_A_4_enc tid2) note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid2, LN ''Kab'' tid1,+                                  s(AV ''A'' tid2), s(MV ''B'' tid2), s(MV ''Text4'' tid2)+                               |}+                               ( Kbd ( s(AV ''A'' tid2) ) ( s(AV ''P'' tid2) ) ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+          next+            case (isoiec_9798_2_6_bdkey_P_3_enc tid3) note_unified facts = this facts+            thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+          qed (insert facts, fastforce+)?+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_6_bdkey_state) A_injective_agreement_P:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_6_bdkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''P'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_6_bdkey_A_3 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_6_bdkey_P &+          ( tid1, isoiec_9798_2_6_bdkey_P_3 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),+             s(MV ''Ra'' tid1), LN ''Kab'' tid1, s(MV ''Text4'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''P'' tid0),+                  LN ''Ra'' tid0, s(MV ''Kab'' tid0), s(MV ''Text4'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),+                              s(MV ''Text4'' tid0)+                           |}+                           ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_6_bdkey_P_3_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_6_bdkey_state) B_injective_agreement_P:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_6_bdkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(MV ''P'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_6_bdkey_B_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_6_bdkey_P &+          ( tid1, isoiec_9798_2_6_bdkey_P_3 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),+             s(MV ''Rb'' tid1), LN ''Kab'' tid1, s(MV ''Text3'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),+                  LN ''Rb'' tid0, s(MV ''Kab'' tid0), s(MV ''Text3'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(AV ''B'' tid0),+                              s(MV ''Text3'' tid0)+                           |}+                           ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_6_bdkey_P_3_enc_1 tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++role isoiec_9798_2_5_special_TTP_bdkey_A+where "isoiec_9798_2_5_special_TTP_bdkey_A =+  [ Send ''leak_A'' <| sN ''TVPa'', sN ''TNa'' |>+  , Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''A'', sAV ''P'', sN ''TVPa'', sAV ''B'',+                  sMV ''Text1''+               |>+  , Recv ''2'' <| sAV ''P'', sAV ''A'', sMV ''Text4'',+                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_2_1'', sN ''TVPa'',+                          sMV ''Kab'', sAV ''B'', sMV ''Text3''+                       |>+                       ( sKbd (AVar ''A'') (AVar ''P'') ),+                  sMV ''TokenPA_for_B''+               |>+  , Recv ''text_3'' <| sMV ''Text5'', sMV ''Text6'' |>+  , Send ''3'' <| sAV ''A'', sAV ''B'', sMV ''Text6'', sAV ''P'',+                  sMV ''TokenPA_for_B'',+                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_3'', sN ''TNa'', sAV ''B'',+                          sMV ''Text5''+                       |>+                       ( sMV ''Kab'' )+               |>+  , Recv ''4'' <| sAV ''B'', sAV ''A'', sMV ''Text8'',+                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_4'', sMV ''TNb'', sAV ''A'',+                          sMV ''Text7''+                       |>+                       ( sMV ''Kab'' )+               |>+  ]"++role isoiec_9798_2_5_special_TTP_bdkey_B+where "isoiec_9798_2_5_special_TTP_bdkey_B =+  [ Send ''leak_B'' ( sN ''TNb'' )+  , Recv ''3'' <| sMV ''A'', sAV ''B'', sMV ''Text6'', sMV ''P'',+                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_2_2'', sMV ''TNp'',+                          sMV ''Kab'', sMV ''A'', sMV ''Text2''+                       |>+                       ( sKbd (AVar ''B'') (MVar ''P'') ),+                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_3'', sMV ''TNa'', sAV ''B'',+                          sMV ''Text5''+                       |>+                       ( sMV ''Kab'' )+               |>+  , Recv ''text_4'' <| sMV ''Text7'', sMV ''Text8'' |>+  , Send ''4'' <| sAV ''B'', sMV ''A'', sMV ''Text8'',+                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_4'', sN ''TNb'', sMV ''A'',+                          sMV ''Text7''+                       |>+                       ( sMV ''Kab'' )+               |>+  ]"++role isoiec_9798_2_5_special_TTP_bdkey_P+where "isoiec_9798_2_5_special_TTP_bdkey_P =+  [ Send ''leak_P'' ( sN ''TNp'' )+  , Recv ''1'' <| sMV ''A'', sAV ''P'', sMV ''TVPa'', sMV ''B'',+                  sMV ''Text1''+               |>+  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'', sMV ''Text4'' |>+  , Send ''2'' <| sAV ''P'', sMV ''A'', sMV ''Text4'',+                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_2_1'', sMV ''TVPa'',+                          sN ''Kab'', sMV ''B'', sMV ''Text3''+                       |>+                       ( sKbd (MVar ''A'') (AVar ''P'') ),+                  PEnc <| sC ''isoiec_9798_2_5_special_TTP_enc_2_2'', sN ''TNp'',+                          sN ''Kab'', sMV ''A'', sMV ''Text2''+                       |>+                       ( sKbd (MVar ''B'') (AVar ''P'') )+               |>+  ]"++protocol isoiec_9798_2_5_special_TTP_bdkey+where "isoiec_9798_2_5_special_TTP_bdkey =+{ isoiec_9798_2_5_special_TTP_bdkey_A,+  isoiec_9798_2_5_special_TTP_bdkey_B, isoiec_9798_2_5_special_TTP_bdkey_P+}"++locale restricted_isoiec_9798_2_5_special_TTP_bdkey_state = isoiec_9798_2_5_special_TTP_bdkey_state ++  assumes different_actors_A_P:+    "!! tid0 tid1.+       [| roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_A;+         roleMap r tid1 = Some isoiec_9798_2_5_special_TTP_bdkey_P;+         s(AV ''P'' tid1) = s(AV ''A'' tid0)+       |] ==> False"++type_invariant isoiec_9798_2_5_special_TTP_bdkey_msc_typing for isoiec_9798_2_5_special_TTP_bdkey+where "isoiec_9798_2_5_special_TTP_bdkey_msc_typing = mk_typing+  [ ((isoiec_9798_2_5_special_TTP_bdkey_B, ''A''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3))+  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''A''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_1))+  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''B''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_1))+  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Kab''),+     (SumT (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_2) (NonceT isoiec_9798_2_5_special_TTP_bdkey_P ''Kab'')))+  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''Kab''),+     (SumT (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3) (NonceT isoiec_9798_2_5_special_TTP_bdkey_P ''Kab'')))+  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''P''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3))+  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''TNa''),+     (SumT (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3) (NonceT isoiec_9798_2_5_special_TTP_bdkey_A ''TNa'')))+  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''TNb''),+     (SumT (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_4) (NonceT isoiec_9798_2_5_special_TTP_bdkey_B ''TNb'')))+  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''TNp''),+     (SumT (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3) (NonceT isoiec_9798_2_5_special_TTP_bdkey_P ''TNp'')))+  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''TVPa''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_1))+  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text1''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_text_1))+  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''Text1''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_1))+  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''Text2''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3))+  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''Text2''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_text_2))+  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text3''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_2))+  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''Text3''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_text_2))+  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text4''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_2))+  , ((isoiec_9798_2_5_special_TTP_bdkey_P, ''Text4''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_P_text_2))+  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text5''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_text_3))+  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''Text5''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3))+  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text6''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_text_3))+  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''Text6''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_3))+  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text7''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_4))+  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''Text7''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_text_4))+  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''Text8''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_4))+  , ((isoiec_9798_2_5_special_TTP_bdkey_B, ''Text8''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_B_text_4))+  , ((isoiec_9798_2_5_special_TTP_bdkey_A, ''TokenPA_for_B''),+     (KnownT isoiec_9798_2_5_special_TTP_bdkey_A_2))+  ]"++sublocale isoiec_9798_2_5_special_TTP_bdkey_state < isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_2_5_special_TTP_bdkey_msc_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_2_5_special_TTP_bdkey_msc_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_2_5_special_TTP_bdkey_A_2_Kab t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid0,+               s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_A_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid0,+               s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_A_2_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_A_2_TokenPA_for_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_A_text_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_A_text_3_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_A_4_TNb t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_4'', s(MV ''TNb'' tid0),+               s(AV ''A'' tid0), s(MV ''Text7'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_A_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_4'', s(MV ''TNb'' tid0),+               s(AV ''A'' tid0), s(MV ''Text7'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_A_4_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_Kab t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid0),+               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_P t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_TNa t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_3'', s(MV ''TNa'' tid0),+               s(AV ''B'' tid0), s(MV ''Text5'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_TNp t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid0),+               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid0),+               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_3'', s(MV ''TNa'' tid0),+               s(AV ''B'' tid0), s(MV ''Text5'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_B_3_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_B_text_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_B_text_4_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_P_1_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_P_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_P_1_TVPa t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_P_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_P_text_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_P_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_P_text_2_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_2_5_special_TTP_bdkey_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end+++lemma (in restricted_isoiec_9798_2_5_special_TTP_bdkey_state) P_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_P"+    "RLKR(s(AV ''P'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''B'' tid0)) ~: reveals t"+    "LN ''Kab'' tid0 : knows t"+  shows "False"+using facts proof(sources! " LN ''Kab'' tid0 ")+  case isoiec_9798_2_5_special_TTP_bdkey_P_2_Kab note_unified facts = this facts+  thus ?thesis by (fastforce dest!: ltk_secrecy)+next+  case isoiec_9798_2_5_special_TTP_bdkey_P_2_Kab_1 note_unified facts = this facts+  thus ?thesis by (fastforce dest!: ltk_secrecy)+qed (insert facts, fastforce+)?++lemma (in restricted_isoiec_9798_2_5_special_TTP_bdkey_state) A_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_A"+    "RLKR(s(AV ''A'' tid0)) ~: reveals t"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(AV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_5_special_TTP_bdkey_A_2 ) : steps t"+    "s(MV ''Kab'' tid0) : knows t"+  shows "False"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid0,+                          s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)+                       |}+                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc tid1) note_unified facts = this facts+    hence "Kbd ( s(AV ''P'' tid1) )+               ( s(MV ''A'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) )"+      by simp note facts = this facts+    thus ?thesis proof(cases rule: Kbd_cases)+      case noswap note_unified facts = this facts+      thus ?thesis by (fastforce dest: different_actors_A_P intro: event_predOrdI)+    next+      case swapped note_unified facts = this facts+      thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+    qed (fastforce+)?+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_5_special_TTP_bdkey_state) B_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_5_special_TTP_bdkey_B_3 ) : steps t"+    "s(MV ''Kab'' tid0) : knows t"+  shows "False"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid0),+                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)+                       |}+                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc_1 tid1) note_unified facts = this facts+    hence "Kbd ( s(AV ''P'' tid1) )+               ( s(MV ''B'' tid1) ) = Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) )"+      by simp note facts = this facts+    thus ?thesis proof(cases rule: Kbd_cases)+      case noswap note_unified facts = this facts+      thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+    next+      case swapped note_unified facts = this facts+      thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+    qed (fastforce+)?+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_5_special_TTP_bdkey_state) A_injective_agreement_B:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(AV ''P'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_5_special_TTP_bdkey_A_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_5_special_TTP_bdkey_B &+          ( tid1, isoiec_9798_2_5_special_TTP_bdkey_B_4 ) : steps t &+          {| s(MV ''A'' tid1), s(AV ''B'' tid1), s(MV ''P'' tid1),+             s(MV ''Kab'' tid1), s(MV ''TNa'' tid1), s(MV ''Text5'' tid1),+             LN ''TNb'' tid1, s(MV ''Text7'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''P'' tid0),+                  s(MV ''Kab'' tid0), LN ''TNa'' tid0, s(MV ''Text5'' tid0),+                  s(MV ''TNb'' tid0), s(MV ''Text7'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc tid1) note_unified facts = this facts+        hence "Kbd ( s(AV ''P'' tid1) )+                   ( s(MV ''A'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) )"+          by simp note facts = this facts+        thus ?thesis proof(cases rule: Kbd_cases)+          case noswap note_unified facts = this facts+          thus ?thesis by (fastforce dest: different_actors_A_P intro: event_predOrdI)+        next+          case swapped note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_4'', s(MV ''TNb'' tid0),+                                  s(AV ''A'' tid0), s(MV ''Text7'' tid0)+                               |}+                               ( LN ''Kab'' tid1 ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+          next+            case (isoiec_9798_2_5_special_TTP_bdkey_B_4_enc tid2) note_unified facts = this facts+            thus ?thesis proof(sources! "+                             Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_3'', s(MV ''TNa'' tid2),+                                    s(AV ''B'' tid2), s(MV ''Text5'' tid2)+                                 |}+                                 ( LN ''Kab'' tid1 ) ")+              case fake note_unified facts = this facts+              thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+            next+              case (isoiec_9798_2_5_special_TTP_bdkey_A_3_enc tid3) note_unified facts = this facts+              thus ?thesis proof(sources! "+                               Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid3,+                                      LN ''Kab'' tid1, s(AV ''B'' tid2), s(MV ''Text3'' tid3)+                                   |}+                                   ( Kbd ( s(AV ''A'' tid3) ) ( s(AV ''P'' tid3) ) ) ")+                case fake note_unified facts = this facts+                thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+              next+                case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc tid4) note_unified facts = this facts+                thus ?thesis proof(sources! "+                                 Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid2),+                                        LN ''Kab'' tid1, s(AV ''A'' tid0), s(MV ''Text2'' tid2)+                                     |}+                                     ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid2) ) ) ")+                  case fake note_unified facts = this facts+                  thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+                next+                  case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc_1 tid3) note_unified facts = this facts+                  thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+                qed (insert facts, fastforce+)?+              qed (insert facts, fastforce+)?+            qed (insert facts, fastforce+)?+          qed (insert facts, fastforce+)?+        qed (fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_5_special_TTP_bdkey_state) B_non_injective_agreement_A:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_5_special_TTP_bdkey_B_3 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_2_5_special_TTP_bdkey_A &+        ( tid1, isoiec_9798_2_5_special_TTP_bdkey_A_3 ) : steps t &+        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(AV ''P'' tid1),+           s(MV ''Kab'' tid1), LN ''TNa'' tid1, s(MV ''Text5'' tid1)+        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),+                s(MV ''Kab'' tid0), s(MV ''TNa'' tid0), s(MV ''Text5'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_3'', s(MV ''TNa'' tid0),+                          s(AV ''B'' tid0), s(MV ''Text5'' tid0)+                       |}+                       ( s(MV ''Kab'' tid0) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest: B_secret_Kab intro: event_predOrdI)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_A_3_enc tid1) note_unified facts = this facts+    thus ?thesis proof(sources! "+                     Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid1,+                            s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid1)+                         |}+                         ( Kbd ( s(AV ''A'' tid1) ) ( s(AV ''P'' tid1) ) ) ")+      case fake note_unified facts = this facts+      thus ?thesis by (fastforce dest: B_secret_Kab intro: event_predOrdI)+    next+      case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc tid2) note_unified facts = this facts+      hence "Kbd ( s(AV ''P'' tid2) )+                 ( s(MV ''A'' tid2) ) = Kbd ( s(AV ''A'' tid1) ) ( s(AV ''P'' tid1) )"+        by simp note facts = this facts+      thus ?thesis proof(cases rule: Kbd_cases)+        case noswap note_unified facts = this facts+        thus ?thesis by (fastforce dest: different_actors_A_P intro: event_predOrdI)+      next+        case swapped note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid0),+                                LN ''Kab'' tid2, s(MV ''A'' tid0), s(MV ''Text2'' tid0)+                             |}+                             ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc_1 tid3) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (fastforce+)?+    qed (insert facts, fastforce+)?+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_5_special_TTP_bdkey_state) A_injective_agreement_P:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(AV ''P'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_5_special_TTP_bdkey_A_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_5_special_TTP_bdkey_P &+          ( tid1, isoiec_9798_2_5_special_TTP_bdkey_P_2 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1), LN ''Kab'' tid1,+             s(MV ''TVPa'' tid1), s(MV ''Text3'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''P'' tid0),+                  s(MV ''Kab'' tid0), LN ''TVPa'' tid0, s(MV ''Text3'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc tid1) note_unified facts = this facts+        hence "Kbd ( s(AV ''P'' tid1) )+                   ( s(MV ''A'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) )"+          by simp note facts = this facts+        thus ?thesis proof(cases rule: Kbd_cases)+          case noswap note_unified facts = this facts+          thus ?thesis by (fastforce dest: different_actors_A_P intro: event_predOrdI)+        next+          case swapped note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_5_special_TTP_bdkey_state) B_non_injective_agreement_P:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_special_TTP_bdkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_5_special_TTP_bdkey_B_3 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_2_5_special_TTP_bdkey_P &+        ( tid1, isoiec_9798_2_5_special_TTP_bdkey_P_2 ) : steps t &+        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1), LN ''Kab'' tid1,+           LN ''TNp'' tid1, s(MV ''Text2'' tid1)+        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),+                s(MV ''Kab'' tid0), s(MV ''TNp'' tid0), s(MV ''Text2'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_2'', s(MV ''TNp'' tid0),+                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)+                       |}+                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc_1 tid1) note_unified facts = this facts+    hence "Kbd ( s(AV ''P'' tid1) )+               ( s(MV ''B'' tid1) ) = Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) )"+      by simp note facts = this facts+    thus ?thesis proof(cases rule: Kbd_cases)+      case noswap note_unified facts = this facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_3'', s(MV ''TNa'' tid0),+                              s(AV ''B'' tid0), s(MV ''Text5'' tid0)+                           |}+                           ( LN ''Kab'' tid1 ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+      next+        case (isoiec_9798_2_5_special_TTP_bdkey_A_3_enc tid2) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_2_5_special_TTP_enc_2_1'', LN ''TVPa'' tid2,+                                LN ''Kab'' tid1, s(AV ''B'' tid0), s(MV ''Text3'' tid2)+                             |}+                             ( Kbd ( s(AV ''A'' tid2) ) ( s(AV ''P'' tid2) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+        next+          case (isoiec_9798_2_5_special_TTP_bdkey_P_2_enc tid3) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    next+      case swapped note_unified facts = this facts+      thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+    qed (fastforce+)?+  qed (insert facts, fastforce+)?+qed++role isoiec_9798_2_6_special_TTP_bdkey_A+where "isoiec_9798_2_6_special_TTP_bdkey_A =+  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>+  , Recv ''text_2'' ( sMV ''Text2'' )+  , Send ''2'' <| sAV ''A'', sAV ''P'', sN ''Ra'', sMV ''Rb'', sMV ''B'',+                  sMV ''Text2''+               |>+  , Recv ''3'' <| sAV ''P'', sAV ''A'', sMV ''Text5'',+                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_3_1'', sN ''Ra'',+                          sMV ''Kab'', sMV ''B'', sMV ''Text4''+                       |>+                       ( sKbd (AVar ''A'') (AVar ''P'') ),+                  sMV ''TokenPA_for_B''+               |>+  , Recv ''text_4'' <| sMV ''Text6'', sMV ''Text7'' |>+  , Send ''4'' <| sAV ''A'', sMV ''B'', sMV ''Text7'', sAV ''P'',+                  sMV ''TokenPA_for_B'',+                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_4'', sN ''Rpa'', sMV ''Rb'',+                          sMV ''Text6''+                       |>+                       ( sMV ''Kab'' )+               |>+  , Recv ''5'' <| sMV ''B'', sAV ''A'', sMV ''Text9'',+                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_5'', sMV ''Rb'', sN ''Rpa'',+                          sMV ''Text8''+                       |>+                       ( sMV ''Kab'' )+               |>+  ]"++role isoiec_9798_2_6_special_TTP_bdkey_B+where "isoiec_9798_2_6_special_TTP_bdkey_B =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>+  , Recv ''4'' <| sAV ''A'', sAV ''B'', sMV ''Text7'', sMV ''P'',+                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_3_2'', sN ''Rb'',+                          sMV ''Kab'', sAV ''A'', sMV ''Text3''+                       |>+                       ( sKbd (AVar ''B'') (MVar ''P'') ),+                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_4'', sMV ''Rpa'', sN ''Rb'',+                          sMV ''Text6''+                       |>+                       ( sMV ''Kab'' )+               |>+  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>+  , Send ''5'' <| sAV ''B'', sAV ''A'', sMV ''Text9'',+                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_5'', sN ''Rb'', sMV ''Rpa'',+                          sMV ''Text8''+                       |>+                       ( sMV ''Kab'' )+               |>+  ]"++role isoiec_9798_2_6_special_TTP_bdkey_P+where "isoiec_9798_2_6_special_TTP_bdkey_P =+  [ Recv ''2'' <| sMV ''A'', sAV ''P'', sMV ''Ra'', sMV ''Rb'', sMV ''B'',+                  sMV ''Text2''+               |>+  , Recv ''text_3'' <| sMV ''Text3'', sMV ''Text4'', sMV ''Text5'' |>+  , Send ''3'' <| sAV ''P'', sMV ''A'', sMV ''Text5'',+                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_3_1'', sMV ''Ra'',+                          sN ''Kab'', sMV ''B'', sMV ''Text4''+                       |>+                       ( sKbd (MVar ''A'') (AVar ''P'') ),+                  PEnc <| sC ''isoiec_9798_2_6_special_TTP_enc_3_2'', sMV ''Rb'',+                          sN ''Kab'', sMV ''A'', sMV ''Text3''+                       |>+                       ( sKbd (MVar ''B'') (AVar ''P'') )+               |>+  ]"++protocol isoiec_9798_2_6_special_TTP_bdkey+where "isoiec_9798_2_6_special_TTP_bdkey =+{ isoiec_9798_2_6_special_TTP_bdkey_A,+  isoiec_9798_2_6_special_TTP_bdkey_B, isoiec_9798_2_6_special_TTP_bdkey_P+}"++locale restricted_isoiec_9798_2_6_special_TTP_bdkey_state = isoiec_9798_2_6_special_TTP_bdkey_state ++  assumes different_actors_A_P:+    "!! tid0 tid1.+       [| roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_A;+         roleMap r tid1 = Some isoiec_9798_2_6_special_TTP_bdkey_P;+         s(AV ''P'' tid1) = s(AV ''A'' tid0)+       |] ==> False"+  assumes different_actors_B_P:+    "!! tid0 tid1.+       [| roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_B;+         roleMap r tid1 = Some isoiec_9798_2_6_special_TTP_bdkey_P;+         s(AV ''P'' tid1) = s(AV ''B'' tid0)+       |] ==> False"++type_invariant isoiec_9798_2_6_special_TTP_bdkey_msc_typing for isoiec_9798_2_6_special_TTP_bdkey+where "isoiec_9798_2_6_special_TTP_bdkey_msc_typing = mk_typing+  [ ((isoiec_9798_2_6_special_TTP_bdkey_P, ''A''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_2))+  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''B''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_1))+  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''B''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_2))+  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Kab''),+     (SumT (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_3) (NonceT isoiec_9798_2_6_special_TTP_bdkey_P ''Kab'')))+  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Kab''),+     (SumT (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_4) (NonceT isoiec_9798_2_6_special_TTP_bdkey_P ''Kab'')))+  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''P''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_4))+  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''Ra''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_2))+  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Rb''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_1))+  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''Rb''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_2))+  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Rpa''),+     (SumT (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_4) (NonceT isoiec_9798_2_6_special_TTP_bdkey_A ''Rpa'')))+  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text1''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_1))+  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Text1''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_text_1))+  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text2''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_text_2))+  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''Text2''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_2))+  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Text3''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_4))+  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''Text3''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_text_3))+  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text4''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_3))+  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''Text4''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_text_3))+  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text5''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_3))+  , ((isoiec_9798_2_6_special_TTP_bdkey_P, ''Text5''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_P_text_3))+  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text6''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_text_4))+  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Text6''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_4))+  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text7''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_text_4))+  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Text7''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_4))+  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text8''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_5))+  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Text8''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_text_5))+  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''Text9''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_5))+  , ((isoiec_9798_2_6_special_TTP_bdkey_B, ''Text9''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_B_text_5))+  , ((isoiec_9798_2_6_special_TTP_bdkey_A, ''TokenPA_for_B''),+     (KnownT isoiec_9798_2_6_special_TTP_bdkey_A_3))+  ]"++sublocale isoiec_9798_2_6_special_TTP_bdkey_state < isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_2_6_special_TTP_bdkey_msc_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_2_6_special_TTP_bdkey_msc_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_2_6_special_TTP_bdkey_A_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_A_1_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_A_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_A_3_Kab t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_1'', LN ''Ra'' tid0,+               s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_A_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_1'', LN ''Ra'' tid0,+               s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)+            |}+            ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_A_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_A_3_TokenPA_for_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_A_text_4_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_A_text_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_A_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_5'', s(MV ''Rb'' tid0),+               LN ''Rpa'' tid0, s(MV ''Text8'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_A_5_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Kab t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_2'', LN ''Rb'' tid0,+               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_B_4_P t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Rpa t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_4'', s(MV ''Rpa'' tid0),+               LN ''Rb'' tid0, s(MV ''Text6'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_2'', LN ''Rb'' tid0,+               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)+            |}+            ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_4'', s(MV ''Rpa'' tid0),+               LN ''Rb'' tid0, s(MV ''Text6'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_B_text_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_B_text_5_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_P_2_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_P_2_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_P_2_Ra t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_P_2_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_P_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_P_text_3_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_P_text_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_P_text_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_2_6_special_TTP_bdkey_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++++lemma (in restricted_isoiec_9798_2_6_special_TTP_bdkey_state) P_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_P"+    "RLKR(s(AV ''P'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''B'' tid0)) ~: reveals t"+    "LN ''Kab'' tid0 : knows t"+  shows "False"+using facts proof(sources! " LN ''Kab'' tid0 ")+  case isoiec_9798_2_6_special_TTP_bdkey_P_3_Kab note_unified facts = this facts+  thus ?thesis by (fastforce dest!: ltk_secrecy)+next+  case isoiec_9798_2_6_special_TTP_bdkey_P_3_Kab_1 note_unified facts = this facts+  thus ?thesis by (fastforce dest!: ltk_secrecy)+qed (insert facts, fastforce+)?++lemma (in restricted_isoiec_9798_2_6_special_TTP_bdkey_state) A_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_A"+    "RLKR(s(AV ''A'' tid0)) ~: reveals t"+    "RLKR(s(AV ''P'' tid0)) ~: reveals t"+    "RLKR(s(MV ''B'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_6_special_TTP_bdkey_A_3 ) : steps t"+    "s(MV ''Kab'' tid0) : knows t"+  shows "False"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_1'', LN ''Ra'' tid0,+                          s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)+                       |}+                       ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc tid1) note_unified facts = this facts+    hence "Kbd ( s(AV ''P'' tid1) )+               ( s(MV ''A'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) )"+      by simp note facts = this facts+    thus ?thesis proof(cases rule: Kbd_cases)+      case noswap note_unified facts = this facts+      thus ?thesis by (fastforce dest: different_actors_A_P intro: event_predOrdI)+    next+      case swapped note_unified facts = this facts+      thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+    qed (fastforce+)?+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_6_special_TTP_bdkey_state) B_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_B"+    "RLKR(s(AV ''A'' tid0)) ~: reveals t"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_6_special_TTP_bdkey_B_4 ) : steps t"+    "s(MV ''Kab'' tid0) : knows t"+  shows "False"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_2'', LN ''Rb'' tid0,+                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)+                       |}+                       ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc_1 tid1) note_unified facts = this facts+    hence "Kbd ( s(AV ''P'' tid1) )+               ( s(MV ''B'' tid1) ) = Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) )"+      by simp note facts = this facts+    thus ?thesis proof(cases rule: Kbd_cases)+      case noswap note_unified facts = this facts+      thus ?thesis by (fastforce dest: different_actors_B_P intro: event_predOrdI)+    next+      case swapped note_unified facts = this facts+      thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+    qed (fastforce+)?+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_6_special_TTP_bdkey_state) A_injective_agreement_B:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''P'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_6_special_TTP_bdkey_A_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_6_special_TTP_bdkey_B &+          ( tid1, isoiec_9798_2_6_special_TTP_bdkey_B_5 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''P'' tid1),+             s(MV ''Kab'' tid1), s(MV ''Rpa'' tid1), LN ''Rb'' tid1,+             s(MV ''Text6'' tid1), s(MV ''Text8'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''P'' tid0),+                  s(MV ''Kab'' tid0), LN ''Rpa'' tid0, s(MV ''Rb'' tid0),+                  s(MV ''Text6'' tid0), s(MV ''Text8'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_1'', LN ''Ra'' tid0,+                              s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)+                           |}+                           ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc tid1) note_unified facts = this facts+        hence "Kbd ( s(AV ''P'' tid1) )+                   ( s(MV ''A'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) )"+          by simp note facts = this facts+        thus ?thesis proof(cases rule: Kbd_cases)+          case noswap note_unified facts = this facts+          thus ?thesis by (fastforce dest: different_actors_A_P intro: event_predOrdI)+        next+          case swapped note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_5'', s(MV ''Rb'' tid0),+                                  LN ''Rpa'' tid0, s(MV ''Text8'' tid0)+                               |}+                               ( LN ''Kab'' tid1 ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+          next+            case (isoiec_9798_2_6_special_TTP_bdkey_B_5_enc tid2) note_unified facts = this facts+            thus ?thesis proof(sources! "+                             Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_2'', LN ''Rb'' tid2,+                                    LN ''Kab'' tid1, s(AV ''A'' tid2), s(MV ''Text3'' tid2)+                                 |}+                                 ( Kbd ( s(AV ''B'' tid2) ) ( s(MV ''P'' tid2) ) ) ")+              case fake note_unified facts = this facts+              thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+            next+              case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc_1 tid3) note_unified facts = this facts+              hence "Kbd ( s(AV ''P'' tid0) )+                         ( s(MV ''B'' tid0) ) = Kbd ( s(AV ''B'' tid2) ) ( s(MV ''P'' tid2) )"+                by simp note facts = this facts+              thus ?thesis proof(cases rule: Kbd_cases)+                case noswap note_unified facts = this facts+                thus ?thesis by (fastforce dest: different_actors_B_P intro: event_predOrdI)+              next+                case swapped note_unified facts = this facts+                thus ?thesis proof(sources! "+                                 Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_4'', LN ''Rpa'' tid0,+                                        LN ''Rb'' tid2, s(MV ''Text6'' tid2)+                                     |}+                                     ( LN ''Kab'' tid1 ) ")+                  case fake note_unified facts = this facts+                  thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+                next+                  case (isoiec_9798_2_6_special_TTP_bdkey_A_4_enc tid3) note_unified facts = this facts+                  thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+                qed (insert facts, fastforce+)?+              qed (fastforce+)?+            qed (insert facts, fastforce+)?+          qed (insert facts, fastforce+)?+        qed (fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_6_special_TTP_bdkey_state) B_injective_agreement_A:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(MV ''P'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_6_special_TTP_bdkey_B_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_6_special_TTP_bdkey_A &+          ( tid1, isoiec_9798_2_6_special_TTP_bdkey_A_4 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),+             s(MV ''Kab'' tid1), LN ''Rpa'' tid1, s(MV ''Rb'' tid1),+             s(MV ''Text6'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),+                  s(MV ''Kab'' tid0), s(MV ''Rpa'' tid0), LN ''Rb'' tid0,+                  s(MV ''Text6'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_2'', LN ''Rb'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc_1 tid1) note_unified facts = this facts+        hence "Kbd ( s(AV ''P'' tid1) )+                   ( s(MV ''B'' tid1) ) = Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) )"+          by simp note facts = this facts+        thus ?thesis proof(cases rule: Kbd_cases)+          case noswap note_unified facts = this facts+          thus ?thesis by (fastforce dest: different_actors_B_P intro: event_predOrdI)+        next+          case swapped note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_4'', s(MV ''Rpa'' tid0),+                                  LN ''Rb'' tid0, s(MV ''Text6'' tid0)+                               |}+                               ( LN ''Kab'' tid1 ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+          next+            case (isoiec_9798_2_6_special_TTP_bdkey_A_4_enc tid2) note_unified facts = this facts+            thus ?thesis proof(sources! "+                             Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_1'', LN ''Ra'' tid2,+                                    LN ''Kab'' tid1, s(MV ''B'' tid2), s(MV ''Text4'' tid2)+                                 |}+                                 ( Kbd ( s(AV ''A'' tid2) ) ( s(AV ''P'' tid2) ) ) ")+              case fake note_unified facts = this facts+              thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+            next+              case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc tid3) note_unified facts = this facts+              hence "Kbd ( s(AV ''A'' tid2) )+                         ( s(AV ''P'' tid2) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid1) )"+                by simp note facts = this facts+              thus ?thesis proof(cases rule: Kbd_cases)+                case noswap note_unified facts = this facts+                thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+              next+                case swapped note_unified facts = this facts+                thus ?thesis by (fastforce dest: different_actors_A_P intro: event_predOrdI)+              qed (fastforce+)?+            qed (insert facts, fastforce+)?+          qed (insert facts, fastforce+)?+        qed (fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_6_special_TTP_bdkey_state) A_injective_agreement_P:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''P'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_6_special_TTP_bdkey_A_3 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_6_special_TTP_bdkey_P &+          ( tid1, isoiec_9798_2_6_special_TTP_bdkey_P_3 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),+             s(MV ''Ra'' tid1), LN ''Kab'' tid1, s(MV ''Text4'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''P'' tid0),+                  LN ''Ra'' tid0, s(MV ''Kab'' tid0), s(MV ''Text4'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_1'', LN ''Ra'' tid0,+                              s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)+                           |}+                           ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc tid1) note_unified facts = this facts+        hence "Kbd ( s(AV ''P'' tid1) )+                   ( s(MV ''A'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) )"+          by simp note facts = this facts+        thus ?thesis proof(cases rule: Kbd_cases)+          case noswap note_unified facts = this facts+          thus ?thesis by (fastforce dest: different_actors_A_P intro: event_predOrdI)+        next+          case swapped note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_6_special_TTP_bdkey_state) B_injective_agreement_P:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_6_special_TTP_bdkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(MV ''P'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_6_special_TTP_bdkey_B_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_6_special_TTP_bdkey_P &+          ( tid1, isoiec_9798_2_6_special_TTP_bdkey_P_3 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),+             s(MV ''Rb'' tid1), LN ''Kab'' tid1, s(MV ''Text3'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),+                  LN ''Rb'' tid0, s(MV ''Kab'' tid0), s(MV ''Text3'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_6_special_TTP_enc_3_2'', LN ''Rb'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_6_special_TTP_bdkey_P_3_enc_1 tid1) note_unified facts = this facts+        hence "Kbd ( s(AV ''P'' tid1) )+                   ( s(MV ''B'' tid1) ) = Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) )"+          by simp note facts = this facts+        thus ?thesis proof(cases rule: Kbd_cases)+          case noswap note_unified facts = this facts+          thus ?thesis by (fastforce dest: different_actors_B_P intro: event_predOrdI)+        next+          case swapped note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj) qed  end
data/examples/iso9798/isabelle-proofs/isoiec-9798-2-udkey_cert_auto.thy view
@@ -1,2190 +1,2370 @@ theory "isoiec-9798-2-udkey_cert_auto" imports-  "../ESPLogic"-begin--role isoiec_9798_2_1_udkey_A-where "isoiec_9798_2_1_udkey_A =-  [ Send ''leak_A'' ( sN ''TNA'' )-  , Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>-  , Send ''1'' <| sAV ''A'', sAV ''B'', sMV ''Text2'',-                  PEnc <| sC ''isoiec_9798_2_1_enc_1'', sN ''TNA'', sMV ''Text1'' |>-                       ( sK ''A'' ''B'' )-               |>-  ]"--role isoiec_9798_2_1_udkey_B-where "isoiec_9798_2_1_udkey_B =-  [ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Text2'',-                  PEnc <| sC ''isoiec_9798_2_1_enc_1'', sMV ''TNA'', sMV ''Text1'' |>-                       ( PSymK ( sMV ''A'' ) ( sAV ''B'' ) )-               |>-  ]"--protocol isoiec_9798_2_1_udkey-where "isoiec_9798_2_1_udkey =-{ isoiec_9798_2_1_udkey_A, isoiec_9798_2_1_udkey_B }"--locale restricted_isoiec_9798_2_1_udkey_state = isoiec_9798_2_1_udkey_state--type_invariant isoiec_9798_2_1_udkey_msc_typing for isoiec_9798_2_1_udkey-where "isoiec_9798_2_1_udkey_msc_typing = mk_typing-  [ ((isoiec_9798_2_1_udkey_B, ''A''), (KnownT isoiec_9798_2_1_udkey_B_1))-  , ((isoiec_9798_2_1_udkey_B, ''TNA''),-     (SumT (KnownT isoiec_9798_2_1_udkey_B_1) (NonceT isoiec_9798_2_1_udkey_A ''TNA'')))-  , ((isoiec_9798_2_1_udkey_A, ''Text1''),-     (KnownT isoiec_9798_2_1_udkey_A_text_1))-  , ((isoiec_9798_2_1_udkey_B, ''Text1''),-     (KnownT isoiec_9798_2_1_udkey_B_1))-  , ((isoiec_9798_2_1_udkey_A, ''Text2''),-     (KnownT isoiec_9798_2_1_udkey_A_text_1))-  , ((isoiec_9798_2_1_udkey_B, ''Text2''),-     (KnownT isoiec_9798_2_1_udkey_B_1))-  ]"--sublocale isoiec_9798_2_1_udkey_state < isoiec_9798_2_1_udkey_msc_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_2_1_udkey_msc_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_2_1_udkey_msc_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_2_1_udkey_A_text_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_1_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_1_udkey_A_text_1_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_1_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_1_udkey_B_1_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_1_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_1_udkey_B_1_TNA t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_1_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_1_enc_1'', s(MV ''TNA'' tid0),-               s(MV ''Text1'' tid0)-            |}-            ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_1_udkey_B_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_1_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_1_enc_1'', s(MV ''TNA'' tid0),-               s(MV ''Text1'' tid0)-            |}-            ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_1_udkey_B_1_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_1_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_2_1_udkey_msc_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_2_1_udkey_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end--lemma (in restricted_isoiec_9798_2_1_udkey_state) B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_1_udkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_1_udkey_B_1 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_1_udkey_A &-        ( tid1, isoiec_9798_2_1_udkey_A_1 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,-           s(MV ''Text1'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),-                s(MV ''Text1'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_1_enc_1'', s(MV ''TNA'' tid0),-                          s(MV ''Text1'' tid0)-                       |}-                       ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_1_udkey_A_1_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--role isoiec_9798_2_2_udkey_A-where "isoiec_9798_2_2_udkey_A =-  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''RB'', sMV ''Text1'' |>-  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>-  , Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'',-                  PEnc <| sC ''isoiec_9798_2_2_enc_2'', sMV ''RB'', sMV ''Text2'' |>-                       ( PSymK ( sAV ''A'' ) ( sMV ''B'' ) )-               |>-  ]"--role isoiec_9798_2_2_udkey_B-where "isoiec_9798_2_2_udkey_B =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''RB'', sMV ''Text1'' |>-  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'',-                  PEnc <| sC ''isoiec_9798_2_2_enc_2'', sN ''RB'', sMV ''Text2'' |>-                       ( sK ''A'' ''B'' )-               |>-  ]"--protocol isoiec_9798_2_2_udkey-where "isoiec_9798_2_2_udkey =-{ isoiec_9798_2_2_udkey_A, isoiec_9798_2_2_udkey_B }"--locale restricted_isoiec_9798_2_2_udkey_state = isoiec_9798_2_2_udkey_state--type_invariant isoiec_9798_2_2_udkey_msc_typing for isoiec_9798_2_2_udkey-where "isoiec_9798_2_2_udkey_msc_typing = mk_typing-  [ ((isoiec_9798_2_2_udkey_A, ''B''), (KnownT isoiec_9798_2_2_udkey_A_1))-  , ((isoiec_9798_2_2_udkey_A, ''RB''), (KnownT isoiec_9798_2_2_udkey_A_1))-  , ((isoiec_9798_2_2_udkey_A, ''Text1''),-     (KnownT isoiec_9798_2_2_udkey_A_1))-  , ((isoiec_9798_2_2_udkey_B, ''Text1''),-     (KnownT isoiec_9798_2_2_udkey_B_text_1))-  , ((isoiec_9798_2_2_udkey_A, ''Text2''),-     (KnownT isoiec_9798_2_2_udkey_A_text_2))-  , ((isoiec_9798_2_2_udkey_B, ''Text2''),-     (KnownT isoiec_9798_2_2_udkey_B_2))-  , ((isoiec_9798_2_2_udkey_A, ''Text3''),-     (KnownT isoiec_9798_2_2_udkey_A_text_2))-  , ((isoiec_9798_2_2_udkey_B, ''Text3''),-     (KnownT isoiec_9798_2_2_udkey_B_2))-  ]"--sublocale isoiec_9798_2_2_udkey_state < isoiec_9798_2_2_udkey_msc_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_2_2_udkey_msc_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_2_2_udkey_msc_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_2_2_udkey_A_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_2_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_2_udkey_A_1_RB t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_2_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_2_udkey_A_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_2_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_2_udkey_A_text_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_2_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_2_udkey_A_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_2_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_2_udkey_B_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_2_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_2_enc_2'', LN ''RB'' tid0, s(MV ''Text2'' tid0)-            |}-            ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_2_udkey_B_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_2_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_2_2_udkey_msc_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_2_2_udkey_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end--lemma (in restricted_isoiec_9798_2_2_udkey_state) B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_2_udkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_2_udkey_B_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_2_udkey_A &-        ( tid1, isoiec_9798_2_2_udkey_A_2 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(MV ''RB'' tid1),-           s(MV ''Text2'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''RB'' tid0,-                s(MV ''Text2'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_2_enc_2'', LN ''RB'' tid0, s(MV ''Text2'' tid0)-                       |}-                       ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_2_udkey_A_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--role isoiec_9798_2_3_udkey_A-where "isoiec_9798_2_3_udkey_A =-  [ Send ''leak_A'' ( sN ''TNA'' )-  , Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>-  , Send ''1'' <| sAV ''A'', sAV ''B'', sMV ''Text2'',-                  PEnc <| sC ''isoiec_9798_2_3_enc_1'', sN ''TNA'', sMV ''Text1'' |>-                       ( sK ''A'' ''B'' )-               |>-  , Recv ''2'' <| sAV ''B'', sAV ''A'', sMV ''Text4'',-                  PEnc <| sC ''isoiec_9798_2_3_enc_2'', sMV ''TNB'', sMV ''Text3'' |>-                       ( sK ''B'' ''A'' )-               |>-  ]"--role isoiec_9798_2_3_udkey_B-where "isoiec_9798_2_3_udkey_B =-  [ Send ''leak_B'' ( sN ''TNB'' )-  , Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Text2'',-                  PEnc <| sC ''isoiec_9798_2_3_enc_1'', sMV ''TNA'', sMV ''Text1'' |>-                       ( PSymK ( sMV ''A'' ) ( sAV ''B'' ) )-               |>-  , Recv ''text_2'' <| sMV ''Text3'', sMV ''Text4'' |>-  , Send ''2'' <| sAV ''B'', sMV ''A'', sMV ''Text4'',-                  PEnc <| sC ''isoiec_9798_2_3_enc_2'', sN ''TNB'', sMV ''Text3'' |>-                       ( PSymK ( sAV ''B'' ) ( sMV ''A'' ) )-               |>-  ]"--protocol isoiec_9798_2_3_udkey-where "isoiec_9798_2_3_udkey =-{ isoiec_9798_2_3_udkey_A, isoiec_9798_2_3_udkey_B }"--locale restricted_isoiec_9798_2_3_udkey_state = isoiec_9798_2_3_udkey_state--type_invariant isoiec_9798_2_3_udkey_msc_typing for isoiec_9798_2_3_udkey-where "isoiec_9798_2_3_udkey_msc_typing = mk_typing-  [ ((isoiec_9798_2_3_udkey_B, ''A''), (KnownT isoiec_9798_2_3_udkey_B_1))-  , ((isoiec_9798_2_3_udkey_B, ''TNA''),-     (SumT (KnownT isoiec_9798_2_3_udkey_B_1) (NonceT isoiec_9798_2_3_udkey_A ''TNA'')))-  , ((isoiec_9798_2_3_udkey_A, ''TNB''),-     (SumT (KnownT isoiec_9798_2_3_udkey_A_2) (NonceT isoiec_9798_2_3_udkey_B ''TNB'')))-  , ((isoiec_9798_2_3_udkey_A, ''Text1''),-     (KnownT isoiec_9798_2_3_udkey_A_text_1))-  , ((isoiec_9798_2_3_udkey_B, ''Text1''),-     (KnownT isoiec_9798_2_3_udkey_B_1))-  , ((isoiec_9798_2_3_udkey_A, ''Text2''),-     (KnownT isoiec_9798_2_3_udkey_A_text_1))-  , ((isoiec_9798_2_3_udkey_B, ''Text2''),-     (KnownT isoiec_9798_2_3_udkey_B_1))-  , ((isoiec_9798_2_3_udkey_A, ''Text3''),-     (KnownT isoiec_9798_2_3_udkey_A_2))-  , ((isoiec_9798_2_3_udkey_B, ''Text3''),-     (KnownT isoiec_9798_2_3_udkey_B_text_2))-  , ((isoiec_9798_2_3_udkey_A, ''Text4''),-     (KnownT isoiec_9798_2_3_udkey_A_2))-  , ((isoiec_9798_2_3_udkey_B, ''Text4''),-     (KnownT isoiec_9798_2_3_udkey_B_text_2))-  ]"--sublocale isoiec_9798_2_3_udkey_state < isoiec_9798_2_3_udkey_msc_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_2_3_udkey_msc_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_2_3_udkey_msc_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_2_3_udkey_A_text_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_udkey_A_text_1_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_udkey_A_2_TNB t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_3_enc_2'', s(MV ''TNB'' tid0),-               s(MV ''Text3'' tid0)-            |}-            ( K ( s(AV ''B'' tid0) ) ( s(AV ''A'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_3_udkey_A_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_3_enc_2'', s(MV ''TNB'' tid0),-               s(MV ''Text3'' tid0)-            |}-            ( K ( s(AV ''B'' tid0) ) ( s(AV ''A'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_3_udkey_A_2_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_udkey_B_1_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_udkey_B_1_TNA t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_3_enc_1'', s(MV ''TNA'' tid0),-               s(MV ''Text1'' tid0)-            |}-            ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_3_udkey_B_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_3_enc_1'', s(MV ''TNA'' tid0),-               s(MV ''Text1'' tid0)-            |}-            ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_3_udkey_B_1_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_udkey_B_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_3_udkey_B_text_2_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_2_3_udkey_msc_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_2_3_udkey_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end--lemma (in restricted_isoiec_9798_2_3_udkey_state) A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_3_udkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_3_udkey_A_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_3_udkey_B &-        ( tid1, isoiec_9798_2_3_udkey_B_2 ) : steps t &-        {| s(MV ''A'' tid1), s(AV ''B'' tid1), LN ''TNB'' tid1,-           s(MV ''Text3'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNB'' tid0),-                s(MV ''Text3'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_3_enc_2'', s(MV ''TNB'' tid0),-                          s(MV ''Text3'' tid0)-                       |}-                       ( K ( s(AV ''B'' tid0) ) ( s(AV ''A'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_3_udkey_B_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_3_udkey_state) B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_3_udkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_3_udkey_B_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_3_udkey_A &-        ( tid1, isoiec_9798_2_3_udkey_A_1 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,-           s(MV ''Text1'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),-                s(MV ''Text1'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_3_enc_1'', s(MV ''TNA'' tid0),-                          s(MV ''Text1'' tid0)-                       |}-                       ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_3_udkey_A_1_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--role isoiec_9798_2_4_udkey_A-where "isoiec_9798_2_4_udkey_A =-  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''RB'', sMV ''Text1'' |>-  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>-  , Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'',-                  PEnc <| sC ''isoiec_9798_2_4_enc_1'', sN ''RA'', sMV ''RB'',-                          sMV ''Text2''-                       |>-                       ( PSymK ( sAV ''A'' ) ( sMV ''B'' ) )-               |>-  , Recv ''3'' <| sMV ''B'', sAV ''A'', sMV ''Text5'',-                  PEnc <| sC ''isoiec_9798_2_4_enc_2'', sMV ''RB'', sN ''RA'',-                          sMV ''Text4''-                       |>-                       ( PSymK ( sMV ''B'' ) ( sAV ''A'' ) )-               |>-  ]"--role isoiec_9798_2_4_udkey_B-where "isoiec_9798_2_4_udkey_B =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''RB'', sMV ''Text1'' |>-  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'',-                  PEnc <| sC ''isoiec_9798_2_4_enc_1'', sMV ''RA'', sN ''RB'',-                          sMV ''Text2''-                       |>-                       ( sK ''A'' ''B'' )-               |>-  , Recv ''text_3'' <| sMV ''Text4'', sMV ''Text5'' |>-  , Send ''3'' <| sAV ''B'', sAV ''A'', sMV ''Text5'',-                  PEnc <| sC ''isoiec_9798_2_4_enc_2'', sN ''RB'', sMV ''RA'',-                          sMV ''Text4''-                       |>-                       ( sK ''B'' ''A'' )-               |>-  ]"--protocol isoiec_9798_2_4_udkey-where "isoiec_9798_2_4_udkey =-{ isoiec_9798_2_4_udkey_A, isoiec_9798_2_4_udkey_B }"--locale restricted_isoiec_9798_2_4_udkey_state = isoiec_9798_2_4_udkey_state--type_invariant isoiec_9798_2_4_udkey_msc_typing for isoiec_9798_2_4_udkey-where "isoiec_9798_2_4_udkey_msc_typing = mk_typing-  [ ((isoiec_9798_2_4_udkey_A, ''B''), (KnownT isoiec_9798_2_4_udkey_A_1))-  , ((isoiec_9798_2_4_udkey_B, ''RA''),-     (SumT (KnownT isoiec_9798_2_4_udkey_B_2) (NonceT isoiec_9798_2_4_udkey_A ''RA'')))-  , ((isoiec_9798_2_4_udkey_A, ''RB''), (KnownT isoiec_9798_2_4_udkey_A_1))-  , ((isoiec_9798_2_4_udkey_A, ''Text1''),-     (KnownT isoiec_9798_2_4_udkey_A_1))-  , ((isoiec_9798_2_4_udkey_B, ''Text1''),-     (KnownT isoiec_9798_2_4_udkey_B_text_1))-  , ((isoiec_9798_2_4_udkey_A, ''Text2''),-     (KnownT isoiec_9798_2_4_udkey_A_text_2))-  , ((isoiec_9798_2_4_udkey_B, ''Text2''),-     (KnownT isoiec_9798_2_4_udkey_B_2))-  , ((isoiec_9798_2_4_udkey_A, ''Text3''),-     (KnownT isoiec_9798_2_4_udkey_A_text_2))-  , ((isoiec_9798_2_4_udkey_B, ''Text3''),-     (KnownT isoiec_9798_2_4_udkey_B_2))-  , ((isoiec_9798_2_4_udkey_A, ''Text4''),-     (KnownT isoiec_9798_2_4_udkey_A_3))-  , ((isoiec_9798_2_4_udkey_B, ''Text4''),-     (KnownT isoiec_9798_2_4_udkey_B_text_3))-  , ((isoiec_9798_2_4_udkey_A, ''Text5''),-     (KnownT isoiec_9798_2_4_udkey_A_3))-  , ((isoiec_9798_2_4_udkey_B, ''Text5''),-     (KnownT isoiec_9798_2_4_udkey_B_text_3))-  ]"--sublocale isoiec_9798_2_4_udkey_state < isoiec_9798_2_4_udkey_msc_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_2_4_udkey_msc_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_2_4_udkey_msc_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_2_4_udkey_A_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_udkey_A_1_RB t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_udkey_A_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_udkey_A_text_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_udkey_A_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_udkey_A_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_4_enc_2'', s(MV ''RB'' tid0), LN ''RA'' tid0,-               s(MV ''Text4'' tid0)-            |}-            ( K ( s(MV ''B'' tid0) ) ( s(AV ''A'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_4_udkey_A_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_udkey_B_2_RA t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_4_enc_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,-               s(MV ''Text2'' tid0)-            |}-            ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_4_udkey_B_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_4_enc_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,-               s(MV ''Text2'' tid0)-            |}-            ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_4_udkey_B_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_udkey_B_text_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_4_udkey_B_text_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_2_4_udkey_msc_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_2_4_udkey_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end--lemma (in restricted_isoiec_9798_2_4_udkey_state) A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_4_udkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_4_udkey_A_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_4_udkey_B &-        ( tid1, isoiec_9798_2_4_udkey_B_3 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''RA'' tid1), LN ''RB'' tid1,-           s(MV ''Text2'' tid1), s(MV ''Text4'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''RA'' tid0,-                s(MV ''RB'' tid0), s(MV ''Text2'' tid0), s(MV ''Text4'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_4_enc_2'', s(MV ''RB'' tid0), LN ''RA'' tid0,-                          s(MV ''Text4'' tid0)-                       |}-                       ( K ( s(MV ''B'' tid0) ) ( s(AV ''A'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_4_udkey_B_3_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_2_4_enc_1'', LN ''RA'' tid0, LN ''RB'' tid1,-                            s(MV ''Text2'' tid1)-                         |}-                         ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid1) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest!: ltk_secrecy)-    next-      case (isoiec_9798_2_4_udkey_A_2_enc tid2) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_4_udkey_state) B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_4_udkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_4_udkey_B_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_4_udkey_A &-        ( tid1, isoiec_9798_2_4_udkey_A_2 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''RA'' tid1, s(MV ''RB'' tid1),-           s(MV ''Text2'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''RA'' tid0),-                LN ''RB'' tid0, s(MV ''Text2'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_4_enc_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,-                          s(MV ''Text2'' tid0)-                       |}-                       ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_4_udkey_A_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--role isoiec_9798_2_5_udkey_A-where "isoiec_9798_2_5_udkey_A =-  [ Send ''leak_A'' <| sN ''TVPa'', sN ''TNa'' |>-  , Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''A'', sAV ''P'', sN ''TVPa'', sAV ''B'',-                  sMV ''Text1''-               |>-  , Recv ''2'' <| sAV ''P'', sAV ''A'', sMV ''Text4'',-                  PEnc <| sC ''isoiec_9798_2_5_enc_2_1'', sN ''TVPa'', sMV ''Kab'',-                          sAV ''B'', sMV ''Text3''-                       |>-                       ( sK ''A'' ''P'' ),-                  sMV ''TokenPA_for_B''-               |>-  , Recv ''text_3'' <| sMV ''Text5'', sMV ''Text6'' |>-  , Send ''3'' <| sAV ''A'', sAV ''B'', sMV ''Text6'', sAV ''P'',-                  sMV ''TokenPA_for_B'',-                  PEnc <| sC ''isoiec_9798_2_5_enc_3'', sN ''TNa'', sAV ''B'',-                          sMV ''Text5''-                       |>-                       ( sMV ''Kab'' )-               |>-  , Recv ''4'' <| sAV ''B'', sAV ''A'', sMV ''Text8'',-                  PEnc <| sC ''isoiec_9798_2_5_enc_4'', sMV ''TNb'', sAV ''A'',-                          sMV ''Text7''-                       |>-                       ( sMV ''Kab'' )-               |>-  ]"--role isoiec_9798_2_5_udkey_B-where "isoiec_9798_2_5_udkey_B =-  [ Send ''leak_B'' ( sN ''TNb'' )-  , Recv ''3'' <| sMV ''A'', sAV ''B'', sMV ''Text6'', sMV ''P'',-                  PEnc <| sC ''isoiec_9798_2_5_enc_2_2'', sMV ''TNp'', sMV ''Kab'',-                          sMV ''A'', sMV ''Text2''-                       |>-                       ( PSymK ( sAV ''B'' ) ( sMV ''P'' ) ),-                  PEnc <| sC ''isoiec_9798_2_5_enc_3'', sMV ''TNa'', sAV ''B'',-                          sMV ''Text5''-                       |>-                       ( sMV ''Kab'' )-               |>-  , Recv ''text_4'' <| sMV ''Text7'', sMV ''Text8'' |>-  , Send ''4'' <| sAV ''B'', sMV ''A'', sMV ''Text8'',-                  PEnc <| sC ''isoiec_9798_2_5_enc_4'', sN ''TNb'', sMV ''A'',-                          sMV ''Text7''-                       |>-                       ( sMV ''Kab'' )-               |>-  ]"--role isoiec_9798_2_5_udkey_P-where "isoiec_9798_2_5_udkey_P =-  [ Send ''leak_P'' ( sN ''TNp'' )-  , Recv ''1'' <| sMV ''A'', sAV ''P'', sMV ''TVPa'', sMV ''B'',-                  sMV ''Text1''-               |>-  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'', sMV ''Text4'' |>-  , Send ''2'' <| sAV ''P'', sMV ''A'', sMV ''Text4'',-                  PEnc <| sC ''isoiec_9798_2_5_enc_2_1'', sMV ''TVPa'', sN ''Kab'',-                          sMV ''B'', sMV ''Text3''-                       |>-                       ( PSymK ( sMV ''A'' ) ( sAV ''P'' ) ),-                  PEnc <| sC ''isoiec_9798_2_5_enc_2_2'', sN ''TNp'', sN ''Kab'',-                          sMV ''A'', sMV ''Text2''-                       |>-                       ( PSymK ( sMV ''B'' ) ( sAV ''P'' ) )-               |>-  ]"--protocol isoiec_9798_2_5_udkey-where "isoiec_9798_2_5_udkey =-{ isoiec_9798_2_5_udkey_A, isoiec_9798_2_5_udkey_B,-  isoiec_9798_2_5_udkey_P-}"--locale restricted_isoiec_9798_2_5_udkey_state = isoiec_9798_2_5_udkey_state--type_invariant isoiec_9798_2_5_udkey_msc_typing for isoiec_9798_2_5_udkey-where "isoiec_9798_2_5_udkey_msc_typing = mk_typing-  [ ((isoiec_9798_2_5_udkey_B, ''A''), (KnownT isoiec_9798_2_5_udkey_B_3))-  , ((isoiec_9798_2_5_udkey_P, ''A''), (KnownT isoiec_9798_2_5_udkey_P_1))-  , ((isoiec_9798_2_5_udkey_P, ''B''), (KnownT isoiec_9798_2_5_udkey_P_1))-  , ((isoiec_9798_2_5_udkey_A, ''Kab''),-     (SumT (KnownT isoiec_9798_2_5_udkey_A_2) (NonceT isoiec_9798_2_5_udkey_P ''Kab'')))-  , ((isoiec_9798_2_5_udkey_B, ''Kab''),-     (SumT (KnownT isoiec_9798_2_5_udkey_B_3) (NonceT isoiec_9798_2_5_udkey_P ''Kab'')))-  , ((isoiec_9798_2_5_udkey_B, ''P''), (KnownT isoiec_9798_2_5_udkey_B_3))-  , ((isoiec_9798_2_5_udkey_B, ''TNa''),-     (SumT (KnownT isoiec_9798_2_5_udkey_B_3) (NonceT isoiec_9798_2_5_udkey_A ''TNa'')))-  , ((isoiec_9798_2_5_udkey_A, ''TNb''),-     (SumT (KnownT isoiec_9798_2_5_udkey_A_4) (NonceT isoiec_9798_2_5_udkey_B ''TNb'')))-  , ((isoiec_9798_2_5_udkey_B, ''TNp''),-     (SumT (KnownT isoiec_9798_2_5_udkey_B_3) (NonceT isoiec_9798_2_5_udkey_P ''TNp'')))-  , ((isoiec_9798_2_5_udkey_P, ''TVPa''),-     (KnownT isoiec_9798_2_5_udkey_P_1))-  , ((isoiec_9798_2_5_udkey_A, ''Text1''),-     (KnownT isoiec_9798_2_5_udkey_A_text_1))-  , ((isoiec_9798_2_5_udkey_P, ''Text1''),-     (KnownT isoiec_9798_2_5_udkey_P_1))-  , ((isoiec_9798_2_5_udkey_B, ''Text2''),-     (KnownT isoiec_9798_2_5_udkey_B_3))-  , ((isoiec_9798_2_5_udkey_P, ''Text2''),-     (KnownT isoiec_9798_2_5_udkey_P_text_2))-  , ((isoiec_9798_2_5_udkey_A, ''Text3''),-     (KnownT isoiec_9798_2_5_udkey_A_2))-  , ((isoiec_9798_2_5_udkey_P, ''Text3''),-     (KnownT isoiec_9798_2_5_udkey_P_text_2))-  , ((isoiec_9798_2_5_udkey_A, ''Text4''),-     (KnownT isoiec_9798_2_5_udkey_A_2))-  , ((isoiec_9798_2_5_udkey_P, ''Text4''),-     (KnownT isoiec_9798_2_5_udkey_P_text_2))-  , ((isoiec_9798_2_5_udkey_A, ''Text5''),-     (KnownT isoiec_9798_2_5_udkey_A_text_3))-  , ((isoiec_9798_2_5_udkey_B, ''Text5''),-     (KnownT isoiec_9798_2_5_udkey_B_3))-  , ((isoiec_9798_2_5_udkey_A, ''Text6''),-     (KnownT isoiec_9798_2_5_udkey_A_text_3))-  , ((isoiec_9798_2_5_udkey_B, ''Text6''),-     (KnownT isoiec_9798_2_5_udkey_B_3))-  , ((isoiec_9798_2_5_udkey_A, ''Text7''),-     (KnownT isoiec_9798_2_5_udkey_A_4))-  , ((isoiec_9798_2_5_udkey_B, ''Text7''),-     (KnownT isoiec_9798_2_5_udkey_B_text_4))-  , ((isoiec_9798_2_5_udkey_A, ''Text8''),-     (KnownT isoiec_9798_2_5_udkey_A_4))-  , ((isoiec_9798_2_5_udkey_B, ''Text8''),-     (KnownT isoiec_9798_2_5_udkey_B_text_4))-  , ((isoiec_9798_2_5_udkey_A, ''TokenPA_for_B''),-     (KnownT isoiec_9798_2_5_udkey_A_2))-  ]"--sublocale isoiec_9798_2_5_udkey_state < isoiec_9798_2_5_udkey_msc_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_2_5_udkey_msc_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_2_5_udkey_msc_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_2_5_udkey_A_2_Kab t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,-               s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)-            |}-            ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_udkey_A_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,-               s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)-            |}-            ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_udkey_A_2_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_A_2_TokenPA_for_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_A_text_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_A_text_3_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_A_4_TNb t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_4'', s(MV ''TNb'' tid0),-               s(AV ''A'' tid0), s(MV ''Text7'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_udkey_A_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_4'', s(MV ''TNb'' tid0),-               s(AV ''A'' tid0), s(MV ''Text7'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_udkey_A_4_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_B_3_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_B_3_Kab t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),-               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)-            |}-            ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_udkey_B_3_P t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_B_3_TNa t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid0),-               s(AV ''B'' tid0), s(MV ''Text5'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_udkey_B_3_TNp t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),-               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)-            |}-            ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_udkey_B_3_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),-               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)-            |}-            ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_udkey_B_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid0),-               s(AV ''B'' tid0), s(MV ''Text5'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_5_udkey_B_3_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_B_text_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_B_text_4_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_P_1_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_P_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_P_1_TVPa t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_P_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_P_text_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_P_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_5_udkey_P_text_2_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_2_5_udkey_msc_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_2_5_udkey_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end--lemma (in restricted_isoiec_9798_2_5_udkey_state) P_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_udkey_P"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "LN ''Kab'' tid0 : knows t"-  shows "False"-using facts proof(sources! " LN ''Kab'' tid0 ")-  case isoiec_9798_2_5_udkey_P_2_Kab note_unified facts = this facts-  thus ?thesis by (fastsimp dest!: ltk_secrecy)-next-  case isoiec_9798_2_5_udkey_P_2_Kab_1 note_unified facts = this facts-  thus ?thesis by (fastsimp dest!: ltk_secrecy)-qed (insert facts, fastsimp+)?--lemma (in restricted_isoiec_9798_2_5_udkey_state) A_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_udkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_udkey_A_2 ) : steps t"-    "s(MV ''Kab'' tid0) : knows t"-  shows "False"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_udkey_P_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_5_udkey_state) B_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_udkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_udkey_B_3 ) : steps t"-    "s(MV ''Kab'' tid0) : knows t"-  shows "False"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),-                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)-                       |}-                       ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_udkey_P_2_enc_1 tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_5_udkey_state) A_non_injective_agreement_B:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_udkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_udkey_A_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_5_udkey_B &-        ( tid1, isoiec_9798_2_5_udkey_B_4 ) : steps t &-        {| s(MV ''A'' tid1), s(AV ''B'' tid1), s(MV ''P'' tid1),-           s(MV ''Kab'' tid1), s(MV ''TNa'' tid1), s(MV ''Text5'' tid1),-           LN ''TNb'' tid1, s(MV ''Text7'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''P'' tid0),-                s(MV ''Kab'' tid0), LN ''TNa'' tid0, s(MV ''Text5'' tid0),-                s(MV ''TNb'' tid0), s(MV ''Text7'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_udkey_P_2_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_2_5_enc_4'', s(MV ''TNb'' tid0),-                            s(AV ''A'' tid0), s(MV ''Text7'' tid0)-                         |}-                         ( LN ''Kab'' tid1 ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-    next-      case (isoiec_9798_2_5_udkey_B_4_enc tid2) note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid2),-                              LN ''Kab'' tid1, s(AV ''A'' tid0), s(MV ''Text2'' tid2)-                           |}-                           ( K ( s(AV ''B'' tid2) ) ( s(MV ''P'' tid2) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-      next-        case (isoiec_9798_2_5_udkey_P_2_enc_1 tid3) note_unified facts = this facts-        thus ?thesis proof(sources! "-                         Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid2),-                                s(AV ''B'' tid0), s(MV ''Text5'' tid2)-                             |}-                             ( LN ''Kab'' tid1 ) ")-          case fake note_unified facts = this facts-          thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-        next-          case (isoiec_9798_2_5_udkey_A_3_enc tid3) note_unified facts = this facts-          thus ?thesis proof(sources! "-                           Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid3, LN ''Kab'' tid1,-                                  s(AV ''B'' tid0), s(MV ''Text3'' tid3)-                               |}-                               ( K ( s(AV ''A'' tid3) ) ( s(AV ''P'' tid3) ) ) ")-            case fake note_unified facts = this facts-            thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-          next-            case (isoiec_9798_2_5_udkey_P_2_enc tid4) note_unified facts = this facts-            thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-          qed (insert facts, fastsimp+)?-        qed (insert facts, fastsimp+)?-      qed (insert facts, fastsimp+)?-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_5_udkey_state) B_non_injective_agreement_A:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_udkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_udkey_B_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_5_udkey_A &-        ( tid1, isoiec_9798_2_5_udkey_A_3 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(AV ''P'' tid1),-           s(MV ''Kab'' tid1), LN ''TNa'' tid1, s(MV ''Text5'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),-                s(MV ''Kab'' tid0), s(MV ''TNa'' tid0), s(MV ''Text5'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),-                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)-                       |}-                       ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_udkey_P_2_enc_1 tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid0),-                            s(AV ''B'' tid0), s(MV ''Text5'' tid0)-                         |}-                         ( LN ''Kab'' tid1 ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-    next-      case (isoiec_9798_2_5_udkey_A_3_enc tid2) note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid2, LN ''Kab'' tid1,-                              s(AV ''B'' tid0), s(MV ''Text3'' tid2)-                           |}-                           ( K ( s(AV ''A'' tid2) ) ( s(AV ''P'' tid2) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-      next-        case (isoiec_9798_2_5_udkey_P_2_enc tid3) note_unified facts = this facts-        thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-      qed (insert facts, fastsimp+)?-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_5_udkey_state) A_non_injective_agreement_P:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_udkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_udkey_A_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_5_udkey_P &-        ( tid1, isoiec_9798_2_5_udkey_P_2 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1), LN ''Kab'' tid1,-           s(MV ''TVPa'' tid1), s(MV ''Text3'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''P'' tid0),-                s(MV ''Kab'' tid0), LN ''TVPa'' tid0, s(MV ''Text3'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_udkey_P_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_5_udkey_state) B_non_injective_agreement_P:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_5_udkey_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_5_udkey_B_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_5_udkey_P &-        ( tid1, isoiec_9798_2_5_udkey_P_2 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1), LN ''Kab'' tid1,-           LN ''TNp'' tid1, s(MV ''Text2'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),-                s(MV ''Kab'' tid0), s(MV ''TNp'' tid0), s(MV ''Text2'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),-                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)-                       |}-                       ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_5_udkey_P_2_enc_1 tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--role isoiec_9798_2_6_udkey_A-where "isoiec_9798_2_6_udkey_A =-  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>-  , Recv ''text_2'' ( sMV ''Text2'' )-  , Send ''2'' <| sAV ''A'', sAV ''P'', sN ''Ra'', sMV ''Rb'', sMV ''B'',-                  sMV ''Text2''-               |>-  , Recv ''3'' <| sAV ''P'', sAV ''A'', sMV ''Text5'',-                  PEnc <| sC ''isoiec_9798_2_6_enc_3_1'', sN ''Ra'', sMV ''Kab'',-                          sMV ''B'', sMV ''Text4''-                       |>-                       ( sK ''A'' ''P'' ),-                  sMV ''TokenPA_for_B''-               |>-  , Recv ''text_4'' <| sMV ''Text6'', sMV ''Text7'' |>-  , Send ''4'' <| sAV ''A'', sMV ''B'', sMV ''Text7'', sAV ''P'',-                  sMV ''TokenPA_for_B'',-                  PEnc <| sC ''isoiec_9798_2_6_enc_4'', sN ''Rpa'', sMV ''Rb'',-                          sMV ''Text6''-                       |>-                       ( sMV ''Kab'' )-               |>-  , Recv ''5'' <| sMV ''B'', sAV ''A'', sMV ''Text9'',-                  PEnc <| sC ''isoiec_9798_2_6_enc_5'', sMV ''Rb'', sN ''Rpa'',-                          sMV ''Text8''-                       |>-                       ( sMV ''Kab'' )-               |>-  ]"--role isoiec_9798_2_6_udkey_B-where "isoiec_9798_2_6_udkey_B =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>-  , Recv ''4'' <| sAV ''A'', sAV ''B'', sMV ''Text7'', sMV ''P'',-                  PEnc <| sC ''isoiec_9798_2_6_enc_3_2'', sN ''Rb'', sMV ''Kab'',-                          sAV ''A'', sMV ''Text3''-                       |>-                       ( PSymK ( sAV ''B'' ) ( sMV ''P'' ) ),-                  PEnc <| sC ''isoiec_9798_2_6_enc_4'', sMV ''Rpa'', sN ''Rb'',-                          sMV ''Text6''-                       |>-                       ( sMV ''Kab'' )-               |>-  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>-  , Send ''5'' <| sAV ''B'', sAV ''A'', sMV ''Text9'',-                  PEnc <| sC ''isoiec_9798_2_6_enc_5'', sN ''Rb'', sMV ''Rpa'',-                          sMV ''Text8''-                       |>-                       ( sMV ''Kab'' )-               |>-  ]"--role isoiec_9798_2_6_udkey_P-where "isoiec_9798_2_6_udkey_P =-  [ Recv ''2'' <| sMV ''A'', sAV ''P'', sMV ''Ra'', sMV ''Rb'', sMV ''B'',-                  sMV ''Text2''-               |>-  , Recv ''text_3'' <| sMV ''Text3'', sMV ''Text4'', sMV ''Text5'' |>-  , Send ''3'' <| sAV ''P'', sMV ''A'', sMV ''Text5'',-                  PEnc <| sC ''isoiec_9798_2_6_enc_3_1'', sMV ''Ra'', sN ''Kab'',-                          sMV ''B'', sMV ''Text4''-                       |>-                       ( PSymK ( sMV ''A'' ) ( sAV ''P'' ) ),-                  PEnc <| sC ''isoiec_9798_2_6_enc_3_2'', sMV ''Rb'', sN ''Kab'',-                          sMV ''A'', sMV ''Text3''-                       |>-                       ( PSymK ( sMV ''B'' ) ( sAV ''P'' ) )-               |>-  ]"--protocol isoiec_9798_2_6_udkey-where "isoiec_9798_2_6_udkey =-{ isoiec_9798_2_6_udkey_A, isoiec_9798_2_6_udkey_B,-  isoiec_9798_2_6_udkey_P-}"--locale restricted_isoiec_9798_2_6_udkey_state = isoiec_9798_2_6_udkey_state--type_invariant isoiec_9798_2_6_udkey_msc_typing for isoiec_9798_2_6_udkey-where "isoiec_9798_2_6_udkey_msc_typing = mk_typing-  [ ((isoiec_9798_2_6_udkey_P, ''A''), (KnownT isoiec_9798_2_6_udkey_P_2))-  , ((isoiec_9798_2_6_udkey_A, ''B''), (KnownT isoiec_9798_2_6_udkey_A_1))-  , ((isoiec_9798_2_6_udkey_P, ''B''), (KnownT isoiec_9798_2_6_udkey_P_2))-  , ((isoiec_9798_2_6_udkey_A, ''Kab''),-     (SumT (KnownT isoiec_9798_2_6_udkey_A_3) (NonceT isoiec_9798_2_6_udkey_P ''Kab'')))-  , ((isoiec_9798_2_6_udkey_B, ''Kab''),-     (SumT (KnownT isoiec_9798_2_6_udkey_B_4) (NonceT isoiec_9798_2_6_udkey_P ''Kab'')))-  , ((isoiec_9798_2_6_udkey_B, ''P''), (KnownT isoiec_9798_2_6_udkey_B_4))-  , ((isoiec_9798_2_6_udkey_P, ''Ra''), (KnownT isoiec_9798_2_6_udkey_P_2))-  , ((isoiec_9798_2_6_udkey_A, ''Rb''), (KnownT isoiec_9798_2_6_udkey_A_1))-  , ((isoiec_9798_2_6_udkey_P, ''Rb''), (KnownT isoiec_9798_2_6_udkey_P_2))-  , ((isoiec_9798_2_6_udkey_B, ''Rpa''),-     (SumT (KnownT isoiec_9798_2_6_udkey_B_4) (NonceT isoiec_9798_2_6_udkey_A ''Rpa'')))-  , ((isoiec_9798_2_6_udkey_A, ''Text1''),-     (KnownT isoiec_9798_2_6_udkey_A_1))-  , ((isoiec_9798_2_6_udkey_B, ''Text1''),-     (KnownT isoiec_9798_2_6_udkey_B_text_1))-  , ((isoiec_9798_2_6_udkey_A, ''Text2''),-     (KnownT isoiec_9798_2_6_udkey_A_text_2))-  , ((isoiec_9798_2_6_udkey_P, ''Text2''),-     (KnownT isoiec_9798_2_6_udkey_P_2))-  , ((isoiec_9798_2_6_udkey_B, ''Text3''),-     (KnownT isoiec_9798_2_6_udkey_B_4))-  , ((isoiec_9798_2_6_udkey_P, ''Text3''),-     (KnownT isoiec_9798_2_6_udkey_P_text_3))-  , ((isoiec_9798_2_6_udkey_A, ''Text4''),-     (KnownT isoiec_9798_2_6_udkey_A_3))-  , ((isoiec_9798_2_6_udkey_P, ''Text4''),-     (KnownT isoiec_9798_2_6_udkey_P_text_3))-  , ((isoiec_9798_2_6_udkey_A, ''Text5''),-     (KnownT isoiec_9798_2_6_udkey_A_3))-  , ((isoiec_9798_2_6_udkey_P, ''Text5''),-     (KnownT isoiec_9798_2_6_udkey_P_text_3))-  , ((isoiec_9798_2_6_udkey_A, ''Text6''),-     (KnownT isoiec_9798_2_6_udkey_A_text_4))-  , ((isoiec_9798_2_6_udkey_B, ''Text6''),-     (KnownT isoiec_9798_2_6_udkey_B_4))-  , ((isoiec_9798_2_6_udkey_A, ''Text7''),-     (KnownT isoiec_9798_2_6_udkey_A_text_4))-  , ((isoiec_9798_2_6_udkey_B, ''Text7''),-     (KnownT isoiec_9798_2_6_udkey_B_4))-  , ((isoiec_9798_2_6_udkey_A, ''Text8''),-     (KnownT isoiec_9798_2_6_udkey_A_5))-  , ((isoiec_9798_2_6_udkey_B, ''Text8''),-     (KnownT isoiec_9798_2_6_udkey_B_text_5))-  , ((isoiec_9798_2_6_udkey_A, ''Text9''),-     (KnownT isoiec_9798_2_6_udkey_A_5))-  , ((isoiec_9798_2_6_udkey_B, ''Text9''),-     (KnownT isoiec_9798_2_6_udkey_B_text_5))-  , ((isoiec_9798_2_6_udkey_A, ''TokenPA_for_B''),-     (KnownT isoiec_9798_2_6_udkey_A_3))-  ]"--sublocale isoiec_9798_2_6_udkey_state < isoiec_9798_2_6_udkey_msc_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_2_6_udkey_msc_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_2_6_udkey_msc_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_2_6_udkey_A_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_A_1_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_A_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_A_3_Kab t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,-               s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)-            |}-            ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_udkey_A_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,-               s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)-            |}-            ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_udkey_A_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_A_3_TokenPA_for_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_A_text_4_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_A_text_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_A_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_5'', s(MV ''Rb'' tid0), LN ''Rpa'' tid0,-               s(MV ''Text8'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_udkey_A_5_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_B_4_Kab t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,-               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)-            |}-            ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_udkey_B_4_P t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_B_4_Rpa t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_4'', s(MV ''Rpa'' tid0), LN ''Rb'' tid0,-               s(MV ''Text6'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_udkey_B_4_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,-               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)-            |}-            ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_udkey_B_4_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''isoiec_9798_2_6_enc_4'', s(MV ''Rpa'' tid0), LN ''Rb'' tid0,-               s(MV ''Text6'' tid0)-            |}-            ( s(MV ''Kab'' tid0) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_2_6_udkey_B_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_B_text_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_B_text_5_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_P_2_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_P_2_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_P_2_Ra t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_P_2_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_P_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_P_text_3_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_P_text_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_2_6_udkey_P_text_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_2_6_udkey_msc_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_2_6_udkey_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end--lemma (in restricted_isoiec_9798_2_6_udkey_state) P_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_udkey_P"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "LN ''Kab'' tid0 : knows t"-  shows "False"-using facts proof(sources! " LN ''Kab'' tid0 ")-  case isoiec_9798_2_6_udkey_P_3_Kab note_unified facts = this facts-  thus ?thesis by (fastsimp dest!: ltk_secrecy)-next-  case isoiec_9798_2_6_udkey_P_3_Kab_1 note_unified facts = this facts-  thus ?thesis by (fastsimp dest!: ltk_secrecy)-qed (insert facts, fastsimp+)?--lemma (in restricted_isoiec_9798_2_6_udkey_state) A_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_udkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_udkey_A_3 ) : steps t"-    "s(MV ''Kab'' tid0) : knows t"-  shows "False"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,-                          s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)-                       |}-                       ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_udkey_P_3_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_6_udkey_state) B_secret_Kab:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_udkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_udkey_B_4 ) : steps t"-    "s(MV ''Kab'' tid0) : knows t"-  shows "False"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_udkey_P_3_enc_1 tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_6_udkey_state) A_non_injective_agreement_B:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_udkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_udkey_A_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_6_udkey_B &-        ( tid1, isoiec_9798_2_6_udkey_B_5 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''P'' tid1),-           s(MV ''Kab'' tid1), s(MV ''Rpa'' tid1), LN ''Rb'' tid1,-           s(MV ''Text6'' tid1), s(MV ''Text8'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''P'' tid0),-                s(MV ''Kab'' tid0), LN ''Rpa'' tid0, s(MV ''Rb'' tid0),-                s(MV ''Text6'' tid0), s(MV ''Text8'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,-                          s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)-                       |}-                       ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_udkey_P_3_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_2_6_enc_5'', s(MV ''Rb'' tid0), LN ''Rpa'' tid0,-                            s(MV ''Text8'' tid0)-                         |}-                         ( LN ''Kab'' tid1 ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-    next-      case (isoiec_9798_2_6_udkey_B_5_enc tid2) note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid2, LN ''Kab'' tid1,-                              s(AV ''A'' tid2), s(MV ''Text3'' tid2)-                           |}-                           ( K ( s(AV ''B'' tid2) ) ( s(MV ''P'' tid2) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-      next-        case (isoiec_9798_2_6_udkey_P_3_enc_1 tid3) note_unified facts = this facts-        thus ?thesis proof(sources! "-                         Enc {| LC ''isoiec_9798_2_6_enc_4'', LN ''Rpa'' tid0, LN ''Rb'' tid2,-                                s(MV ''Text6'' tid2)-                             |}-                             ( LN ''Kab'' tid1 ) ")-          case fake note_unified facts = this facts-          thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-        next-          case (isoiec_9798_2_6_udkey_A_4_enc tid3) note_unified facts = this facts-          thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-        qed (insert facts, fastsimp+)?-      qed (insert facts, fastsimp+)?-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_6_udkey_state) B_non_injective_agreement_A:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_udkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_udkey_B_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_6_udkey_A &-        ( tid1, isoiec_9798_2_6_udkey_A_4 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),-           s(MV ''Kab'' tid1), LN ''Rpa'' tid1, s(MV ''Rb'' tid1),-           s(MV ''Text6'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),-                s(MV ''Kab'' tid0), s(MV ''Rpa'' tid0), LN ''Rb'' tid0,-                s(MV ''Text6'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_udkey_P_3_enc_1 tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_2_6_enc_4'', s(MV ''Rpa'' tid0), LN ''Rb'' tid0,-                            s(MV ''Text6'' tid0)-                         |}-                         ( LN ''Kab'' tid1 ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-    next-      case (isoiec_9798_2_6_udkey_A_4_enc tid2) note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid2, LN ''Kab'' tid1,-                              s(MV ''B'' tid2), s(MV ''Text4'' tid2)-                           |}-                           ( K ( s(AV ''A'' tid2) ) ( s(AV ''P'' tid2) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest: P_secret_Kab intro: event_predOrdI)-      next-        case (isoiec_9798_2_6_udkey_P_3_enc tid3) note_unified facts = this facts-        thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-      qed (insert facts, fastsimp+)?-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_6_udkey_state) A_non_injective_agreement_P:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_udkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''P'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_udkey_A_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_6_udkey_P &-        ( tid1, isoiec_9798_2_6_udkey_P_3 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),-           s(MV ''Ra'' tid1), LN ''Kab'' tid1, s(MV ''Text4'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''P'' tid0),-                LN ''Ra'' tid0, s(MV ''Kab'' tid0), s(MV ''Text4'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,-                          s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)-                       |}-                       ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_udkey_P_3_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_2_6_udkey_state) B_non_injective_agreement_P:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_2_6_udkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''P'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_2_6_udkey_B_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_2_6_udkey_P &-        ( tid1, isoiec_9798_2_6_udkey_P_3 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),-           s(MV ''Rb'' tid1), LN ''Kab'' tid1, s(MV ''Text3'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),-                LN ''Rb'' tid0, s(MV ''Kab'' tid0), s(MV ''Text3'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,-                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_2_6_udkey_P_3_enc_1 tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?+  "ESPLogic"+begin++role isoiec_9798_2_1_udkey_A+where "isoiec_9798_2_1_udkey_A =+  [ Send ''leak_A'' ( sN ''TNA'' )+  , Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>+  , Send ''1'' <| sAV ''A'', sAV ''B'', sMV ''Text2'',+                  PEnc <| sC ''isoiec_9798_2_1_enc_1'', sN ''TNA'', sMV ''Text1'' |>+                       ( sK ''A'' ''B'' )+               |>+  ]"++role isoiec_9798_2_1_udkey_B+where "isoiec_9798_2_1_udkey_B =+  [ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Text2'',+                  PEnc <| sC ''isoiec_9798_2_1_enc_1'', sMV ''TNA'', sMV ''Text1'' |>+                       ( PSymK ( sMV ''A'' ) ( sAV ''B'' ) )+               |>+  ]"++protocol isoiec_9798_2_1_udkey+where "isoiec_9798_2_1_udkey =+{ isoiec_9798_2_1_udkey_A, isoiec_9798_2_1_udkey_B }"++locale restricted_isoiec_9798_2_1_udkey_state = isoiec_9798_2_1_udkey_state++type_invariant isoiec_9798_2_1_udkey_msc_typing for isoiec_9798_2_1_udkey+where "isoiec_9798_2_1_udkey_msc_typing = mk_typing+  [ ((isoiec_9798_2_1_udkey_B, ''A''), (KnownT isoiec_9798_2_1_udkey_B_1))+  , ((isoiec_9798_2_1_udkey_B, ''TNA''),+     (SumT (KnownT isoiec_9798_2_1_udkey_B_1) (NonceT isoiec_9798_2_1_udkey_A ''TNA'')))+  , ((isoiec_9798_2_1_udkey_A, ''Text1''),+     (KnownT isoiec_9798_2_1_udkey_A_text_1))+  , ((isoiec_9798_2_1_udkey_B, ''Text1''),+     (KnownT isoiec_9798_2_1_udkey_B_1))+  , ((isoiec_9798_2_1_udkey_A, ''Text2''),+     (KnownT isoiec_9798_2_1_udkey_A_text_1))+  , ((isoiec_9798_2_1_udkey_B, ''Text2''),+     (KnownT isoiec_9798_2_1_udkey_B_1))+  ]"++sublocale isoiec_9798_2_1_udkey_state < isoiec_9798_2_1_udkey_msc_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_2_1_udkey_msc_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_2_1_udkey_msc_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_2_1_udkey_A_text_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_1_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_1_udkey_A_text_1_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_1_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_1_udkey_B_1_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_1_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_1_udkey_B_1_TNA t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_1_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_1_enc_1'', s(MV ''TNA'' tid0),+               s(MV ''Text1'' tid0)+            |}+            ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_1_udkey_B_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_1_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_1_enc_1'', s(MV ''TNA'' tid0),+               s(MV ''Text1'' tid0)+            |}+            ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_1_udkey_B_1_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_1_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_2_1_udkey_msc_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_2_1_udkey_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++lemma (in restricted_isoiec_9798_2_1_udkey_state) B_non_injective_agreement:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_1_udkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_1_udkey_B_1 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_2_1_udkey_A &+        ( tid1, isoiec_9798_2_1_udkey_A_1 ) : steps t &+        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,+           s(MV ''Text1'' tid1)+        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),+                s(MV ''Text1'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_1_enc_1'', s(MV ''TNA'' tid0),+                          s(MV ''Text1'' tid0)+                       |}+                       ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_1_udkey_A_1_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)?+qed++role isoiec_9798_2_2_udkey_A+where "isoiec_9798_2_2_udkey_A =+  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''RB'', sMV ''Text1'' |>+  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>+  , Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'',+                  PEnc <| sC ''isoiec_9798_2_2_enc_2'', sMV ''RB'', sMV ''Text2'' |>+                       ( PSymK ( sAV ''A'' ) ( sMV ''B'' ) )+               |>+  ]"++role isoiec_9798_2_2_udkey_B+where "isoiec_9798_2_2_udkey_B =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''RB'', sMV ''Text1'' |>+  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'',+                  PEnc <| sC ''isoiec_9798_2_2_enc_2'', sN ''RB'', sMV ''Text2'' |>+                       ( sK ''A'' ''B'' )+               |>+  ]"++protocol isoiec_9798_2_2_udkey+where "isoiec_9798_2_2_udkey =+{ isoiec_9798_2_2_udkey_A, isoiec_9798_2_2_udkey_B }"++locale restricted_isoiec_9798_2_2_udkey_state = isoiec_9798_2_2_udkey_state++type_invariant isoiec_9798_2_2_udkey_msc_typing for isoiec_9798_2_2_udkey+where "isoiec_9798_2_2_udkey_msc_typing = mk_typing+  [ ((isoiec_9798_2_2_udkey_A, ''B''), (KnownT isoiec_9798_2_2_udkey_A_1))+  , ((isoiec_9798_2_2_udkey_A, ''RB''), (KnownT isoiec_9798_2_2_udkey_A_1))+  , ((isoiec_9798_2_2_udkey_A, ''Text1''),+     (KnownT isoiec_9798_2_2_udkey_A_1))+  , ((isoiec_9798_2_2_udkey_B, ''Text1''),+     (KnownT isoiec_9798_2_2_udkey_B_text_1))+  , ((isoiec_9798_2_2_udkey_A, ''Text2''),+     (KnownT isoiec_9798_2_2_udkey_A_text_2))+  , ((isoiec_9798_2_2_udkey_B, ''Text2''),+     (KnownT isoiec_9798_2_2_udkey_B_2))+  , ((isoiec_9798_2_2_udkey_A, ''Text3''),+     (KnownT isoiec_9798_2_2_udkey_A_text_2))+  , ((isoiec_9798_2_2_udkey_B, ''Text3''),+     (KnownT isoiec_9798_2_2_udkey_B_2))+  ]"++sublocale isoiec_9798_2_2_udkey_state < isoiec_9798_2_2_udkey_msc_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_2_2_udkey_msc_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_2_2_udkey_msc_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_2_2_udkey_A_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_2_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_2_udkey_A_1_RB t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_2_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_2_udkey_A_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_2_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_2_udkey_A_text_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_2_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_2_udkey_A_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_2_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_2_udkey_B_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_2_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_2_enc_2'', LN ''RB'' tid0, s(MV ''Text2'' tid0)+            |}+            ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_2_udkey_B_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_2_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_2_2_udkey_msc_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_2_2_udkey_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++lemma (in restricted_isoiec_9798_2_2_udkey_state) B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_2_udkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_2_udkey_B_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_2_udkey_A &+          ( tid1, isoiec_9798_2_2_udkey_A_2 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(MV ''RB'' tid1),+             s(MV ''Text2'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''RB'' tid0,+                  s(MV ''Text2'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_2_enc_2'', LN ''RB'' tid0, s(MV ''Text2'' tid0)+                           |}+                           ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_2_udkey_A_2_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++role isoiec_9798_2_3_udkey_A+where "isoiec_9798_2_3_udkey_A =+  [ Send ''leak_A'' ( sN ''TNA'' )+  , Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>+  , Send ''1'' <| sAV ''A'', sAV ''B'', sMV ''Text2'',+                  PEnc <| sC ''isoiec_9798_2_3_enc_1'', sN ''TNA'', sMV ''Text1'' |>+                       ( sK ''A'' ''B'' )+               |>+  , Recv ''2'' <| sAV ''B'', sAV ''A'', sMV ''Text4'',+                  PEnc <| sC ''isoiec_9798_2_3_enc_2'', sMV ''TNB'', sMV ''Text3'' |>+                       ( sK ''B'' ''A'' )+               |>+  ]"++role isoiec_9798_2_3_udkey_B+where "isoiec_9798_2_3_udkey_B =+  [ Send ''leak_B'' ( sN ''TNB'' )+  , Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Text2'',+                  PEnc <| sC ''isoiec_9798_2_3_enc_1'', sMV ''TNA'', sMV ''Text1'' |>+                       ( PSymK ( sMV ''A'' ) ( sAV ''B'' ) )+               |>+  , Recv ''text_2'' <| sMV ''Text3'', sMV ''Text4'' |>+  , Send ''2'' <| sAV ''B'', sMV ''A'', sMV ''Text4'',+                  PEnc <| sC ''isoiec_9798_2_3_enc_2'', sN ''TNB'', sMV ''Text3'' |>+                       ( PSymK ( sAV ''B'' ) ( sMV ''A'' ) )+               |>+  ]"++protocol isoiec_9798_2_3_udkey+where "isoiec_9798_2_3_udkey =+{ isoiec_9798_2_3_udkey_A, isoiec_9798_2_3_udkey_B }"++locale restricted_isoiec_9798_2_3_udkey_state = isoiec_9798_2_3_udkey_state++type_invariant isoiec_9798_2_3_udkey_msc_typing for isoiec_9798_2_3_udkey+where "isoiec_9798_2_3_udkey_msc_typing = mk_typing+  [ ((isoiec_9798_2_3_udkey_B, ''A''), (KnownT isoiec_9798_2_3_udkey_B_1))+  , ((isoiec_9798_2_3_udkey_B, ''TNA''),+     (SumT (KnownT isoiec_9798_2_3_udkey_B_1) (NonceT isoiec_9798_2_3_udkey_A ''TNA'')))+  , ((isoiec_9798_2_3_udkey_A, ''TNB''),+     (SumT (KnownT isoiec_9798_2_3_udkey_A_2) (NonceT isoiec_9798_2_3_udkey_B ''TNB'')))+  , ((isoiec_9798_2_3_udkey_A, ''Text1''),+     (KnownT isoiec_9798_2_3_udkey_A_text_1))+  , ((isoiec_9798_2_3_udkey_B, ''Text1''),+     (KnownT isoiec_9798_2_3_udkey_B_1))+  , ((isoiec_9798_2_3_udkey_A, ''Text2''),+     (KnownT isoiec_9798_2_3_udkey_A_text_1))+  , ((isoiec_9798_2_3_udkey_B, ''Text2''),+     (KnownT isoiec_9798_2_3_udkey_B_1))+  , ((isoiec_9798_2_3_udkey_A, ''Text3''),+     (KnownT isoiec_9798_2_3_udkey_A_2))+  , ((isoiec_9798_2_3_udkey_B, ''Text3''),+     (KnownT isoiec_9798_2_3_udkey_B_text_2))+  , ((isoiec_9798_2_3_udkey_A, ''Text4''),+     (KnownT isoiec_9798_2_3_udkey_A_2))+  , ((isoiec_9798_2_3_udkey_B, ''Text4''),+     (KnownT isoiec_9798_2_3_udkey_B_text_2))+  ]"++sublocale isoiec_9798_2_3_udkey_state < isoiec_9798_2_3_udkey_msc_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_2_3_udkey_msc_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_2_3_udkey_msc_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_2_3_udkey_A_text_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_udkey_A_text_1_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_udkey_A_2_TNB t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_3_enc_2'', s(MV ''TNB'' tid0),+               s(MV ''Text3'' tid0)+            |}+            ( K ( s(AV ''B'' tid0) ) ( s(AV ''A'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_3_udkey_A_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_3_enc_2'', s(MV ''TNB'' tid0),+               s(MV ''Text3'' tid0)+            |}+            ( K ( s(AV ''B'' tid0) ) ( s(AV ''A'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_3_udkey_A_2_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_udkey_B_1_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_udkey_B_1_TNA t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_3_enc_1'', s(MV ''TNA'' tid0),+               s(MV ''Text1'' tid0)+            |}+            ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_3_udkey_B_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_3_enc_1'', s(MV ''TNA'' tid0),+               s(MV ''Text1'' tid0)+            |}+            ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_3_udkey_B_1_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_udkey_B_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_3_udkey_B_text_2_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_2_3_udkey_msc_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_2_3_udkey_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++lemma (in restricted_isoiec_9798_2_3_udkey_state) A_non_injective_agreement:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_3_udkey_A"+    "RLKR(s(AV ''A'' tid0)) ~: reveals t"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_3_udkey_A_2 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_2_3_udkey_B &+        ( tid1, isoiec_9798_2_3_udkey_B_2 ) : steps t &+        {| s(MV ''A'' tid1), s(AV ''B'' tid1), LN ''TNB'' tid1,+           s(MV ''Text3'' tid1)+        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNB'' tid0),+                s(MV ''Text3'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_3_enc_2'', s(MV ''TNB'' tid0),+                          s(MV ''Text3'' tid0)+                       |}+                       ( K ( s(AV ''B'' tid0) ) ( s(AV ''A'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_3_udkey_B_2_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_3_udkey_state) B_non_injective_agreement:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_3_udkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_3_udkey_B_2 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_2_3_udkey_A &+        ( tid1, isoiec_9798_2_3_udkey_A_1 ) : steps t &+        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,+           s(MV ''Text1'' tid1)+        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),+                s(MV ''Text1'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_3_enc_1'', s(MV ''TNA'' tid0),+                          s(MV ''Text1'' tid0)+                       |}+                       ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_3_udkey_A_1_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)?+qed++role isoiec_9798_2_4_udkey_A+where "isoiec_9798_2_4_udkey_A =+  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''RB'', sMV ''Text1'' |>+  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>+  , Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'',+                  PEnc <| sC ''isoiec_9798_2_4_enc_1'', sN ''RA'', sMV ''RB'',+                          sMV ''Text2''+                       |>+                       ( PSymK ( sAV ''A'' ) ( sMV ''B'' ) )+               |>+  , Recv ''3'' <| sMV ''B'', sAV ''A'', sMV ''Text5'',+                  PEnc <| sC ''isoiec_9798_2_4_enc_2'', sMV ''RB'', sN ''RA'',+                          sMV ''Text4''+                       |>+                       ( PSymK ( sMV ''B'' ) ( sAV ''A'' ) )+               |>+  ]"++role isoiec_9798_2_4_udkey_B+where "isoiec_9798_2_4_udkey_B =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''RB'', sMV ''Text1'' |>+  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'',+                  PEnc <| sC ''isoiec_9798_2_4_enc_1'', sMV ''RA'', sN ''RB'',+                          sMV ''Text2''+                       |>+                       ( sK ''A'' ''B'' )+               |>+  , Recv ''text_3'' <| sMV ''Text4'', sMV ''Text5'' |>+  , Send ''3'' <| sAV ''B'', sAV ''A'', sMV ''Text5'',+                  PEnc <| sC ''isoiec_9798_2_4_enc_2'', sN ''RB'', sMV ''RA'',+                          sMV ''Text4''+                       |>+                       ( sK ''B'' ''A'' )+               |>+  ]"++protocol isoiec_9798_2_4_udkey+where "isoiec_9798_2_4_udkey =+{ isoiec_9798_2_4_udkey_A, isoiec_9798_2_4_udkey_B }"++locale restricted_isoiec_9798_2_4_udkey_state = isoiec_9798_2_4_udkey_state++type_invariant isoiec_9798_2_4_udkey_msc_typing for isoiec_9798_2_4_udkey+where "isoiec_9798_2_4_udkey_msc_typing = mk_typing+  [ ((isoiec_9798_2_4_udkey_A, ''B''), (KnownT isoiec_9798_2_4_udkey_A_1))+  , ((isoiec_9798_2_4_udkey_B, ''RA''),+     (SumT (KnownT isoiec_9798_2_4_udkey_B_2) (NonceT isoiec_9798_2_4_udkey_A ''RA'')))+  , ((isoiec_9798_2_4_udkey_A, ''RB''), (KnownT isoiec_9798_2_4_udkey_A_1))+  , ((isoiec_9798_2_4_udkey_A, ''Text1''),+     (KnownT isoiec_9798_2_4_udkey_A_1))+  , ((isoiec_9798_2_4_udkey_B, ''Text1''),+     (KnownT isoiec_9798_2_4_udkey_B_text_1))+  , ((isoiec_9798_2_4_udkey_A, ''Text2''),+     (KnownT isoiec_9798_2_4_udkey_A_text_2))+  , ((isoiec_9798_2_4_udkey_B, ''Text2''),+     (KnownT isoiec_9798_2_4_udkey_B_2))+  , ((isoiec_9798_2_4_udkey_A, ''Text3''),+     (KnownT isoiec_9798_2_4_udkey_A_text_2))+  , ((isoiec_9798_2_4_udkey_B, ''Text3''),+     (KnownT isoiec_9798_2_4_udkey_B_2))+  , ((isoiec_9798_2_4_udkey_A, ''Text4''),+     (KnownT isoiec_9798_2_4_udkey_A_3))+  , ((isoiec_9798_2_4_udkey_B, ''Text4''),+     (KnownT isoiec_9798_2_4_udkey_B_text_3))+  , ((isoiec_9798_2_4_udkey_A, ''Text5''),+     (KnownT isoiec_9798_2_4_udkey_A_3))+  , ((isoiec_9798_2_4_udkey_B, ''Text5''),+     (KnownT isoiec_9798_2_4_udkey_B_text_3))+  ]"++sublocale isoiec_9798_2_4_udkey_state < isoiec_9798_2_4_udkey_msc_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_2_4_udkey_msc_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_2_4_udkey_msc_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_2_4_udkey_A_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_udkey_A_1_RB t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_udkey_A_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_udkey_A_text_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_udkey_A_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_udkey_A_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_4_enc_2'', s(MV ''RB'' tid0), LN ''RA'' tid0,+               s(MV ''Text4'' tid0)+            |}+            ( K ( s(MV ''B'' tid0) ) ( s(AV ''A'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_4_udkey_A_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_udkey_B_2_RA t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_4_enc_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,+               s(MV ''Text2'' tid0)+            |}+            ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_4_udkey_B_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_4_enc_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,+               s(MV ''Text2'' tid0)+            |}+            ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_4_udkey_B_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_udkey_B_text_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_4_udkey_B_text_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_2_4_udkey_msc_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_2_4_udkey_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++lemma (in restricted_isoiec_9798_2_4_udkey_state) A_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_4_udkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_4_udkey_A_3 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_4_udkey_B &+          ( tid1, isoiec_9798_2_4_udkey_B_3 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''RA'' tid1), LN ''RB'' tid1,+             s(MV ''Text2'' tid1), s(MV ''Text4'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''RA'' tid0,+                  s(MV ''RB'' tid0), s(MV ''Text2'' tid0), s(MV ''Text4'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_4_enc_2'', s(MV ''RB'' tid0), LN ''RA'' tid0,+                              s(MV ''Text4'' tid0)+                           |}+                           ( K ( s(MV ''B'' tid0) ) ( s(AV ''A'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_4_udkey_B_3_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_2_4_enc_1'', LN ''RA'' tid0, LN ''RB'' tid1,+                                s(MV ''Text2'' tid1)+                             |}+                             ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid1) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_2_4_udkey_A_2_enc tid2) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_4_udkey_state) B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_4_udkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_4_udkey_B_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_4_udkey_A &+          ( tid1, isoiec_9798_2_4_udkey_A_2 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''RA'' tid1, s(MV ''RB'' tid1),+             s(MV ''Text2'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''RA'' tid0),+                  LN ''RB'' tid0, s(MV ''Text2'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_4_enc_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,+                              s(MV ''Text2'' tid0)+                           |}+                           ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_4_udkey_A_2_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++role isoiec_9798_2_5_udkey_A+where "isoiec_9798_2_5_udkey_A =+  [ Send ''leak_A'' <| sN ''TVPa'', sN ''TNa'' |>+  , Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''A'', sAV ''P'', sN ''TVPa'', sAV ''B'',+                  sMV ''Text1''+               |>+  , Recv ''2'' <| sAV ''P'', sAV ''A'', sMV ''Text4'',+                  PEnc <| sC ''isoiec_9798_2_5_enc_2_1'', sN ''TVPa'', sMV ''Kab'',+                          sAV ''B'', sMV ''Text3''+                       |>+                       ( sK ''A'' ''P'' ),+                  sMV ''TokenPA_for_B''+               |>+  , Recv ''text_3'' <| sMV ''Text5'', sMV ''Text6'' |>+  , Send ''3'' <| sAV ''A'', sAV ''B'', sMV ''Text6'', sAV ''P'',+                  sMV ''TokenPA_for_B'',+                  PEnc <| sC ''isoiec_9798_2_5_enc_3'', sN ''TNa'', sAV ''B'',+                          sMV ''Text5''+                       |>+                       ( sMV ''Kab'' )+               |>+  , Recv ''4'' <| sAV ''B'', sAV ''A'', sMV ''Text8'',+                  PEnc <| sC ''isoiec_9798_2_5_enc_4'', sMV ''TNb'', sAV ''A'',+                          sMV ''Text7''+                       |>+                       ( sMV ''Kab'' )+               |>+  ]"++role isoiec_9798_2_5_udkey_B+where "isoiec_9798_2_5_udkey_B =+  [ Send ''leak_B'' ( sN ''TNb'' )+  , Recv ''3'' <| sMV ''A'', sAV ''B'', sMV ''Text6'', sMV ''P'',+                  PEnc <| sC ''isoiec_9798_2_5_enc_2_2'', sMV ''TNp'', sMV ''Kab'',+                          sMV ''A'', sMV ''Text2''+                       |>+                       ( PSymK ( sAV ''B'' ) ( sMV ''P'' ) ),+                  PEnc <| sC ''isoiec_9798_2_5_enc_3'', sMV ''TNa'', sAV ''B'',+                          sMV ''Text5''+                       |>+                       ( sMV ''Kab'' )+               |>+  , Recv ''text_4'' <| sMV ''Text7'', sMV ''Text8'' |>+  , Send ''4'' <| sAV ''B'', sMV ''A'', sMV ''Text8'',+                  PEnc <| sC ''isoiec_9798_2_5_enc_4'', sN ''TNb'', sMV ''A'',+                          sMV ''Text7''+                       |>+                       ( sMV ''Kab'' )+               |>+  ]"++role isoiec_9798_2_5_udkey_P+where "isoiec_9798_2_5_udkey_P =+  [ Send ''leak_P'' ( sN ''TNp'' )+  , Recv ''1'' <| sMV ''A'', sAV ''P'', sMV ''TVPa'', sMV ''B'',+                  sMV ''Text1''+               |>+  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'', sMV ''Text4'' |>+  , Send ''2'' <| sAV ''P'', sMV ''A'', sMV ''Text4'',+                  PEnc <| sC ''isoiec_9798_2_5_enc_2_1'', sMV ''TVPa'', sN ''Kab'',+                          sMV ''B'', sMV ''Text3''+                       |>+                       ( PSymK ( sMV ''A'' ) ( sAV ''P'' ) ),+                  PEnc <| sC ''isoiec_9798_2_5_enc_2_2'', sN ''TNp'', sN ''Kab'',+                          sMV ''A'', sMV ''Text2''+                       |>+                       ( PSymK ( sMV ''B'' ) ( sAV ''P'' ) )+               |>+  ]"++protocol isoiec_9798_2_5_udkey+where "isoiec_9798_2_5_udkey =+{ isoiec_9798_2_5_udkey_A, isoiec_9798_2_5_udkey_B,+  isoiec_9798_2_5_udkey_P+}"++locale restricted_isoiec_9798_2_5_udkey_state = isoiec_9798_2_5_udkey_state++type_invariant isoiec_9798_2_5_udkey_msc_typing for isoiec_9798_2_5_udkey+where "isoiec_9798_2_5_udkey_msc_typing = mk_typing+  [ ((isoiec_9798_2_5_udkey_B, ''A''), (KnownT isoiec_9798_2_5_udkey_B_3))+  , ((isoiec_9798_2_5_udkey_P, ''A''), (KnownT isoiec_9798_2_5_udkey_P_1))+  , ((isoiec_9798_2_5_udkey_P, ''B''), (KnownT isoiec_9798_2_5_udkey_P_1))+  , ((isoiec_9798_2_5_udkey_A, ''Kab''),+     (SumT (KnownT isoiec_9798_2_5_udkey_A_2) (NonceT isoiec_9798_2_5_udkey_P ''Kab'')))+  , ((isoiec_9798_2_5_udkey_B, ''Kab''),+     (SumT (KnownT isoiec_9798_2_5_udkey_B_3) (NonceT isoiec_9798_2_5_udkey_P ''Kab'')))+  , ((isoiec_9798_2_5_udkey_B, ''P''), (KnownT isoiec_9798_2_5_udkey_B_3))+  , ((isoiec_9798_2_5_udkey_B, ''TNa''),+     (SumT (KnownT isoiec_9798_2_5_udkey_B_3) (NonceT isoiec_9798_2_5_udkey_A ''TNa'')))+  , ((isoiec_9798_2_5_udkey_A, ''TNb''),+     (SumT (KnownT isoiec_9798_2_5_udkey_A_4) (NonceT isoiec_9798_2_5_udkey_B ''TNb'')))+  , ((isoiec_9798_2_5_udkey_B, ''TNp''),+     (SumT (KnownT isoiec_9798_2_5_udkey_B_3) (NonceT isoiec_9798_2_5_udkey_P ''TNp'')))+  , ((isoiec_9798_2_5_udkey_P, ''TVPa''),+     (KnownT isoiec_9798_2_5_udkey_P_1))+  , ((isoiec_9798_2_5_udkey_A, ''Text1''),+     (KnownT isoiec_9798_2_5_udkey_A_text_1))+  , ((isoiec_9798_2_5_udkey_P, ''Text1''),+     (KnownT isoiec_9798_2_5_udkey_P_1))+  , ((isoiec_9798_2_5_udkey_B, ''Text2''),+     (KnownT isoiec_9798_2_5_udkey_B_3))+  , ((isoiec_9798_2_5_udkey_P, ''Text2''),+     (KnownT isoiec_9798_2_5_udkey_P_text_2))+  , ((isoiec_9798_2_5_udkey_A, ''Text3''),+     (KnownT isoiec_9798_2_5_udkey_A_2))+  , ((isoiec_9798_2_5_udkey_P, ''Text3''),+     (KnownT isoiec_9798_2_5_udkey_P_text_2))+  , ((isoiec_9798_2_5_udkey_A, ''Text4''),+     (KnownT isoiec_9798_2_5_udkey_A_2))+  , ((isoiec_9798_2_5_udkey_P, ''Text4''),+     (KnownT isoiec_9798_2_5_udkey_P_text_2))+  , ((isoiec_9798_2_5_udkey_A, ''Text5''),+     (KnownT isoiec_9798_2_5_udkey_A_text_3))+  , ((isoiec_9798_2_5_udkey_B, ''Text5''),+     (KnownT isoiec_9798_2_5_udkey_B_3))+  , ((isoiec_9798_2_5_udkey_A, ''Text6''),+     (KnownT isoiec_9798_2_5_udkey_A_text_3))+  , ((isoiec_9798_2_5_udkey_B, ''Text6''),+     (KnownT isoiec_9798_2_5_udkey_B_3))+  , ((isoiec_9798_2_5_udkey_A, ''Text7''),+     (KnownT isoiec_9798_2_5_udkey_A_4))+  , ((isoiec_9798_2_5_udkey_B, ''Text7''),+     (KnownT isoiec_9798_2_5_udkey_B_text_4))+  , ((isoiec_9798_2_5_udkey_A, ''Text8''),+     (KnownT isoiec_9798_2_5_udkey_A_4))+  , ((isoiec_9798_2_5_udkey_B, ''Text8''),+     (KnownT isoiec_9798_2_5_udkey_B_text_4))+  , ((isoiec_9798_2_5_udkey_A, ''TokenPA_for_B''),+     (KnownT isoiec_9798_2_5_udkey_A_2))+  ]"++sublocale isoiec_9798_2_5_udkey_state < isoiec_9798_2_5_udkey_msc_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_2_5_udkey_msc_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_2_5_udkey_msc_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_2_5_udkey_A_2_Kab t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,+               s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)+            |}+            ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_udkey_A_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,+               s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)+            |}+            ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_udkey_A_2_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_A_2_TokenPA_for_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_A_text_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_A_text_3_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_A_4_TNb t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_4'', s(MV ''TNb'' tid0),+               s(AV ''A'' tid0), s(MV ''Text7'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_udkey_A_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_4'', s(MV ''TNb'' tid0),+               s(AV ''A'' tid0), s(MV ''Text7'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_udkey_A_4_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_B_3_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_B_3_Kab t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),+               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)+            |}+            ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_udkey_B_3_P t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_B_3_TNa t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid0),+               s(AV ''B'' tid0), s(MV ''Text5'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_udkey_B_3_TNp t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),+               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)+            |}+            ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_udkey_B_3_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),+               s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)+            |}+            ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_udkey_B_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid0),+               s(AV ''B'' tid0), s(MV ''Text5'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_5_udkey_B_3_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_B_text_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_B_text_4_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_P_1_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_P_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_P_1_TVPa t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_P_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_P_text_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_P_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_5_udkey_P_text_2_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_2_5_udkey_msc_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_2_5_udkey_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++lemma (in restricted_isoiec_9798_2_5_udkey_state) P_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_udkey_P"+    "RLKR(s(AV ''P'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''B'' tid0)) ~: reveals t"+    "LN ''Kab'' tid0 : knows t"+  shows "False"+using facts proof(sources! " LN ''Kab'' tid0 ")+  case isoiec_9798_2_5_udkey_P_2_Kab note_unified facts = this facts+  thus ?thesis by (fastforce dest!: ltk_secrecy)+next+  case isoiec_9798_2_5_udkey_P_2_Kab_1 note_unified facts = this facts+  thus ?thesis by (fastforce dest!: ltk_secrecy)+qed (insert facts, fastforce+)?++lemma (in restricted_isoiec_9798_2_5_udkey_state) A_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_udkey_A"+    "RLKR(s(AV ''A'' tid0)) ~: reveals t"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(AV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_5_udkey_A_2 ) : steps t"+    "s(MV ''Kab'' tid0) : knows t"+  shows "False"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,+                          s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)+                       |}+                       ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_5_udkey_P_2_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_5_udkey_state) B_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_udkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_5_udkey_B_3 ) : steps t"+    "s(MV ''Kab'' tid0) : knows t"+  shows "False"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),+                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)+                       |}+                       ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_5_udkey_P_2_enc_1 tid1) note_unified facts = this facts+    thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_5_udkey_state) A_injective_agreement_B:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_5_udkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(AV ''P'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_5_udkey_A_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_5_udkey_B &+          ( tid1, isoiec_9798_2_5_udkey_B_4 ) : steps t &+          {| s(MV ''A'' tid1), s(AV ''B'' tid1), s(MV ''P'' tid1),+             s(MV ''Kab'' tid1), s(MV ''TNa'' tid1), s(MV ''Text5'' tid1),+             LN ''TNb'' tid1, s(MV ''Text7'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''P'' tid0),+                  s(MV ''Kab'' tid0), LN ''TNa'' tid0, s(MV ''Text5'' tid0),+                  s(MV ''TNb'' tid0), s(MV ''Text7'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_5_udkey_P_2_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_2_5_enc_4'', s(MV ''TNb'' tid0),+                                s(AV ''A'' tid0), s(MV ''Text7'' tid0)+                             |}+                             ( LN ''Kab'' tid1 ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+        next+          case (isoiec_9798_2_5_udkey_B_4_enc tid2) note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid2),+                                  LN ''Kab'' tid1, s(AV ''A'' tid0), s(MV ''Text2'' tid2)+                               |}+                               ( K ( s(AV ''B'' tid2) ) ( s(MV ''P'' tid2) ) ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+          next+            case (isoiec_9798_2_5_udkey_P_2_enc_1 tid3) note_unified facts = this facts+            thus ?thesis proof(sources! "+                             Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid2),+                                    s(AV ''B'' tid0), s(MV ''Text5'' tid2)+                                 |}+                                 ( LN ''Kab'' tid1 ) ")+              case fake note_unified facts = this facts+              thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+            next+              case (isoiec_9798_2_5_udkey_A_3_enc tid3) note_unified facts = this facts+              thus ?thesis proof(sources! "+                               Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid3, LN ''Kab'' tid1,+                                      s(AV ''B'' tid0), s(MV ''Text3'' tid3)+                                   |}+                                   ( K ( s(AV ''A'' tid3) ) ( s(AV ''P'' tid3) ) ) ")+                case fake note_unified facts = this facts+                thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+              next+                case (isoiec_9798_2_5_udkey_P_2_enc tid4) note_unified facts = this facts+                thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+              qed (insert facts, fastforce+)?+            qed (insert facts, fastforce+)?+          qed (insert facts, fastforce+)?+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_5_udkey_state) B_non_injective_agreement_A:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_udkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_5_udkey_B_3 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_2_5_udkey_A &+        ( tid1, isoiec_9798_2_5_udkey_A_3 ) : steps t &+        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(AV ''P'' tid1),+           s(MV ''Kab'' tid1), LN ''TNa'' tid1, s(MV ''Text5'' tid1)+        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),+                s(MV ''Kab'' tid0), s(MV ''TNa'' tid0), s(MV ''Text5'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),+                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)+                       |}+                       ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_5_udkey_P_2_enc_1 tid1) note_unified facts = this facts+    thus ?thesis proof(sources! "+                     Enc {| LC ''isoiec_9798_2_5_enc_3'', s(MV ''TNa'' tid0),+                            s(AV ''B'' tid0), s(MV ''Text5'' tid0)+                         |}+                         ( LN ''Kab'' tid1 ) ")+      case fake note_unified facts = this facts+      thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+    next+      case (isoiec_9798_2_5_udkey_A_3_enc tid2) note_unified facts = this facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid2, LN ''Kab'' tid1,+                              s(AV ''B'' tid0), s(MV ''Text3'' tid2)+                           |}+                           ( K ( s(AV ''A'' tid2) ) ( s(AV ''P'' tid2) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+      next+        case (isoiec_9798_2_5_udkey_P_2_enc tid3) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed (insert facts, fastforce+)?+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_5_udkey_state) A_injective_agreement_P:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_5_udkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(AV ''P'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_5_udkey_A_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_5_udkey_P &+          ( tid1, isoiec_9798_2_5_udkey_P_2 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1), LN ''Kab'' tid1,+             s(MV ''TVPa'' tid1), s(MV ''Text3'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''P'' tid0),+                  s(MV ''Kab'' tid0), LN ''TVPa'' tid0, s(MV ''Text3'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_5_enc_2_1'', LN ''TVPa'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''B'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_5_udkey_P_2_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_5_udkey_state) B_non_injective_agreement_P:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_5_udkey_B"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_5_udkey_B_3 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_2_5_udkey_P &+        ( tid1, isoiec_9798_2_5_udkey_P_2 ) : steps t &+        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1), LN ''Kab'' tid1,+           LN ''TNp'' tid1, s(MV ''Text2'' tid1)+        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),+                s(MV ''Kab'' tid0), s(MV ''TNp'' tid0), s(MV ''Text2'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_5_enc_2_2'', s(MV ''TNp'' tid0),+                          s(MV ''Kab'' tid0), s(MV ''A'' tid0), s(MV ''Text2'' tid0)+                       |}+                       ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_5_udkey_P_2_enc_1 tid1) note_unified facts = this facts+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)?+qed++role isoiec_9798_2_6_udkey_A+where "isoiec_9798_2_6_udkey_A =+  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>+  , Recv ''text_2'' ( sMV ''Text2'' )+  , Send ''2'' <| sAV ''A'', sAV ''P'', sN ''Ra'', sMV ''Rb'', sMV ''B'',+                  sMV ''Text2''+               |>+  , Recv ''3'' <| sAV ''P'', sAV ''A'', sMV ''Text5'',+                  PEnc <| sC ''isoiec_9798_2_6_enc_3_1'', sN ''Ra'', sMV ''Kab'',+                          sMV ''B'', sMV ''Text4''+                       |>+                       ( sK ''A'' ''P'' ),+                  sMV ''TokenPA_for_B''+               |>+  , Recv ''text_4'' <| sMV ''Text6'', sMV ''Text7'' |>+  , Send ''4'' <| sAV ''A'', sMV ''B'', sMV ''Text7'', sAV ''P'',+                  sMV ''TokenPA_for_B'',+                  PEnc <| sC ''isoiec_9798_2_6_enc_4'', sN ''Rpa'', sMV ''Rb'',+                          sMV ''Text6''+                       |>+                       ( sMV ''Kab'' )+               |>+  , Recv ''5'' <| sMV ''B'', sAV ''A'', sMV ''Text9'',+                  PEnc <| sC ''isoiec_9798_2_6_enc_5'', sMV ''Rb'', sN ''Rpa'',+                          sMV ''Text8''+                       |>+                       ( sMV ''Kab'' )+               |>+  ]"++role isoiec_9798_2_6_udkey_B+where "isoiec_9798_2_6_udkey_B =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>+  , Recv ''4'' <| sAV ''A'', sAV ''B'', sMV ''Text7'', sMV ''P'',+                  PEnc <| sC ''isoiec_9798_2_6_enc_3_2'', sN ''Rb'', sMV ''Kab'',+                          sAV ''A'', sMV ''Text3''+                       |>+                       ( PSymK ( sAV ''B'' ) ( sMV ''P'' ) ),+                  PEnc <| sC ''isoiec_9798_2_6_enc_4'', sMV ''Rpa'', sN ''Rb'',+                          sMV ''Text6''+                       |>+                       ( sMV ''Kab'' )+               |>+  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>+  , Send ''5'' <| sAV ''B'', sAV ''A'', sMV ''Text9'',+                  PEnc <| sC ''isoiec_9798_2_6_enc_5'', sN ''Rb'', sMV ''Rpa'',+                          sMV ''Text8''+                       |>+                       ( sMV ''Kab'' )+               |>+  ]"++role isoiec_9798_2_6_udkey_P+where "isoiec_9798_2_6_udkey_P =+  [ Recv ''2'' <| sMV ''A'', sAV ''P'', sMV ''Ra'', sMV ''Rb'', sMV ''B'',+                  sMV ''Text2''+               |>+  , Recv ''text_3'' <| sMV ''Text3'', sMV ''Text4'', sMV ''Text5'' |>+  , Send ''3'' <| sAV ''P'', sMV ''A'', sMV ''Text5'',+                  PEnc <| sC ''isoiec_9798_2_6_enc_3_1'', sMV ''Ra'', sN ''Kab'',+                          sMV ''B'', sMV ''Text4''+                       |>+                       ( PSymK ( sMV ''A'' ) ( sAV ''P'' ) ),+                  PEnc <| sC ''isoiec_9798_2_6_enc_3_2'', sMV ''Rb'', sN ''Kab'',+                          sMV ''A'', sMV ''Text3''+                       |>+                       ( PSymK ( sMV ''B'' ) ( sAV ''P'' ) )+               |>+  ]"++protocol isoiec_9798_2_6_udkey+where "isoiec_9798_2_6_udkey =+{ isoiec_9798_2_6_udkey_A, isoiec_9798_2_6_udkey_B,+  isoiec_9798_2_6_udkey_P+}"++locale restricted_isoiec_9798_2_6_udkey_state = isoiec_9798_2_6_udkey_state++type_invariant isoiec_9798_2_6_udkey_msc_typing for isoiec_9798_2_6_udkey+where "isoiec_9798_2_6_udkey_msc_typing = mk_typing+  [ ((isoiec_9798_2_6_udkey_P, ''A''), (KnownT isoiec_9798_2_6_udkey_P_2))+  , ((isoiec_9798_2_6_udkey_A, ''B''), (KnownT isoiec_9798_2_6_udkey_A_1))+  , ((isoiec_9798_2_6_udkey_P, ''B''), (KnownT isoiec_9798_2_6_udkey_P_2))+  , ((isoiec_9798_2_6_udkey_A, ''Kab''),+     (SumT (KnownT isoiec_9798_2_6_udkey_A_3) (NonceT isoiec_9798_2_6_udkey_P ''Kab'')))+  , ((isoiec_9798_2_6_udkey_B, ''Kab''),+     (SumT (KnownT isoiec_9798_2_6_udkey_B_4) (NonceT isoiec_9798_2_6_udkey_P ''Kab'')))+  , ((isoiec_9798_2_6_udkey_B, ''P''), (KnownT isoiec_9798_2_6_udkey_B_4))+  , ((isoiec_9798_2_6_udkey_P, ''Ra''), (KnownT isoiec_9798_2_6_udkey_P_2))+  , ((isoiec_9798_2_6_udkey_A, ''Rb''), (KnownT isoiec_9798_2_6_udkey_A_1))+  , ((isoiec_9798_2_6_udkey_P, ''Rb''), (KnownT isoiec_9798_2_6_udkey_P_2))+  , ((isoiec_9798_2_6_udkey_B, ''Rpa''),+     (SumT (KnownT isoiec_9798_2_6_udkey_B_4) (NonceT isoiec_9798_2_6_udkey_A ''Rpa'')))+  , ((isoiec_9798_2_6_udkey_A, ''Text1''),+     (KnownT isoiec_9798_2_6_udkey_A_1))+  , ((isoiec_9798_2_6_udkey_B, ''Text1''),+     (KnownT isoiec_9798_2_6_udkey_B_text_1))+  , ((isoiec_9798_2_6_udkey_A, ''Text2''),+     (KnownT isoiec_9798_2_6_udkey_A_text_2))+  , ((isoiec_9798_2_6_udkey_P, ''Text2''),+     (KnownT isoiec_9798_2_6_udkey_P_2))+  , ((isoiec_9798_2_6_udkey_B, ''Text3''),+     (KnownT isoiec_9798_2_6_udkey_B_4))+  , ((isoiec_9798_2_6_udkey_P, ''Text3''),+     (KnownT isoiec_9798_2_6_udkey_P_text_3))+  , ((isoiec_9798_2_6_udkey_A, ''Text4''),+     (KnownT isoiec_9798_2_6_udkey_A_3))+  , ((isoiec_9798_2_6_udkey_P, ''Text4''),+     (KnownT isoiec_9798_2_6_udkey_P_text_3))+  , ((isoiec_9798_2_6_udkey_A, ''Text5''),+     (KnownT isoiec_9798_2_6_udkey_A_3))+  , ((isoiec_9798_2_6_udkey_P, ''Text5''),+     (KnownT isoiec_9798_2_6_udkey_P_text_3))+  , ((isoiec_9798_2_6_udkey_A, ''Text6''),+     (KnownT isoiec_9798_2_6_udkey_A_text_4))+  , ((isoiec_9798_2_6_udkey_B, ''Text6''),+     (KnownT isoiec_9798_2_6_udkey_B_4))+  , ((isoiec_9798_2_6_udkey_A, ''Text7''),+     (KnownT isoiec_9798_2_6_udkey_A_text_4))+  , ((isoiec_9798_2_6_udkey_B, ''Text7''),+     (KnownT isoiec_9798_2_6_udkey_B_4))+  , ((isoiec_9798_2_6_udkey_A, ''Text8''),+     (KnownT isoiec_9798_2_6_udkey_A_5))+  , ((isoiec_9798_2_6_udkey_B, ''Text8''),+     (KnownT isoiec_9798_2_6_udkey_B_text_5))+  , ((isoiec_9798_2_6_udkey_A, ''Text9''),+     (KnownT isoiec_9798_2_6_udkey_A_5))+  , ((isoiec_9798_2_6_udkey_B, ''Text9''),+     (KnownT isoiec_9798_2_6_udkey_B_text_5))+  , ((isoiec_9798_2_6_udkey_A, ''TokenPA_for_B''),+     (KnownT isoiec_9798_2_6_udkey_A_3))+  ]"++sublocale isoiec_9798_2_6_udkey_state < isoiec_9798_2_6_udkey_msc_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_2_6_udkey_msc_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_2_6_udkey_msc_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_2_6_udkey_A_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_A_1_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_A_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_A_3_Kab t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,+               s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)+            |}+            ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_udkey_A_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,+               s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)+            |}+            ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_udkey_A_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_A_3_TokenPA_for_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_A_text_4_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_A_text_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_A_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_5'', s(MV ''Rb'' tid0), LN ''Rpa'' tid0,+               s(MV ''Text8'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_udkey_A_5_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_B_4_Kab t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,+               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)+            |}+            ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_udkey_B_4_P t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_B_4_Rpa t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_4'', s(MV ''Rpa'' tid0), LN ''Rb'' tid0,+               s(MV ''Text6'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_udkey_B_4_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,+               s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)+            |}+            ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_udkey_B_4_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''isoiec_9798_2_6_enc_4'', s(MV ''Rpa'' tid0), LN ''Rb'' tid0,+               s(MV ''Text6'' tid0)+            |}+            ( s(MV ''Kab'' tid0) ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_2_6_udkey_B_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_B_text_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_B_text_5_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_P_2_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_P_2_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_P_2_Ra t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_P_2_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_P_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_P_text_3_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_P_text_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_2_6_udkey_P_text_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_2_6_udkey_msc_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_2_6_udkey_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++lemma (in restricted_isoiec_9798_2_6_udkey_state) P_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_6_udkey_P"+    "RLKR(s(AV ''P'' tid0)) ~: reveals t"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "RLKR(s(MV ''B'' tid0)) ~: reveals t"+    "LN ''Kab'' tid0 : knows t"+  shows "False"+using facts proof(sources! " LN ''Kab'' tid0 ")+  case isoiec_9798_2_6_udkey_P_3_Kab note_unified facts = this facts+  thus ?thesis by (fastforce dest!: ltk_secrecy)+next+  case isoiec_9798_2_6_udkey_P_3_Kab_1 note_unified facts = this facts+  thus ?thesis by (fastforce dest!: ltk_secrecy)+qed (insert facts, fastforce+)?++lemma (in restricted_isoiec_9798_2_6_udkey_state) A_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_6_udkey_A"+    "RLKR(s(AV ''A'' tid0)) ~: reveals t"+    "RLKR(s(AV ''P'' tid0)) ~: reveals t"+    "RLKR(s(MV ''B'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_6_udkey_A_3 ) : steps t"+    "s(MV ''Kab'' tid0) : knows t"+  shows "False"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,+                          s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)+                       |}+                       ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_6_udkey_P_3_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_6_udkey_state) B_secret_Kab:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_2_6_udkey_B"+    "RLKR(s(AV ''A'' tid0)) ~: reveals t"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "RLKR(s(MV ''P'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_2_6_udkey_B_4 ) : steps t"+    "s(MV ''Kab'' tid0) : knows t"+  shows "False"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,+                          s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)+                       |}+                       ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_2_6_udkey_P_3_enc_1 tid1) note_unified facts = this facts+    thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_2_6_udkey_state) A_injective_agreement_B:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_6_udkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''P'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_6_udkey_A_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_6_udkey_B &+          ( tid1, isoiec_9798_2_6_udkey_B_5 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''P'' tid1),+             s(MV ''Kab'' tid1), s(MV ''Rpa'' tid1), LN ''Rb'' tid1,+             s(MV ''Text6'' tid1), s(MV ''Text8'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''P'' tid0),+                  s(MV ''Kab'' tid0), LN ''Rpa'' tid0, s(MV ''Rb'' tid0),+                  s(MV ''Text6'' tid0), s(MV ''Text8'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,+                              s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)+                           |}+                           ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_6_udkey_P_3_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_2_6_enc_5'', s(MV ''Rb'' tid0), LN ''Rpa'' tid0,+                                s(MV ''Text8'' tid0)+                             |}+                             ( LN ''Kab'' tid1 ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+        next+          case (isoiec_9798_2_6_udkey_B_5_enc tid2) note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid2, LN ''Kab'' tid1,+                                  s(AV ''A'' tid2), s(MV ''Text3'' tid2)+                               |}+                               ( K ( s(AV ''B'' tid2) ) ( s(MV ''P'' tid2) ) ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+          next+            case (isoiec_9798_2_6_udkey_P_3_enc_1 tid3) note_unified facts = this facts+            thus ?thesis proof(sources! "+                             Enc {| LC ''isoiec_9798_2_6_enc_4'', LN ''Rpa'' tid0, LN ''Rb'' tid2,+                                    s(MV ''Text6'' tid2)+                                 |}+                                 ( LN ''Kab'' tid1 ) ")+              case fake note_unified facts = this facts+              thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+            next+              case (isoiec_9798_2_6_udkey_A_4_enc tid3) note_unified facts = this facts+              thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+            qed (insert facts, fastforce+)?+          qed (insert facts, fastforce+)?+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_6_udkey_state) B_injective_agreement_A:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_6_udkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(MV ''P'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_6_udkey_B_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_6_udkey_A &+          ( tid1, isoiec_9798_2_6_udkey_A_4 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),+             s(MV ''Kab'' tid1), LN ''Rpa'' tid1, s(MV ''Rb'' tid1),+             s(MV ''Text6'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),+                  s(MV ''Kab'' tid0), s(MV ''Rpa'' tid0), LN ''Rb'' tid0,+                  s(MV ''Text6'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_6_udkey_P_3_enc_1 tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_2_6_enc_4'', s(MV ''Rpa'' tid0), LN ''Rb'' tid0,+                                s(MV ''Text6'' tid0)+                             |}+                             ( LN ''Kab'' tid1 ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+        next+          case (isoiec_9798_2_6_udkey_A_4_enc tid2) note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid2, LN ''Kab'' tid1,+                                  s(MV ''B'' tid2), s(MV ''Text4'' tid2)+                               |}+                               ( K ( s(AV ''A'' tid2) ) ( s(AV ''P'' tid2) ) ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest: P_secret_Kab intro: event_predOrdI)+          next+            case (isoiec_9798_2_6_udkey_P_3_enc tid3) note_unified facts = this facts+            thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+          qed (insert facts, fastforce+)?+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_6_udkey_state) A_injective_agreement_P:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_6_udkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''P'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_6_udkey_A_3 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_6_udkey_P &+          ( tid1, isoiec_9798_2_6_udkey_P_3 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),+             s(MV ''Ra'' tid1), LN ''Kab'' tid1, s(MV ''Text4'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''P'' tid0),+                  LN ''Ra'' tid0, s(MV ''Kab'' tid0), s(MV ''Text4'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0,+                              s(MV ''Kab'' tid0), s(MV ''B'' tid0), s(MV ''Text4'' tid0)+                           |}+                           ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_6_udkey_P_3_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_2_6_udkey_state) B_injective_agreement_P:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_2_6_udkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(MV ''P'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_2_6_udkey_B_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_2_6_udkey_P &+          ( tid1, isoiec_9798_2_6_udkey_P_3 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''P'' tid1),+             s(MV ''Rb'' tid1), LN ''Kab'' tid1, s(MV ''Text3'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''P'' tid0),+                  LN ''Rb'' tid0, s(MV ''Kab'' tid0), s(MV ''Text3'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0,+                              s(MV ''Kab'' tid0), s(AV ''A'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_2_6_udkey_P_3_enc_1 tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj) qed  end
data/examples/iso9798/isabelle-proofs/isoiec-9798-3_cert_auto.thy view
@@ -1,3320 +1,3726 @@ theory "isoiec-9798-3_cert_auto" imports-  "../ESPLogic"-begin--role isoiec_9798_3_1_A-where "isoiec_9798_3_1_A =-  [ Send ''leak_A'' ( sN ''TNA'' )-  , Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>-  , Send ''1'' <| sAV ''A'', sAV ''B'', sMV ''Text2'',-                  PSign <| sC ''isoiec_9798_3_1_sig_1'', sN ''TNA'', sAV ''B'',-                           sMV ''Text1''-                        |>-                        ( sPK ''A'' )-               |>-  ]"--role isoiec_9798_3_1_B-where "isoiec_9798_3_1_B =-  [ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Text2'',-                  PSign <| sC ''isoiec_9798_3_1_sig_1'', sMV ''TNA'', sAV ''B'',-                           sMV ''Text1''-                        |>-                        ( PAsymPK ( sMV ''A'' ) )-               |>-  ]"--protocol isoiec_9798_3_1-where "isoiec_9798_3_1 = { isoiec_9798_3_1_A, isoiec_9798_3_1_B }"--locale restricted_isoiec_9798_3_1_state = isoiec_9798_3_1_state--type_invariant isoiec_9798_3_1_msc_typing for isoiec_9798_3_1-where "isoiec_9798_3_1_msc_typing = mk_typing-  [ ((isoiec_9798_3_1_B, ''A''), (KnownT isoiec_9798_3_1_B_1))-  , ((isoiec_9798_3_1_B, ''TNA''), (KnownT isoiec_9798_3_1_B_1))-  , ((isoiec_9798_3_1_A, ''Text1''), (KnownT isoiec_9798_3_1_A_text_1))-  , ((isoiec_9798_3_1_B, ''Text1''), (KnownT isoiec_9798_3_1_B_1))-  , ((isoiec_9798_3_1_A, ''Text2''), (KnownT isoiec_9798_3_1_A_text_1))-  , ((isoiec_9798_3_1_B, ''Text2''), (KnownT isoiec_9798_3_1_B_1))-  ]"--sublocale isoiec_9798_3_1_state < isoiec_9798_3_1_msc_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_3_1_msc_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_3_1_msc_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_3_1_A_text_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_1_A_text_1_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_1_B_1_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_1_B_1_TNA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_1_B_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_1_B_1_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_3_1_msc_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_3_1_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end--lemma (in restricted_isoiec_9798_3_1_state) B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_1_B"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_1_B_1 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_1_A &-        ( tid1, isoiec_9798_3_1_A_1 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,-           s(MV ''Text1'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),-                s(MV ''Text1'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_1_sig_1'', s(MV ''TNA'' tid0),-                          s(AV ''B'' tid0), s(MV ''Text1'' tid0)-                       |}-                       ( SK ( s(MV ''A'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_1_A_1_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--role isoiec_9798_3_2_A-where "isoiec_9798_3_2_A =-  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>-  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>-  , Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'',-                  PSign <| sC ''isoiec_9798_3_2_sig_2'', sN ''Ra'', sMV ''Rb'', sMV ''B'',-                           sMV ''Text2''-                        |>-                        ( sPK ''A'' )-               |>-  ]"--role isoiec_9798_3_2_B-where "isoiec_9798_3_2_B =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>-  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'',-                  PSign <| sC ''isoiec_9798_3_2_sig_2'', sMV ''Ra'', sN ''Rb'', sAV ''B'',-                           sMV ''Text2''-                        |>-                        ( sPK ''A'' )-               |>-  ]"--protocol isoiec_9798_3_2-where "isoiec_9798_3_2 = { isoiec_9798_3_2_A, isoiec_9798_3_2_B }"--locale restricted_isoiec_9798_3_2_state = isoiec_9798_3_2_state--type_invariant isoiec_9798_3_2_msc_typing for isoiec_9798_3_2-where "isoiec_9798_3_2_msc_typing = mk_typing-  [ ((isoiec_9798_3_2_A, ''B''), (KnownT isoiec_9798_3_2_A_1))-  , ((isoiec_9798_3_2_B, ''Ra''), (KnownT isoiec_9798_3_2_B_2))-  , ((isoiec_9798_3_2_A, ''Rb''), (KnownT isoiec_9798_3_2_A_1))-  , ((isoiec_9798_3_2_A, ''Text1''), (KnownT isoiec_9798_3_2_A_1))-  , ((isoiec_9798_3_2_B, ''Text1''), (KnownT isoiec_9798_3_2_B_text_1))-  , ((isoiec_9798_3_2_A, ''Text2''), (KnownT isoiec_9798_3_2_A_text_2))-  , ((isoiec_9798_3_2_B, ''Text2''), (KnownT isoiec_9798_3_2_B_2))-  , ((isoiec_9798_3_2_A, ''Text3''), (KnownT isoiec_9798_3_2_A_text_2))-  , ((isoiec_9798_3_2_B, ''Text3''), (KnownT isoiec_9798_3_2_B_2))-  ]"--sublocale isoiec_9798_3_2_state < isoiec_9798_3_2_msc_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_3_2_msc_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_3_2_msc_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_3_2_A_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_2_A_1_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_2_A_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_2_A_text_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_2_A_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_2_B_2_Ra t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_2_B_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_2_B_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_3_2_msc_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_3_2_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end--lemma (in restricted_isoiec_9798_3_2_state) B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_2_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_2_B_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_2_A &-        ( tid1, isoiec_9798_3_2_A_2 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),-           s(MV ''Text2'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),-                LN ''Rb'' tid0, s(MV ''Text2'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_2_sig_2'', s(MV ''Ra'' tid0), LN ''Rb'' tid0,-                          s(AV ''B'' tid0), s(MV ''Text2'' tid0)-                       |}-                       ( SK ( s(AV ''A'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_2_A_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--role isoiec_9798_3_3_A-where "isoiec_9798_3_3_A =-  [ Send ''leak_A'' ( sN ''TNA'' )-  , Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>-  , Send ''1'' <| sAV ''A'', sAV ''B'', sMV ''Text2'',-                  PSign <| sC ''isoiec_9798_3_3_sig_1'', sN ''TNA'', sAV ''B'',-                           sMV ''Text1''-                        |>-                        ( sPK ''A'' )-               |>-  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text4'',-                  PSign <| sC ''isoiec_9798_3_3_sig_2'', sMV ''TNB'', sAV ''A'',-                           sMV ''Text3''-                        |>-                        ( sPK ''B'' )-               |>-  ]"--role isoiec_9798_3_3_B-where "isoiec_9798_3_3_B =-  [ Send ''leak_B'' ( sN ''TNB'' )-  , Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Text2'',-                  PSign <| sC ''isoiec_9798_3_3_sig_1'', sMV ''TNA'', sAV ''B'',-                           sMV ''Text1''-                        |>-                        ( PAsymPK ( sMV ''A'' ) )-               |>-  , Recv ''text_2'' <| sMV ''Text3'', sMV ''Text4'' |>-  , Send ''2'' <| sMV ''A'', sAV ''B'', sMV ''Text4'',-                  PSign <| sC ''isoiec_9798_3_3_sig_2'', sN ''TNB'', sMV ''A'',-                           sMV ''Text3''-                        |>-                        ( sPK ''B'' )-               |>-  ]"--protocol isoiec_9798_3_3-where "isoiec_9798_3_3 = { isoiec_9798_3_3_A, isoiec_9798_3_3_B }"--locale restricted_isoiec_9798_3_3_state = isoiec_9798_3_3_state--type_invariant isoiec_9798_3_3_msc_typing for isoiec_9798_3_3-where "isoiec_9798_3_3_msc_typing = mk_typing-  [ ((isoiec_9798_3_3_B, ''A''), (KnownT isoiec_9798_3_3_B_1))-  , ((isoiec_9798_3_3_B, ''TNA''), (KnownT isoiec_9798_3_3_B_1))-  , ((isoiec_9798_3_3_A, ''TNB''), (KnownT isoiec_9798_3_3_A_2))-  , ((isoiec_9798_3_3_A, ''Text1''), (KnownT isoiec_9798_3_3_A_text_1))-  , ((isoiec_9798_3_3_B, ''Text1''), (KnownT isoiec_9798_3_3_B_1))-  , ((isoiec_9798_3_3_A, ''Text2''), (KnownT isoiec_9798_3_3_A_text_1))-  , ((isoiec_9798_3_3_B, ''Text2''), (KnownT isoiec_9798_3_3_B_1))-  , ((isoiec_9798_3_3_A, ''Text3''), (KnownT isoiec_9798_3_3_A_2))-  , ((isoiec_9798_3_3_B, ''Text3''), (KnownT isoiec_9798_3_3_B_text_2))-  , ((isoiec_9798_3_3_A, ''Text4''), (KnownT isoiec_9798_3_3_A_2))-  , ((isoiec_9798_3_3_B, ''Text4''), (KnownT isoiec_9798_3_3_B_text_2))-  ]"--sublocale isoiec_9798_3_3_state < isoiec_9798_3_3_msc_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_3_3_msc_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_3_3_msc_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_3_3_A_text_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_3_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_3_A_text_1_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_3_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_3_A_2_TNB t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_3_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_3_A_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_3_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_3_A_2_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_3_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_3_B_1_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_3_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_3_B_1_TNA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_3_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_3_B_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_3_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_3_B_1_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_3_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_3_B_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_3_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_3_B_text_2_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_3_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_3_3_msc_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_3_3_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end--lemma (in restricted_isoiec_9798_3_3_state) A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_3_A"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_3_A_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_3_B &-        ( tid1, isoiec_9798_3_3_B_2 ) : steps t &-        {| s(MV ''A'' tid1), s(AV ''B'' tid1), LN ''TNB'' tid1,-           s(MV ''Text3'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNB'' tid0),-                s(MV ''Text3'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_3_sig_2'', s(MV ''TNB'' tid0),-                          s(AV ''A'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( SK ( s(AV ''B'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_3_B_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_3_state) B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_3_B"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_3_B_1 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_3_A &-        ( tid1, isoiec_9798_3_3_A_1 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,-           s(MV ''Text1'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),-                s(MV ''Text1'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_3_sig_1'', s(MV ''TNA'' tid0),-                          s(AV ''B'' tid0), s(MV ''Text1'' tid0)-                       |}-                       ( SK ( s(MV ''A'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_3_A_1_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--role isoiec_9798_3_4_A-where "isoiec_9798_3_4_A =-  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''RB'', sMV ''Text1'' |>-  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>-  , Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'',-                  PSign <| sC ''isoiec_9798_3_4_sig_1'', sN ''RA'', sMV ''RB'', sMV ''B'',-                           sMV ''Text2''-                        |>-                        ( sPK ''A'' )-               |>-  , Recv ''3'' <| sMV ''B'', sAV ''A'', sMV ''Text5'',-                  PSign <| sC ''isoiec_9798_3_4_sig_2'', sMV ''RB'', sN ''RA'', sAV ''A'',-                           sMV ''Text4''-                        |>-                        ( PAsymPK ( sMV ''B'' ) )-               |>-  ]"--role isoiec_9798_3_4_B-where "isoiec_9798_3_4_B =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''RB'', sMV ''Text1'' |>-  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'',-                  PSign <| sC ''isoiec_9798_3_4_sig_1'', sMV ''RA'', sN ''RB'', sAV ''B'',-                           sMV ''Text2''-                        |>-                        ( sPK ''A'' )-               |>-  , Recv ''text_3'' <| sMV ''Text4'', sMV ''Text5'' |>-  , Send ''3'' <| sAV ''B'', sAV ''A'', sMV ''Text5'',-                  PSign <| sC ''isoiec_9798_3_4_sig_2'', sN ''RB'', sMV ''RA'', sAV ''A'',-                           sMV ''Text4''-                        |>-                        ( sPK ''B'' )-               |>-  ]"--protocol isoiec_9798_3_4-where "isoiec_9798_3_4 = { isoiec_9798_3_4_A, isoiec_9798_3_4_B }"--locale restricted_isoiec_9798_3_4_state = isoiec_9798_3_4_state--type_invariant isoiec_9798_3_4_msc_typing for isoiec_9798_3_4-where "isoiec_9798_3_4_msc_typing = mk_typing-  [ ((isoiec_9798_3_4_A, ''B''), (KnownT isoiec_9798_3_4_A_1))-  , ((isoiec_9798_3_4_B, ''RA''), (KnownT isoiec_9798_3_4_B_2))-  , ((isoiec_9798_3_4_A, ''RB''), (KnownT isoiec_9798_3_4_A_1))-  , ((isoiec_9798_3_4_A, ''Text1''), (KnownT isoiec_9798_3_4_A_1))-  , ((isoiec_9798_3_4_B, ''Text1''), (KnownT isoiec_9798_3_4_B_text_1))-  , ((isoiec_9798_3_4_A, ''Text2''), (KnownT isoiec_9798_3_4_A_text_2))-  , ((isoiec_9798_3_4_B, ''Text2''), (KnownT isoiec_9798_3_4_B_2))-  , ((isoiec_9798_3_4_A, ''Text3''), (KnownT isoiec_9798_3_4_A_text_2))-  , ((isoiec_9798_3_4_B, ''Text3''), (KnownT isoiec_9798_3_4_B_2))-  , ((isoiec_9798_3_4_A, ''Text4''), (KnownT isoiec_9798_3_4_A_3))-  , ((isoiec_9798_3_4_B, ''Text4''), (KnownT isoiec_9798_3_4_B_text_3))-  , ((isoiec_9798_3_4_A, ''Text5''), (KnownT isoiec_9798_3_4_A_3))-  , ((isoiec_9798_3_4_B, ''Text5''), (KnownT isoiec_9798_3_4_B_text_3))-  ]"--sublocale isoiec_9798_3_4_state < isoiec_9798_3_4_msc_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_3_4_msc_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_3_4_msc_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_3_4_A_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_4_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_4_A_1_RB t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_4_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_4_A_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_4_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_4_A_text_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_4_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_4_A_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_4_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_4_A_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_4_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_4_A_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_4_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_4_B_2_RA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_4_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_4_B_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_4_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_4_B_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_4_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_4_B_text_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_4_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_4_B_text_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_4_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_3_4_msc_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_3_4_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end--lemma (in restricted_isoiec_9798_3_4_state) A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_4_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_4_A_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_4_B &-        ( tid1, isoiec_9798_3_4_B_3 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''RA'' tid1), LN ''RB'' tid1,-           s(MV ''Text2'' tid1), s(MV ''Text4'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''RA'' tid0,-                s(MV ''RB'' tid0), s(MV ''Text2'' tid0), s(MV ''Text4'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_4_sig_2'', s(MV ''RB'' tid0), LN ''RA'' tid0,-                          s(AV ''A'' tid0), s(MV ''Text4'' tid0)-                       |}-                       ( SK ( s(MV ''B'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_4_B_3_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_3_4_sig_1'', LN ''RA'' tid0, LN ''RB'' tid1,-                            s(AV ''B'' tid1), s(MV ''Text2'' tid1)-                         |}-                         ( SK ( s(AV ''A'' tid0) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest!: ltk_secrecy)-    next-      case (isoiec_9798_3_4_A_2_enc tid2) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_4_state) B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_4_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_4_B_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_4_A &-        ( tid1, isoiec_9798_3_4_A_2 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''RA'' tid1, s(MV ''RB'' tid1),-           s(MV ''Text2'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''RA'' tid0),-                LN ''RB'' tid0, s(MV ''Text2'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_4_sig_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,-                          s(AV ''B'' tid0), s(MV ''Text2'' tid0)-                       |}-                       ( SK ( s(AV ''A'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_4_A_2_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--role isoiec_9798_3_5_A-where "isoiec_9798_3_5_A =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''A'', sAV ''B'', sN ''RA'', sMV ''Text1'' |>-  , Recv ''2'' <| sAV ''B'', sAV ''A'', sMV ''RB'', sMV ''Text2'' |>-  , Recv ''3'' <| sAV ''B'', sAV ''A'', sMV ''Text6'',-                  PSign <| sC ''isoiec_9798_3_5_sig_1'', sMV ''RB'', sN ''RA'', sAV ''A'',-                           sMV ''Text5''-                        |>-                        ( sPK ''B'' )-               |>-  , Recv ''text_4'' <| sMV ''Text3'', sMV ''Text4'' |>-  , Send ''4'' <| sAV ''A'', sAV ''B'', sMV ''Text4'',-                  PSign <| sC ''isoiec_9798_3_5_sig_2'', sN ''RA'', sMV ''RB'', sAV ''B'',-                           sMV ''Text3''-                        |>-                        ( sPK ''A'' )-               |>-  ]"--role isoiec_9798_3_5_B-where "isoiec_9798_3_5_B =-  [ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''RA'', sMV ''Text1'' |>-  , Recv ''text_2'' ( sMV ''Text2'' )-  , Send ''2'' <| sAV ''B'', sMV ''A'', sN ''RB'', sMV ''Text2'' |>-  , Recv ''text_3'' <| sMV ''Text5'', sMV ''Text6'' |>-  , Send ''3'' <| sAV ''B'', sMV ''A'', sMV ''Text6'',-                  PSign <| sC ''isoiec_9798_3_5_sig_1'', sN ''RB'', sMV ''RA'', sMV ''A'',-                           sMV ''Text5''-                        |>-                        ( sPK ''B'' )-               |>-  , Recv ''4'' <| sMV ''A'', sAV ''B'', sMV ''Text4'',-                  PSign <| sC ''isoiec_9798_3_5_sig_2'', sMV ''RA'', sN ''RB'', sAV ''B'',-                           sMV ''Text3''-                        |>-                        ( PAsymPK ( sMV ''A'' ) )-               |>-  ]"--protocol isoiec_9798_3_5-where "isoiec_9798_3_5 = { isoiec_9798_3_5_A, isoiec_9798_3_5_B }"--locale restricted_isoiec_9798_3_5_state = isoiec_9798_3_5_state--type_invariant isoiec_9798_3_5_msc_typing for isoiec_9798_3_5-where "isoiec_9798_3_5_msc_typing = mk_typing-  [ ((isoiec_9798_3_5_B, ''A''), (KnownT isoiec_9798_3_5_B_1))-  , ((isoiec_9798_3_5_B, ''RA''), (KnownT isoiec_9798_3_5_B_1))-  , ((isoiec_9798_3_5_A, ''RB''), (KnownT isoiec_9798_3_5_A_2))-  , ((isoiec_9798_3_5_A, ''Text1''), (KnownT isoiec_9798_3_5_A_text_1))-  , ((isoiec_9798_3_5_B, ''Text1''), (KnownT isoiec_9798_3_5_B_1))-  , ((isoiec_9798_3_5_A, ''Text2''), (KnownT isoiec_9798_3_5_A_2))-  , ((isoiec_9798_3_5_B, ''Text2''), (KnownT isoiec_9798_3_5_B_text_2))-  , ((isoiec_9798_3_5_A, ''Text3''), (KnownT isoiec_9798_3_5_A_text_4))-  , ((isoiec_9798_3_5_B, ''Text3''), (KnownT isoiec_9798_3_5_B_4))-  , ((isoiec_9798_3_5_A, ''Text4''), (KnownT isoiec_9798_3_5_A_text_4))-  , ((isoiec_9798_3_5_B, ''Text4''), (KnownT isoiec_9798_3_5_B_4))-  , ((isoiec_9798_3_5_A, ''Text5''), (KnownT isoiec_9798_3_5_A_3))-  , ((isoiec_9798_3_5_B, ''Text5''), (KnownT isoiec_9798_3_5_B_text_3))-  , ((isoiec_9798_3_5_A, ''Text6''), (KnownT isoiec_9798_3_5_A_3))-  , ((isoiec_9798_3_5_B, ''Text6''), (KnownT isoiec_9798_3_5_B_text_3))-  ]"--sublocale isoiec_9798_3_5_state < isoiec_9798_3_5_msc_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_3_5_msc_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_3_5_msc_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_3_5_A_2_RB t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_5_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_A_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_5_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_A_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_5_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_A_3_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_5_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_A_text_4_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_5_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_A_text_4_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_5_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_B_1_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_5_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_B_1_RA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_5_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_B_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_5_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_B_text_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_5_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_B_text_3_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_5_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_B_4_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_5_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_5_B_4_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_5_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_3_5_msc_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_3_5_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end--lemma (in restricted_isoiec_9798_3_5_state) A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_5_A"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_5_A_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_5_B &-        ( tid1, isoiec_9798_3_5_B_3 ) : steps t &-        {| s(MV ''A'' tid1), s(AV ''B'' tid1), s(MV ''RA'' tid1), LN ''RB'' tid1,-           s(MV ''Text5'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''RA'' tid0,-                s(MV ''RB'' tid0), s(MV ''Text5'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_5_sig_1'', s(MV ''RB'' tid0), LN ''RA'' tid0,-                          s(AV ''A'' tid0), s(MV ''Text5'' tid0)-                       |}-                       ( SK ( s(AV ''B'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_5_B_3_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_5_state) B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_5_B"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_5_B_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_5_A &-        ( tid1, isoiec_9798_3_5_A_4 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''RA'' tid1, s(MV ''RB'' tid1),-           s(MV ''Text3'' tid1), s(MV ''Text5'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''RA'' tid0),-                LN ''RB'' tid0, s(MV ''Text3'' tid0), s(MV ''Text5'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_5_sig_2'', s(MV ''RA'' tid0), LN ''RB'' tid0,-                          s(AV ''B'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( SK ( s(MV ''A'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_5_A_4_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_3_5_sig_1'', LN ''RB'' tid0, LN ''RA'' tid1,-                            s(AV ''A'' tid1), s(MV ''Text5'' tid1)-                         |}-                         ( SK ( s(AV ''B'' tid0) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest!: ltk_secrecy)-    next-      case (isoiec_9798_3_5_B_3_enc tid2) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--role isoiec_9798_3_6_1_A-where "isoiec_9798_3_6_1_A =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''A'', sAV ''B'', sN ''Ra'', sMV ''Text1'' |>-  , Recv ''2'' <| sAV ''A'', sAV ''B'', sN ''Ra'', sMV ''Rb'',-                  sMV ''Text3'', sMV ''TokenBA''-               |>-  , Recv ''text_3'' ( sMV ''Text4'' )-  , Send ''3'' <| sAV ''A'', sAV ''T'', sN ''Rpa'', sMV ''Rb'', sAV ''B'',-                  sMV ''Text4''-               |>-  , Recv ''4'' <| sAV ''T'', sAV ''A'', sMV ''Text7'', sAV ''A'',-                  sPK ''A'', sAV ''B'', sMV ''pkB'',-                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_4_1'', sN ''Rpa'', sAV ''B'',-                           sMV ''pkB'', sMV ''Text6''-                        |>-                        ( sPK ''T'' ),-                  sMV ''TokenTA_for_B''-               |>-  , Send ''check_4_out'' ( PEnc <| sC ''check_4'', sMV ''TokenBA'' |>-                                ( sN ''check_nonce_4'' )-                         )-  , Recv ''check_4_in'' ( PEnc <| sC ''check_4'',-                                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_2'', sAV ''B'', sN ''Ra'',-                                           sMV ''Rb'', sAV ''A'', sMV ''Text2''-                                        |>-                                        ( sMV ''pkB'' )-                               |>-                               ( sN ''check_nonce_4'' )-                        )-  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>-  , Send ''5'' <| sAV ''A'', sAV ''B'', sMV ''Text9'', sAV ''T'',-                  sMV ''TokenTA_for_B'',-                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_5'', sMV ''Rb'', sN ''Ra'',-                           sAV ''B'', sAV ''A'', sMV ''Text8''-                        |>-                        ( sPK ''A'' )-               |>-  ]"--role isoiec_9798_3_6_1_B-where "isoiec_9798_3_6_1_B =-  [ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Ra'', sMV ''Text1'' |>-  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>-  , Send ''2'' <| sMV ''A'', sAV ''B'', sMV ''Ra'', sN ''Rb'',-                  sMV ''Text3'',-                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_2'', sAV ''B'', sMV ''Ra'',-                           sN ''Rb'', sMV ''A'', sMV ''Text2''-                        |>-                        ( sPK ''B'' )-               |>-  , Recv ''5'' <| sMV ''A'', sAV ''B'', sMV ''Text9'', sMV ''T'',-                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_4_2'', sN ''Rb'', sMV ''A'',-                           sMV ''pkA'', sMV ''Text5''-                        |>-                        ( PAsymPK ( sMV ''T'' ) ),-                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_5'', sN ''Rb'', sMV ''Ra5'',-                           sAV ''B'', sMV ''A'', sMV ''Text8''-                        |>-                        ( sMV ''pkA'' )-               |>-  ]"--role isoiec_9798_3_6_1_T-where "isoiec_9798_3_6_1_T =-  [ Recv ''3'' <| sMV ''A'', sAV ''T'', sMV ''Rpa'', sMV ''Rb'', sMV ''B'',-                  sMV ''Text4''-               |>-  , Recv ''text_4'' <| sMV ''Text5'', sMV ''Text6'', sMV ''Text7'' |>-  , Send ''4'' <| sAV ''T'', sMV ''A'', sMV ''Text7'', sMV ''A'',-                  PAsymPK ( sMV ''A'' ), sMV ''B'', PAsymPK ( sMV ''B'' ),-                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_4_1'', sMV ''Rpa'', sMV ''B'',-                           PAsymPK ( sMV ''B'' ), sMV ''Text6''-                        |>-                        ( sPK ''T'' ),-                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_4_2'', sMV ''Rb'', sMV ''A'',-                           PAsymPK ( sMV ''A'' ), sMV ''Text5''-                        |>-                        ( sPK ''T'' )-               |>-  ]"--protocol isoiec_9798_3_6_1-where "isoiec_9798_3_6_1 =-{ isoiec_9798_3_6_1_A, isoiec_9798_3_6_1_B, isoiec_9798_3_6_1_T }"--locale restricted_isoiec_9798_3_6_1_state = isoiec_9798_3_6_1_state--type_invariant isoiec_9798_3_6_1_msc_typing for isoiec_9798_3_6_1-where "isoiec_9798_3_6_1_msc_typing = mk_typing-  [ ((isoiec_9798_3_6_1_B, ''A''), (KnownT isoiec_9798_3_6_1_B_1))-  , ((isoiec_9798_3_6_1_T, ''A''), (KnownT isoiec_9798_3_6_1_T_3))-  , ((isoiec_9798_3_6_1_T, ''B''), (KnownT isoiec_9798_3_6_1_T_3))-  , ((isoiec_9798_3_6_1_B, ''Ra''), (KnownT isoiec_9798_3_6_1_B_1))-  , ((isoiec_9798_3_6_1_B, ''Ra5''), (KnownT isoiec_9798_3_6_1_B_5))-  , ((isoiec_9798_3_6_1_A, ''Rb''), (KnownT isoiec_9798_3_6_1_A_2))-  , ((isoiec_9798_3_6_1_T, ''Rb''), (KnownT isoiec_9798_3_6_1_T_3))-  , ((isoiec_9798_3_6_1_T, ''Rpa''), (KnownT isoiec_9798_3_6_1_T_3))-  , ((isoiec_9798_3_6_1_B, ''T''), (KnownT isoiec_9798_3_6_1_B_5))-  , ((isoiec_9798_3_6_1_A, ''Text1''), (KnownT isoiec_9798_3_6_1_A_text_1))-  , ((isoiec_9798_3_6_1_B, ''Text1''), (KnownT isoiec_9798_3_6_1_B_1))-  , ((isoiec_9798_3_6_1_A, ''Text2''),-     (KnownT isoiec_9798_3_6_1_A_check_4_in))-  , ((isoiec_9798_3_6_1_B, ''Text2''), (KnownT isoiec_9798_3_6_1_B_text_2))-  , ((isoiec_9798_3_6_1_A, ''Text3''), (KnownT isoiec_9798_3_6_1_A_2))-  , ((isoiec_9798_3_6_1_B, ''Text3''), (KnownT isoiec_9798_3_6_1_B_text_2))-  , ((isoiec_9798_3_6_1_A, ''Text4''), (KnownT isoiec_9798_3_6_1_A_text_3))-  , ((isoiec_9798_3_6_1_T, ''Text4''), (KnownT isoiec_9798_3_6_1_T_3))-  , ((isoiec_9798_3_6_1_B, ''Text5''), (KnownT isoiec_9798_3_6_1_B_5))-  , ((isoiec_9798_3_6_1_T, ''Text5''), (KnownT isoiec_9798_3_6_1_T_text_4))-  , ((isoiec_9798_3_6_1_A, ''Text6''), (KnownT isoiec_9798_3_6_1_A_4))-  , ((isoiec_9798_3_6_1_T, ''Text6''), (KnownT isoiec_9798_3_6_1_T_text_4))-  , ((isoiec_9798_3_6_1_A, ''Text7''), (KnownT isoiec_9798_3_6_1_A_4))-  , ((isoiec_9798_3_6_1_T, ''Text7''), (KnownT isoiec_9798_3_6_1_T_text_4))-  , ((isoiec_9798_3_6_1_A, ''Text8''), (KnownT isoiec_9798_3_6_1_A_text_5))-  , ((isoiec_9798_3_6_1_B, ''Text8''), (KnownT isoiec_9798_3_6_1_B_5))-  , ((isoiec_9798_3_6_1_A, ''Text9''), (KnownT isoiec_9798_3_6_1_A_text_5))-  , ((isoiec_9798_3_6_1_B, ''Text9''), (KnownT isoiec_9798_3_6_1_B_5))-  , ((isoiec_9798_3_6_1_A, ''TokenBA''), (KnownT isoiec_9798_3_6_1_A_2))-  , ((isoiec_9798_3_6_1_A, ''TokenTA_for_B''),-     (KnownT isoiec_9798_3_6_1_A_4))-  , ((isoiec_9798_3_6_1_B, ''pkA''), (KnownT isoiec_9798_3_6_1_B_5))-  , ((isoiec_9798_3_6_1_A, ''pkB''), (KnownT isoiec_9798_3_6_1_A_4))-  ]"--sublocale isoiec_9798_3_6_1_state < isoiec_9798_3_6_1_msc_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_3_6_1_msc_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_3_6_1_msc_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_3_6_1_A_2_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_A_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_A_2_TokenBA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_A_4_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_A_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_A_4_TokenTA_for_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_A_4_pkB t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_A_check_4_in_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''check_4'',-               {| LC ''isoiec_9798_3_6_opt_1_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,-                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-               |},-               Enc {| LC ''isoiec_9798_3_6_opt_1_sig_2'', s(AV ''B'' tid0),-                      LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-                   |}-                   ( inv(s(MV ''pkB'' tid0)) )-            |}-            ( LN ''check_nonce_4'' tid0 ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_3_6_1_A_text_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_A_text_5_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_B_1_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_B_1_Ra t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_B_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_B_text_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_B_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_B_5_Ra5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_B_5_T t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_B_5_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_B_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_B_5_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_B_5_pkA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_T_3_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_T_3_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_T_3_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_T_3_Rpa t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_T_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_T_text_4_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_T_text_4_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_1_T_text_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_3_6_1_msc_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_3_6_1_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end--lemma (in restricted_isoiec_9798_3_6_1_state) A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_6_1_A"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(AV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_6_1_A_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_6_1_B &-        ( tid1, isoiec_9798_3_6_1_B_2 ) : steps t &-        {| s(MV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,-           s(MV ''Text2'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''Ra'' tid0,-                s(MV ''Rb'' tid0), s(MV ''Text2'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''check_4'',-                          {| LC ''isoiec_9798_3_6_opt_1_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,-                             s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-                          |},-                          Enc {| LC ''isoiec_9798_3_6_opt_1_sig_2'', s(AV ''B'' tid0),-                                 LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-                              |}-                              ( inv(s(MV ''pkB'' tid0)) )-                       |}-                       ( LN ''check_nonce_4'' tid0 ) ")-    case fake note_unified facts = this facts-    thus ?thesis proof(sources! " LN ''check_nonce_4'' tid0 ")-    qed (insert facts, fastsimp+)?-  next-    case (isoiec_9798_3_6_1_A_check_4_out_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_3_6_opt_1_sig_2'', s(AV ''B'' tid0),-                            LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-                         |}-                         ( inv(s(MV ''pkB'' tid0)) ) ")-      case fake note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_3_6_opt_1_sig_4_1'', LN ''Rpa'' tid0,-                              s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text6'' tid0)-                           |}-                           ( SK ( s(AV ''T'' tid0) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest!: ltk_secrecy)-      next-        case (isoiec_9798_3_6_1_T_4_enc tid1) note_unified facts = this facts-        thus ?thesis by (fastsimp dest!: ltk_secrecy)-      qed (insert facts, fastsimp+)?-    next-      case (isoiec_9798_3_6_1_B_2_enc tid1) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_6_1_state) B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_6_1_B"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_6_1_B_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_6_1_A &-        ( tid1, isoiec_9798_3_6_1_A_5 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),-           s(MV ''Text8'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra5'' tid0),-                LN ''Rb'' tid0, s(MV ''Text8'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_6_opt_1_sig_4_2'', LN ''Rb'' tid0,-                          s(MV ''A'' tid0), s(MV ''pkA'' tid0), s(MV ''Text5'' tid0)-                       |}-                       ( SK ( s(MV ''T'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_6_1_T_4_enc_1 tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_3_6_opt_1_sig_5'', LN ''Rb'' tid0,-                            s(MV ''Ra5'' tid0), s(AV ''B'' tid0), s(MV ''A'' tid0),-                            s(MV ''Text8'' tid0)-                         |}-                         ( SK ( s(MV ''A'' tid0) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest!: ltk_secrecy)-    next-      case (isoiec_9798_3_6_1_A_5_enc tid2) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_6_1_state) A_non_injective_agreement_T:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_6_1_A"-    "RLKR(s(AV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_6_1_A_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_6_1_T &-        ( tid1, isoiec_9798_3_6_1_T_4 ) : steps t &-        {| s(MV ''B'' tid1), s(AV ''T'' tid1), s(MV ''Rpa'' tid1),-           PK ( s(MV ''B'' tid1) ), s(MV ''Text6'' tid1)-        |} = {| s(AV ''B'' tid0), s(AV ''T'' tid0), LN ''Rpa'' tid0,-                s(MV ''pkB'' tid0), s(MV ''Text6'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_6_opt_1_sig_4_1'', LN ''Rpa'' tid0,-                          s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text6'' tid0)-                       |}-                       ( SK ( s(AV ''T'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_6_1_T_4_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_6_1_state) B_non_injective_agreement_T:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_6_1_B"-    "RLKR(s(MV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_6_1_B_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_6_1_T &-        ( tid1, isoiec_9798_3_6_1_T_4 ) : steps t &-        {| s(MV ''A'' tid1), s(AV ''T'' tid1), s(MV ''Rb'' tid1),-           PK ( s(MV ''A'' tid1) ), s(MV ''Text5'' tid1)-        |} = {| s(MV ''A'' tid0), s(MV ''T'' tid0), LN ''Rb'' tid0,-                s(MV ''pkA'' tid0), s(MV ''Text5'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_6_opt_1_sig_4_2'', LN ''Rb'' tid0,-                          s(MV ''A'' tid0), s(MV ''pkA'' tid0), s(MV ''Text5'' tid0)-                       |}-                       ( SK ( s(MV ''T'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_6_1_T_4_enc_1 tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--role isoiec_9798_3_6_2_A-where "isoiec_9798_3_6_2_A =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''A'', sAV ''B'', sN ''Ra'', sMV ''Text1'' |>-  , Recv ''2'' <| sAV ''A'', sAV ''B'', sN ''Ra'', sMV ''Rb'',-                  sMV ''Text3'', sMV ''TokenBA''-               |>-  , Recv ''text_3'' ( sMV ''Text4'' )-  , Send ''3'' <| sAV ''A'', sAV ''T'', sN ''Rpa'', sMV ''Rb'', sAV ''B'',-                  sMV ''Text4''-               |>-  , Recv ''4'' <| sAV ''T'', sAV ''A'', sMV ''Text7'', sAV ''A'',-                  sPK ''A'', sAV ''B'', sMV ''pkB'', sMV ''TokenTA''-               |>-  , Send ''check_4_out'' ( PEnc <| sC ''check_4'', sMV ''TokenTA'',-                                   sMV ''TokenBA''-                                |>-                                ( sN ''check_nonce_4'' )-                         )-  , Recv ''check_4_in'' ( PEnc <| sC ''check_4'',-                                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_4'', sN ''Rpa'', sMV ''Rb'',-                                           sAV ''A'', sMV ''pkA'', sAV ''B'', sMV ''pkB'', sMV ''Text5''-                                        |>-                                        ( sPK ''T'' ),-                                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_2'', sAV ''B'', sN ''Ra'',-                                           sMV ''Rb'', sAV ''A'', sMV ''Text2''-                                        |>-                                        ( sMV ''pkB'' )-                               |>-                               ( sN ''check_nonce_4'' )-                        )-  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>-  , Send ''5'' <| sAV ''A'', sAV ''B'', sN ''Rpa'', sMV ''Text9'',-                  sAV ''T'', sMV ''TokenTA'',-                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_5'', sMV ''Rb'', sN ''Ra'',-                           sAV ''B'', sAV ''A'', sMV ''Text8''-                        |>-                        ( sPK ''A'' )-               |>-  ]"--role isoiec_9798_3_6_2_B-where "isoiec_9798_3_6_2_B =-  [ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Ra'', sMV ''Text1'' |>-  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>-  , Send ''2'' <| sMV ''A'', sAV ''B'', sMV ''Ra'', sN ''Rb'',-                  sMV ''Text3'',-                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_2'', sAV ''B'', sMV ''Ra'',-                           sN ''Rb'', sMV ''A'', sMV ''Text2''-                        |>-                        ( sPK ''B'' )-               |>-  , Recv ''5'' <| sMV ''A'', sAV ''B'', sMV ''Rpa'', sMV ''Text9'',-                  sMV ''T'',-                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_4'', sMV ''Rpa'', sN ''Rb'',-                           sMV ''A'', sMV ''pkA'', sAV ''B'', sMV ''pkB'', sMV ''Text5''-                        |>-                        ( PAsymPK ( sMV ''T'' ) ),-                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_5'', sN ''Rb'', sMV ''Ra5'',-                           sAV ''B'', sMV ''A'', sMV ''Text8''-                        |>-                        ( sMV ''pkA'' )-               |>-  ]"--role isoiec_9798_3_6_2_T-where "isoiec_9798_3_6_2_T =-  [ Recv ''3'' <| sMV ''A'', sAV ''T'', sMV ''Rpa'', sMV ''Rb'', sMV ''B'',-                  sMV ''Text4''-               |>-  , Recv ''text_4'' <| sMV ''Text5'', sMV ''Text7'' |>-  , Send ''4'' <| sAV ''T'', sMV ''A'', sMV ''Text7'', sMV ''A'',-                  PAsymPK ( sMV ''A'' ), sMV ''B'', PAsymPK ( sMV ''B'' ),-                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_4'', sMV ''Rpa'', sMV ''Rb'',-                           sMV ''A'', PAsymPK ( sMV ''A'' ), sMV ''B'', PAsymPK ( sMV ''B'' ),-                           sMV ''Text5''-                        |>-                        ( sPK ''T'' )-               |>-  ]"--protocol isoiec_9798_3_6_2-where "isoiec_9798_3_6_2 =-{ isoiec_9798_3_6_2_A, isoiec_9798_3_6_2_B, isoiec_9798_3_6_2_T }"--locale restricted_isoiec_9798_3_6_2_state = isoiec_9798_3_6_2_state--type_invariant isoiec_9798_3_6_2_msc_typing for isoiec_9798_3_6_2-where "isoiec_9798_3_6_2_msc_typing = mk_typing-  [ ((isoiec_9798_3_6_2_B, ''A''), (KnownT isoiec_9798_3_6_2_B_1))-  , ((isoiec_9798_3_6_2_T, ''A''), (KnownT isoiec_9798_3_6_2_T_3))-  , ((isoiec_9798_3_6_2_T, ''B''), (KnownT isoiec_9798_3_6_2_T_3))-  , ((isoiec_9798_3_6_2_B, ''Ra''), (KnownT isoiec_9798_3_6_2_B_1))-  , ((isoiec_9798_3_6_2_B, ''Ra5''), (KnownT isoiec_9798_3_6_2_B_5))-  , ((isoiec_9798_3_6_2_A, ''Rb''), (KnownT isoiec_9798_3_6_2_A_2))-  , ((isoiec_9798_3_6_2_T, ''Rb''), (KnownT isoiec_9798_3_6_2_T_3))-  , ((isoiec_9798_3_6_2_B, ''Rpa''), (KnownT isoiec_9798_3_6_2_B_5))-  , ((isoiec_9798_3_6_2_T, ''Rpa''), (KnownT isoiec_9798_3_6_2_T_3))-  , ((isoiec_9798_3_6_2_B, ''T''), (KnownT isoiec_9798_3_6_2_B_5))-  , ((isoiec_9798_3_6_2_A, ''Text1''), (KnownT isoiec_9798_3_6_2_A_text_1))-  , ((isoiec_9798_3_6_2_B, ''Text1''), (KnownT isoiec_9798_3_6_2_B_1))-  , ((isoiec_9798_3_6_2_A, ''Text2''),-     (KnownT isoiec_9798_3_6_2_A_check_4_in))-  , ((isoiec_9798_3_6_2_B, ''Text2''), (KnownT isoiec_9798_3_6_2_B_text_2))-  , ((isoiec_9798_3_6_2_A, ''Text3''), (KnownT isoiec_9798_3_6_2_A_2))-  , ((isoiec_9798_3_6_2_B, ''Text3''), (KnownT isoiec_9798_3_6_2_B_text_2))-  , ((isoiec_9798_3_6_2_A, ''Text4''), (KnownT isoiec_9798_3_6_2_A_text_3))-  , ((isoiec_9798_3_6_2_T, ''Text4''), (KnownT isoiec_9798_3_6_2_T_3))-  , ((isoiec_9798_3_6_2_A, ''Text5''),-     (KnownT isoiec_9798_3_6_2_A_check_4_in))-  , ((isoiec_9798_3_6_2_B, ''Text5''), (KnownT isoiec_9798_3_6_2_B_5))-  , ((isoiec_9798_3_6_2_T, ''Text5''), (KnownT isoiec_9798_3_6_2_T_text_4))-  , ((isoiec_9798_3_6_2_A, ''Text7''), (KnownT isoiec_9798_3_6_2_A_4))-  , ((isoiec_9798_3_6_2_T, ''Text7''), (KnownT isoiec_9798_3_6_2_T_text_4))-  , ((isoiec_9798_3_6_2_A, ''Text8''), (KnownT isoiec_9798_3_6_2_A_text_5))-  , ((isoiec_9798_3_6_2_B, ''Text8''), (KnownT isoiec_9798_3_6_2_B_5))-  , ((isoiec_9798_3_6_2_A, ''Text9''), (KnownT isoiec_9798_3_6_2_A_text_5))-  , ((isoiec_9798_3_6_2_B, ''Text9''), (KnownT isoiec_9798_3_6_2_B_5))-  , ((isoiec_9798_3_6_2_A, ''TokenBA''), (KnownT isoiec_9798_3_6_2_A_2))-  , ((isoiec_9798_3_6_2_A, ''TokenTA''), (KnownT isoiec_9798_3_6_2_A_4))-  , ((isoiec_9798_3_6_2_A, ''pkA''),-     (KnownT isoiec_9798_3_6_2_A_check_4_in))-  , ((isoiec_9798_3_6_2_B, ''pkA''), (KnownT isoiec_9798_3_6_2_B_5))-  , ((isoiec_9798_3_6_2_A, ''pkB''), (KnownT isoiec_9798_3_6_2_A_4))-  , ((isoiec_9798_3_6_2_B, ''pkB''), (KnownT isoiec_9798_3_6_2_B_5))-  ]"--sublocale isoiec_9798_3_6_2_state < isoiec_9798_3_6_2_msc_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_3_6_2_msc_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_3_6_2_msc_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_3_6_2_A_2_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_A_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_A_2_TokenBA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_A_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_A_4_TokenTA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_A_4_pkB t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_A_check_4_in_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''check_4'',-               {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,-                     s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                     s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                  |},-                  Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,-                         s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                         s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                      |}-                      ( SK ( s(AV ''T'' tid0) ) )-               |},-               {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,-                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-               |},-               Enc {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0),-                      LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-                   |}-                   ( inv(s(MV ''pkB'' tid0)) )-            |}-            ( LN ''check_nonce_4'' tid0 ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_3_6_2_A_check_4_in_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''check_4'',-               {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,-                     s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                     s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                  |},-                  Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,-                         s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                         s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                      |}-                      ( SK ( s(AV ''T'' tid0) ) )-               |},-               {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,-                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-               |},-               Enc {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0),-                      LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-                   |}-                   ( inv(s(MV ''pkB'' tid0)) )-            |}-            ( LN ''check_nonce_4'' tid0 ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_3_6_2_A_check_4_in_pkA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''check_4'',-               {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,-                     s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                     s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                  |},-                  Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,-                         s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                         s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                      |}-                      ( SK ( s(AV ''T'' tid0) ) )-               |},-               {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,-                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-               |},-               Enc {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0),-                      LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-                   |}-                   ( inv(s(MV ''pkB'' tid0)) )-            |}-            ( LN ''check_nonce_4'' tid0 ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_3_6_2_A_text_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_A_text_5_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_1_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_1_Ra t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_text_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_text_2_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_5_Ra5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_5_Rpa t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_5_T t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_5_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_5_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_5_pkA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_B_5_pkB t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_T_3_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_T_3_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_T_3_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_T_3_Rpa t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_T_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_T_text_4_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_6_2_T_text_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_3_6_2_msc_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_3_6_2_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end--lemma (in restricted_isoiec_9798_3_6_2_state) A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_6_2_A"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "RLKR(s(AV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_6_2_A_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_6_2_B &-        ( tid1, isoiec_9798_3_6_2_B_2 ) : steps t &-        {| s(MV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,-           s(MV ''Text2'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''Ra'' tid0,-                s(MV ''Rb'' tid0), s(MV ''Text2'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''check_4'',-                          {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,-                                s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                                s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                             |},-                             Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,-                                    s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                                    s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                                 |}-                                 ( SK ( s(AV ''T'' tid0) ) )-                          |},-                          {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,-                             s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-                          |},-                          Enc {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0),-                                 LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-                              |}-                              ( inv(s(MV ''pkB'' tid0)) )-                       |}-                       ( LN ''check_nonce_4'' tid0 ) ")-    case fake note_unified facts = this facts-    thus ?thesis proof(sources! " LN ''check_nonce_4'' tid0 ")-    qed (insert facts, fastsimp+)?-  next-    case (isoiec_9798_3_6_2_A_check_4_out_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0),-                            LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-                         |}-                         ( inv(s(MV ''pkB'' tid0)) ) ")-      case fake note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,-                              s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                              s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                           |}-                           ( SK ( s(AV ''T'' tid0) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest!: ltk_secrecy)-      next-        case (isoiec_9798_3_6_2_T_4_enc tid1) note_unified facts = this facts-        thus ?thesis by (fastsimp dest!: ltk_secrecy)-      qed (insert facts, fastsimp+)?-    next-      case (isoiec_9798_3_6_2_B_2_enc tid1) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_6_2_state) B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_6_2_B"-    "RLKR(s(MV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_6_2_B_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_6_2_A &-        ( tid1, isoiec_9798_3_6_2_A_5 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),-           s(MV ''Text8'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra5'' tid0),-                LN ''Rb'' tid0, s(MV ''Text8'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', s(MV ''Rpa'' tid0),-                          LN ''Rb'' tid0, s(MV ''A'' tid0), s(MV ''pkA'' tid0), s(AV ''B'' tid0),-                          s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                       |}-                       ( SK ( s(MV ''T'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_6_2_T_4_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_3_6_opt_2_sig_5'', LN ''Rb'' tid0,-                            s(MV ''Ra5'' tid0), s(AV ''B'' tid0), s(MV ''A'' tid0),-                            s(MV ''Text8'' tid0)-                         |}-                         ( SK ( s(MV ''A'' tid0) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest!: ltk_secrecy)-    next-      case (isoiec_9798_3_6_2_A_5_enc tid2) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_6_2_state) A_non_injective_agreement_T:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_6_2_A"-    "RLKR(s(AV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_6_2_A_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_6_2_T &-        ( tid1, isoiec_9798_3_6_2_T_4 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''T'' tid1),-           s(MV ''Rpa'' tid1), s(MV ''Rb'' tid1), PK ( s(MV ''A'' tid1) ),-           PK ( s(MV ''B'' tid1) ), s(MV ''Text5'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''T'' tid0),-                LN ''Rpa'' tid0, s(MV ''Rb'' tid0), s(MV ''pkA'' tid0),-                s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''check_4'',-                          {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,-                                s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                                s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                             |},-                             Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,-                                    s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                                    s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                                 |}-                                 ( SK ( s(AV ''T'' tid0) ) )-                          |},-                          {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,-                             s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-                          |},-                          Enc {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0),-                                 LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)-                              |}-                              ( inv(s(MV ''pkB'' tid0)) )-                       |}-                       ( LN ''check_nonce_4'' tid0 ) ")-    case fake note_unified facts = this facts-    thus ?thesis proof(sources! " LN ''check_nonce_4'' tid0 ")-    qed (insert facts, fastsimp+)?-  next-    case (isoiec_9798_3_6_2_A_check_4_out_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,-                            s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                            s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                         |}-                         ( SK ( s(AV ''T'' tid0) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest!: ltk_secrecy)-    next-      case (isoiec_9798_3_6_2_T_4_enc tid1) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_6_2_state) B_non_injective_agreement_T:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_6_2_B"-    "RLKR(s(MV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_6_2_B_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_6_2_T &-        ( tid1, isoiec_9798_3_6_2_T_4 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''T'' tid1),-           s(MV ''Rpa'' tid1), s(MV ''Rb'' tid1), PK ( s(MV ''A'' tid1) ),-           PK ( s(MV ''B'' tid1) ), s(MV ''Text5'' tid1)-        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''T'' tid0),-                s(MV ''Rpa'' tid0), LN ''Rb'' tid0, s(MV ''pkA'' tid0),-                s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', s(MV ''Rpa'' tid0),-                          LN ''Rb'' tid0, s(MV ''A'' tid0), s(MV ''pkA'' tid0), s(AV ''B'' tid0),-                          s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)-                       |}-                       ( SK ( s(MV ''T'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_6_2_T_4_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--role isoiec_9798_3_7_1_A-where "isoiec_9798_3_7_1_A =-  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>-  , Recv ''text_2'' ( sMV ''Text2'' )-  , Send ''2'' <| sAV ''A'', sAV ''T'', sN ''Rpa'', sMV ''Rb'', sAV ''A'',-                  sMV ''B'', sMV ''Text2''-               |>-  , Recv ''3'' <| sAV ''T'', sAV ''A'', sMV ''Text5'', sAV ''A'',-                  sPK ''A'', sMV ''B'', sMV ''pkB'',-                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_3_1'', sN ''Rpa'', sMV ''B'',-                           sMV ''pkB'', sMV ''Text4''-                        |>-                        ( sPK ''T'' ),-                  sMV ''TokenTA_for_B''-               |>-  , Recv ''text_4'' <| sMV ''Text6'', sMV ''Text7'' |>-  , Send ''4'' <| sAV ''A'', sMV ''B'', sN ''Rpa'', sMV ''Text7'',-                  sAV ''T'', sMV ''TokenTA_for_B'',-                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_4'', sMV ''Rb'', sN ''Ra'',-                           sMV ''B'', sAV ''A'', sMV ''Text6''-                        |>-                        ( sPK ''A'' )-               |>-  , Recv ''5'' <| sAV ''A'', sMV ''B'', sN ''Ra'', sMV ''Rb'',-                  sMV ''Text9'',-                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_5'', sN ''Ra'', sMV ''Rb'',-                           sAV ''A'', sMV ''B'', sMV ''Text8''-                        |>-                        ( sMV ''pkB'' )-               |>-  ]"--role isoiec_9798_3_7_1_B-where "isoiec_9798_3_7_1_B =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>-  , Recv ''4'' <| sAV ''A'', sAV ''B'', sMV ''Rpa'', sMV ''Text9'',-                  sMV ''T'',-                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_3_2'', sN ''Rb'', sAV ''A'',-                           sMV ''pkA'', sMV ''Text3''-                        |>-                        ( PAsymPK ( sMV ''T'' ) ),-                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_4'', sN ''Rb'', sMV ''Ra'',-                           sAV ''B'', sAV ''A'', sMV ''Text6''-                        |>-                        ( sMV ''pkA'' )-               |>-  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>-  , Send ''5'' <| sAV ''A'', sAV ''B'', sMV ''Ra'', sN ''Rb'',-                  sMV ''Text9'',-                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_5'', sMV ''Ra'', sN ''Rb'',-                           sAV ''A'', sAV ''B'', sMV ''Text8''-                        |>-                        ( sPK ''B'' )-               |>-  ]"--role isoiec_9798_3_7_1_T-where "isoiec_9798_3_7_1_T =-  [ Recv ''2'' <| sMV ''A'', sAV ''T'', sMV ''Rpa'', sMV ''Rb'', sMV ''A'',-                  sMV ''B'', sMV ''Text2''-               |>-  , Recv ''text_3'' <| sMV ''Text3'', sMV ''Text4'', sMV ''Text5'' |>-  , Send ''3'' <| sAV ''T'', sMV ''A'', sMV ''Text5'', sMV ''A'',-                  PAsymPK ( sMV ''A'' ), sMV ''B'', PAsymPK ( sMV ''B'' ),-                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_3_1'', sMV ''Rpa'', sMV ''B'',-                           PAsymPK ( sMV ''B'' ), sMV ''Text4''-                        |>-                        ( sPK ''T'' ),-                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_3_2'', sMV ''Rb'', sMV ''A'',-                           PAsymPK ( sMV ''A'' ), sMV ''Text3''-                        |>-                        ( sPK ''T'' )-               |>-  ]"--protocol isoiec_9798_3_7_1-where "isoiec_9798_3_7_1 =-{ isoiec_9798_3_7_1_A, isoiec_9798_3_7_1_B, isoiec_9798_3_7_1_T }"--locale restricted_isoiec_9798_3_7_1_state = isoiec_9798_3_7_1_state--type_invariant isoiec_9798_3_7_1_msc_typing for isoiec_9798_3_7_1-where "isoiec_9798_3_7_1_msc_typing = mk_typing-  [ ((isoiec_9798_3_7_1_T, ''A''), (KnownT isoiec_9798_3_7_1_T_2))-  , ((isoiec_9798_3_7_1_A, ''B''), (KnownT isoiec_9798_3_7_1_A_1))-  , ((isoiec_9798_3_7_1_T, ''B''), (KnownT isoiec_9798_3_7_1_T_2))-  , ((isoiec_9798_3_7_1_B, ''Ra''), (KnownT isoiec_9798_3_7_1_B_4))-  , ((isoiec_9798_3_7_1_A, ''Rb''), (KnownT isoiec_9798_3_7_1_A_1))-  , ((isoiec_9798_3_7_1_T, ''Rb''), (KnownT isoiec_9798_3_7_1_T_2))-  , ((isoiec_9798_3_7_1_B, ''Rpa''), (KnownT isoiec_9798_3_7_1_B_4))-  , ((isoiec_9798_3_7_1_T, ''Rpa''), (KnownT isoiec_9798_3_7_1_T_2))-  , ((isoiec_9798_3_7_1_B, ''T''), (KnownT isoiec_9798_3_7_1_B_4))-  , ((isoiec_9798_3_7_1_A, ''Text1''), (KnownT isoiec_9798_3_7_1_A_1))-  , ((isoiec_9798_3_7_1_B, ''Text1''), (KnownT isoiec_9798_3_7_1_B_text_1))-  , ((isoiec_9798_3_7_1_A, ''Text2''), (KnownT isoiec_9798_3_7_1_A_text_2))-  , ((isoiec_9798_3_7_1_T, ''Text2''), (KnownT isoiec_9798_3_7_1_T_2))-  , ((isoiec_9798_3_7_1_B, ''Text3''), (KnownT isoiec_9798_3_7_1_B_4))-  , ((isoiec_9798_3_7_1_T, ''Text3''), (KnownT isoiec_9798_3_7_1_T_text_3))-  , ((isoiec_9798_3_7_1_A, ''Text4''), (KnownT isoiec_9798_3_7_1_A_3))-  , ((isoiec_9798_3_7_1_T, ''Text4''), (KnownT isoiec_9798_3_7_1_T_text_3))-  , ((isoiec_9798_3_7_1_A, ''Text5''), (KnownT isoiec_9798_3_7_1_A_3))-  , ((isoiec_9798_3_7_1_T, ''Text5''), (KnownT isoiec_9798_3_7_1_T_text_3))-  , ((isoiec_9798_3_7_1_A, ''Text6''), (KnownT isoiec_9798_3_7_1_A_text_4))-  , ((isoiec_9798_3_7_1_B, ''Text6''), (KnownT isoiec_9798_3_7_1_B_4))-  , ((isoiec_9798_3_7_1_A, ''Text7''), (KnownT isoiec_9798_3_7_1_A_text_4))-  , ((isoiec_9798_3_7_1_A, ''Text8''), (KnownT isoiec_9798_3_7_1_A_5))-  , ((isoiec_9798_3_7_1_B, ''Text8''), (KnownT isoiec_9798_3_7_1_B_text_5))-  , ((isoiec_9798_3_7_1_A, ''Text9''), (KnownT isoiec_9798_3_7_1_A_5))-  , ((isoiec_9798_3_7_1_B, ''Text9''), (KnownT isoiec_9798_3_7_1_B_4))-  , ((isoiec_9798_3_7_1_A, ''TokenTA_for_B''),-     (KnownT isoiec_9798_3_7_1_A_3))-  , ((isoiec_9798_3_7_1_B, ''pkA''), (KnownT isoiec_9798_3_7_1_B_4))-  , ((isoiec_9798_3_7_1_A, ''pkB''), (KnownT isoiec_9798_3_7_1_A_3))-  ]"--sublocale isoiec_9798_3_7_1_state < isoiec_9798_3_7_1_msc_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_3_7_1_msc_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_3_7_1_msc_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_3_7_1_A_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_A_1_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_A_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_A_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_A_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_A_3_TokenTA_for_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_A_3_pkB t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_A_text_4_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_A_text_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_A_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_A_5_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_B_4_Ra t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_B_4_Rpa t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_B_4_T t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_B_4_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_B_4_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_B_4_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_B_4_pkA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_B_text_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_T_2_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_T_2_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_T_2_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_T_2_Rpa t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_T_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_T_text_3_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_T_text_3_Text4 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_1_T_text_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_3_7_1_msc_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_3_7_1_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end--lemma (in restricted_isoiec_9798_3_7_1_state) A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_7_1_A"-    "RLKR(s(AV ''T'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_7_1_A_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_7_1_B &-        ( tid1, isoiec_9798_3_7_1_B_5 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,-           s(MV ''Text8'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''Ra'' tid0,-                s(MV ''Rb'' tid0), s(MV ''Text8'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_7_opt_1_sig_3_1'', LN ''Rpa'' tid0,-                          s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text4'' tid0)-                       |}-                       ( SK ( s(AV ''T'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_7_1_T_3_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_3_7_opt_1_sig_5'', LN ''Ra'' tid0,-                            s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),-                            s(MV ''Text8'' tid0)-                         |}-                         ( SK ( s(MV ''B'' tid0) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest!: ltk_secrecy)-    next-      case (isoiec_9798_3_7_1_B_5_enc tid2) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_7_1_state) B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_7_1_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_7_1_B_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_7_1_A &-        ( tid1, isoiec_9798_3_7_1_A_4 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),-           s(MV ''Text6'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),-                LN ''Rb'' tid0, s(MV ''Text6'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_7_opt_1_sig_3_2'', LN ''Rb'' tid0,-                          s(AV ''A'' tid0), s(MV ''pkA'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( SK ( s(MV ''T'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_7_1_T_3_enc_1 tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_3_7_opt_1_sig_4'', LN ''Rb'' tid0,-                            s(MV ''Ra'' tid0), s(AV ''B'' tid0), s(AV ''A'' tid0),-                            s(MV ''Text6'' tid0)-                         |}-                         ( SK ( s(AV ''A'' tid0) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest!: ltk_secrecy)-    next-      case (isoiec_9798_3_7_1_A_4_enc tid2) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_7_1_state) A_non_injective_agreement_T:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_7_1_A"-    "RLKR(s(AV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_7_1_A_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_7_1_T &-        ( tid1, isoiec_9798_3_7_1_T_3 ) : steps t &-        {| s(MV ''B'' tid1), s(AV ''T'' tid1), s(MV ''Rpa'' tid1),-           PK ( s(MV ''B'' tid1) ), s(MV ''Text4'' tid1)-        |} = {| s(MV ''B'' tid0), s(AV ''T'' tid0), LN ''Rpa'' tid0,-                s(MV ''pkB'' tid0), s(MV ''Text4'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_7_opt_1_sig_3_1'', LN ''Rpa'' tid0,-                          s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text4'' tid0)-                       |}-                       ( SK ( s(AV ''T'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_7_1_T_3_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_7_1_state) B_non_injective_agreement_T:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_7_1_B"-    "RLKR(s(MV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_7_1_B_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_7_1_T &-        ( tid1, isoiec_9798_3_7_1_T_3 ) : steps t &-        {| s(MV ''A'' tid1), s(AV ''T'' tid1), s(MV ''Rb'' tid1),-           PK ( s(MV ''A'' tid1) ), s(MV ''Text3'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''T'' tid0), LN ''Rb'' tid0,-                s(MV ''pkA'' tid0), s(MV ''Text3'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_7_opt_1_sig_3_2'', LN ''Rb'' tid0,-                          s(AV ''A'' tid0), s(MV ''pkA'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( SK ( s(MV ''T'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_7_1_T_3_enc_1 tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?-qed--role isoiec_9798_3_7_2_A-where "isoiec_9798_3_7_2_A =-  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>-  , Recv ''text_2'' ( sMV ''Text2'' )-  , Send ''2'' <| sAV ''A'', sAV ''T'', sN ''Rpa'', sMV ''Rb'', sAV ''A'',-                  sMV ''B'', sMV ''Text2''-               |>-  , Recv ''3'' <| sAV ''T'', sAV ''A'', sMV ''Text5'', sAV ''A'',-                  sPK ''A'', sMV ''B'', sMV ''pkB'', sMV ''TokenTA''-               |>-  , Send ''check_3_out'' ( PEnc <| sC ''check_4'', sMV ''TokenTA'' |>-                                ( sN ''check_nonce_4'' )-                         )-  , Recv ''check_3_in'' ( PEnc <| sC ''check_4'',-                                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_3'', sN ''Rpa'', sMV ''Rb'',-                                           sAV ''A'', sMV ''pkA'', sMV ''B'', sMV ''pkB'', sMV ''Text3''-                                        |>-                                        ( sPK ''T'' )-                               |>-                               ( sN ''check_nonce_4'' )-                        )-  , Recv ''text_4'' <| sMV ''Text6'', sMV ''Text7'' |>-  , Send ''4'' <| sAV ''A'', sMV ''B'', sN ''Rpa'', sMV ''Text7'',-                  sAV ''T'', sMV ''TokenTA'',-                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_4'', sMV ''Rb'', sN ''Ra'',-                           sMV ''B'', sAV ''A'', sMV ''Text6''-                        |>-                        ( sPK ''A'' )-               |>-  , Recv ''5'' <| sAV ''A'', sMV ''B'', sN ''Ra'', sMV ''Rb'',-                  sMV ''Text9'',-                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_5'', sN ''Ra'', sMV ''Rb'',-                           sAV ''A'', sMV ''B'', sMV ''Text8''-                        |>-                        ( sMV ''pkB'' )-               |>-  ]"--role isoiec_9798_3_7_2_B-where "isoiec_9798_3_7_2_B =-  [ Recv ''text_1'' ( sMV ''Text1'' )-  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>-  , Recv ''4'' <| sAV ''A'', sAV ''B'', sMV ''Rpa'', sMV ''Text9'',-                  sMV ''T'',-                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_3'', sMV ''Rpa'', sN ''Rb'',-                           sAV ''A'', sMV ''pkA'', sAV ''B'', sMV ''pkB'', sMV ''Text3''-                        |>-                        ( PAsymPK ( sMV ''T'' ) ),-                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_4'', sN ''Rb'', sMV ''Ra'',-                           sAV ''B'', sAV ''A'', sMV ''Text6''-                        |>-                        ( sMV ''pkA'' )-               |>-  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>-  , Send ''5'' <| sAV ''A'', sAV ''B'', sMV ''Ra'', sN ''Rb'',-                  sMV ''Text9'',-                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_5'', sMV ''Ra'', sN ''Rb'',-                           sAV ''A'', sAV ''B'', sMV ''Text8''-                        |>-                        ( sPK ''B'' )-               |>-  ]"--role isoiec_9798_3_7_2_T-where "isoiec_9798_3_7_2_T =-  [ Recv ''2'' <| sMV ''A'', sAV ''T'', sMV ''Rpa'', sMV ''Rb'', sMV ''A'',-                  sMV ''B'', sMV ''Text2''-               |>-  , Recv ''text_3'' <| sMV ''Text3'', sMV ''Text5'' |>-  , Send ''3'' <| sAV ''T'', sMV ''A'', sMV ''Text5'', sMV ''A'',-                  PAsymPK ( sMV ''A'' ), sMV ''B'', PAsymPK ( sMV ''B'' ),-                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_3'', sMV ''Rpa'', sMV ''Rb'',-                           sMV ''A'', PAsymPK ( sMV ''A'' ), sMV ''B'', PAsymPK ( sMV ''B'' ),-                           sMV ''Text3''-                        |>-                        ( sPK ''T'' )-               |>-  ]"--protocol isoiec_9798_3_7_2-where "isoiec_9798_3_7_2 =-{ isoiec_9798_3_7_2_A, isoiec_9798_3_7_2_B, isoiec_9798_3_7_2_T }"--locale restricted_isoiec_9798_3_7_2_state = isoiec_9798_3_7_2_state--type_invariant isoiec_9798_3_7_2_msc_typing for isoiec_9798_3_7_2-where "isoiec_9798_3_7_2_msc_typing = mk_typing-  [ ((isoiec_9798_3_7_2_T, ''A''), (KnownT isoiec_9798_3_7_2_T_2))-  , ((isoiec_9798_3_7_2_A, ''B''), (KnownT isoiec_9798_3_7_2_A_1))-  , ((isoiec_9798_3_7_2_T, ''B''), (KnownT isoiec_9798_3_7_2_T_2))-  , ((isoiec_9798_3_7_2_B, ''Ra''), (KnownT isoiec_9798_3_7_2_B_4))-  , ((isoiec_9798_3_7_2_A, ''Rb''), (KnownT isoiec_9798_3_7_2_A_1))-  , ((isoiec_9798_3_7_2_T, ''Rb''), (KnownT isoiec_9798_3_7_2_T_2))-  , ((isoiec_9798_3_7_2_B, ''Rpa''), (KnownT isoiec_9798_3_7_2_B_4))-  , ((isoiec_9798_3_7_2_T, ''Rpa''), (KnownT isoiec_9798_3_7_2_T_2))-  , ((isoiec_9798_3_7_2_B, ''T''), (KnownT isoiec_9798_3_7_2_B_4))-  , ((isoiec_9798_3_7_2_A, ''Text1''), (KnownT isoiec_9798_3_7_2_A_1))-  , ((isoiec_9798_3_7_2_B, ''Text1''), (KnownT isoiec_9798_3_7_2_B_text_1))-  , ((isoiec_9798_3_7_2_A, ''Text2''), (KnownT isoiec_9798_3_7_2_A_text_2))-  , ((isoiec_9798_3_7_2_T, ''Text2''), (KnownT isoiec_9798_3_7_2_T_2))-  , ((isoiec_9798_3_7_2_A, ''Text3''),-     (KnownT isoiec_9798_3_7_2_A_check_3_in))-  , ((isoiec_9798_3_7_2_B, ''Text3''), (KnownT isoiec_9798_3_7_2_B_4))-  , ((isoiec_9798_3_7_2_T, ''Text3''), (KnownT isoiec_9798_3_7_2_T_text_3))-  , ((isoiec_9798_3_7_2_A, ''Text5''), (KnownT isoiec_9798_3_7_2_A_3))-  , ((isoiec_9798_3_7_2_T, ''Text5''), (KnownT isoiec_9798_3_7_2_T_text_3))-  , ((isoiec_9798_3_7_2_A, ''Text6''), (KnownT isoiec_9798_3_7_2_A_text_4))-  , ((isoiec_9798_3_7_2_B, ''Text6''), (KnownT isoiec_9798_3_7_2_B_4))-  , ((isoiec_9798_3_7_2_A, ''Text7''), (KnownT isoiec_9798_3_7_2_A_text_4))-  , ((isoiec_9798_3_7_2_A, ''Text8''), (KnownT isoiec_9798_3_7_2_A_5))-  , ((isoiec_9798_3_7_2_B, ''Text8''), (KnownT isoiec_9798_3_7_2_B_text_5))-  , ((isoiec_9798_3_7_2_A, ''Text9''), (KnownT isoiec_9798_3_7_2_A_5))-  , ((isoiec_9798_3_7_2_B, ''Text9''), (KnownT isoiec_9798_3_7_2_B_4))-  , ((isoiec_9798_3_7_2_A, ''TokenTA''), (KnownT isoiec_9798_3_7_2_A_3))-  , ((isoiec_9798_3_7_2_A, ''pkA''),-     (KnownT isoiec_9798_3_7_2_A_check_3_in))-  , ((isoiec_9798_3_7_2_B, ''pkA''), (KnownT isoiec_9798_3_7_2_B_4))-  , ((isoiec_9798_3_7_2_A, ''pkB''), (KnownT isoiec_9798_3_7_2_A_3))-  , ((isoiec_9798_3_7_2_B, ''pkB''), (KnownT isoiec_9798_3_7_2_B_4))-  ]"--sublocale isoiec_9798_3_7_2_state < isoiec_9798_3_7_2_msc_typing_state-proof --  have "(t,r,s) : approx isoiec_9798_3_7_2_msc_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF isoiec_9798_3_7_2_msc_typing.monoTyp, completeness_cases_rule])-    case (isoiec_9798_3_7_2_A_1_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_A_1_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_A_1_Text1 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_A_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_A_3_TokenTA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_A_3_pkB t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_A_check_3_in_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''check_4'',-               {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,-                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                  s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-               |},-               Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,-                      s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                      s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-                   |}-                   ( SK ( s(AV ''T'' tid0) ) )-            |}-            ( LN ''check_nonce_4'' tid0 ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_3_7_2_A_check_3_in_pkA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc {| LC ''check_4'',-               {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,-                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                  s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-               |},-               Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,-                      s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                      s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-                   |}-                   ( SK ( s(AV ''T'' tid0) ) )-            |}-            ( LN ''check_nonce_4'' tid0 ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?-  next-    case (isoiec_9798_3_7_2_A_text_4_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_A_text_4_Text7 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_A_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_A_5_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_B_4_Ra t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_B_4_Rpa t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_B_4_T t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_B_4_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_B_4_Text6 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_B_4_Text9 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_B_4_pkA t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_B_4_pkB t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_B_text_5_Text8 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_T_2_A t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_T_2_B t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_T_2_Rb t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_T_2_Rpa t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_T_2_Text2 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_T_text_3_Text3 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  next-    case (isoiec_9798_3_7_2_T_text_3_Text5 t r s tid0) note facts = this-    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)-  qed-  thus "isoiec_9798_3_7_2_msc_typing_state t r s" by unfold_locales auto-qed--text{* Prove secrecy of long-term keys. *}-context isoiec_9798_3_7_2_state begin--  (* This rule is unsafe in general, but OK here, -     as we are only reasoning about static compromise. -  *)-  lemma static_longterm_key_reveal[dest!]:-    "predOrd t (LKR a) e ==> RLKR a : reveals t"-    by (auto intro: compr_predOrdI)--  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "RLKR m ~: reveals t"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_sym_ud_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-    shows "False"-  using facts by (sources "K m1 m2")--  lemma longterm_sym_bd_key_secrecy:-    assumes facts:-      "Kbd m1 m2 : knows t"-      "RLKR m1 ~: reveals t"-      "RLKR m2 ~: reveals t"-      "m1 : Agent"-      "m2 : Agent"-    shows "False"-  proof --    from facts -    have "KShr (agents {m1, m2}) : knows t"-      by (auto simp: Kbd_def)-    thus ?thesis using facts-    proof (sources "KShr (agents {m1, m2})")-    qed (auto simp: agents_def Agent_def)-  qed--  lemmas ltk_secrecy =-    longterm_sym_ud_key_secrecy-    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]-    longterm_sym_bd_key_secrecy-    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]--end--lemma (in restricted_isoiec_9798_3_7_2_state) A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_7_2_A"-    "RLKR(s(AV ''T'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_7_2_A_5 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_7_2_B &-        ( tid1, isoiec_9798_3_7_2_B_5 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,-           s(MV ''Text8'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''Ra'' tid0,-                s(MV ''Rb'' tid0), s(MV ''Text8'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''check_4'',-                          {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,-                             s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                             s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-                          |},-                          Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,-                                 s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                                 s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-                              |}-                              ( SK ( s(AV ''T'' tid0) ) )-                       |}-                       ( LN ''check_nonce_4'' tid0 ) ")-    case fake note_unified facts = this facts-    thus ?thesis proof(sources! " LN ''check_nonce_4'' tid0 ")-    qed (insert facts, fastsimp+)?-  next-    case (isoiec_9798_3_7_2_A_check_3_out_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,-                            s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                            s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-                         |}-                         ( SK ( s(AV ''T'' tid0) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest!: ltk_secrecy)-    next-      case (isoiec_9798_3_7_2_T_3_enc tid1) note_unified facts = this facts-      thus ?thesis proof(sources! "-                       Enc {| LC ''isoiec_9798_3_7_opt_2_sig_5'', LN ''Ra'' tid0,-                              s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),-                              s(MV ''Text8'' tid0)-                           |}-                           ( SK ( s(MV ''B'' tid0) ) ) ")-        case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest!: ltk_secrecy)-      next-        case (isoiec_9798_3_7_2_B_5_enc tid2) note_unified facts = this facts-        thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-      qed (insert facts, fastsimp+)?-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_7_2_state) B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_7_2_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_7_2_B_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_7_2_A &-        ( tid1, isoiec_9798_3_7_2_A_4 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),-           s(MV ''Text6'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),-                LN ''Rb'' tid0, s(MV ''Text6'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', s(MV ''Rpa'' tid0),-                          LN ''Rb'' tid0, s(AV ''A'' tid0), s(MV ''pkA'' tid0), s(AV ''B'' tid0),-                          s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( SK ( s(MV ''T'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_7_2_T_3_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_3_7_opt_2_sig_4'', LN ''Rb'' tid0,-                            s(MV ''Ra'' tid0), s(AV ''B'' tid0), s(AV ''A'' tid0),-                            s(MV ''Text6'' tid0)-                         |}-                         ( SK ( s(AV ''A'' tid0) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest!: ltk_secrecy)-    next-      case (isoiec_9798_3_7_2_A_4_enc tid2) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_7_2_state) A_non_injective_agreement_T:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_7_2_A"-    "RLKR(s(AV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_7_2_A_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_7_2_T &-        ( tid1, isoiec_9798_3_7_2_T_3 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''T'' tid1),-           s(MV ''Rpa'' tid1), s(MV ''Rb'' tid1), PK ( s(MV ''A'' tid1) ),-           PK ( s(MV ''B'' tid1) ), s(MV ''Text3'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''T'' tid0),-                LN ''Rpa'' tid0, s(MV ''Rb'' tid0), s(MV ''pkA'' tid0),-                s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''check_4'',-                          {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,-                             s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                             s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-                          |},-                          Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,-                                 s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                                 s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-                              |}-                              ( SK ( s(AV ''T'' tid0) ) )-                       |}-                       ( LN ''check_nonce_4'' tid0 ) ")-    case fake note_unified facts = this facts-    thus ?thesis proof(sources! " LN ''check_nonce_4'' tid0 ")-    qed (insert facts, fastsimp+)?-  next-    case (isoiec_9798_3_7_2_A_check_3_out_enc tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,-                            s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),-                            s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-                         |}-                         ( SK ( s(AV ''T'' tid0) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest!: ltk_secrecy)-    next-      case (isoiec_9798_3_7_2_T_3_enc tid1) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_3_7_2_state) B_non_injective_agreement_T:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_3_7_2_B"-    "RLKR(s(MV ''T'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_3_7_2_B_4 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_3_7_2_T &-        ( tid1, isoiec_9798_3_7_2_T_3 ) : steps t &-        {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''T'' tid1),-           s(MV ''Rpa'' tid1), s(MV ''Rb'' tid1), PK ( s(MV ''A'' tid1) ),-           PK ( s(MV ''B'' tid1) ), s(MV ''Text3'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''T'' tid0),-                s(MV ''Rpa'' tid0), LN ''Rb'' tid0, s(MV ''pkA'' tid0),-                s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', s(MV ''Rpa'' tid0),-                          LN ''Rb'' tid0, s(AV ''A'' tid0), s(MV ''pkA'' tid0), s(AV ''B'' tid0),-                          s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)-                       |}-                       ( SK ( s(MV ''T'' tid0) ) ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_3_7_2_T_3_enc tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?+  "ESPLogic"+begin++role isoiec_9798_3_1_A+where "isoiec_9798_3_1_A =+  [ Send ''leak_A'' ( sN ''TNA'' )+  , Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>+  , Send ''1'' <| sAV ''A'', sAV ''B'', sMV ''Text2'',+                  PSign <| sC ''isoiec_9798_3_1_sig_1'', sN ''TNA'', sAV ''B'',+                           sMV ''Text1''+                        |>+                        ( sPK ''A'' )+               |>+  ]"++role isoiec_9798_3_1_B+where "isoiec_9798_3_1_B =+  [ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Text2'',+                  PSign <| sC ''isoiec_9798_3_1_sig_1'', sMV ''TNA'', sAV ''B'',+                           sMV ''Text1''+                        |>+                        ( PAsymPK ( sMV ''A'' ) )+               |>+  ]"++protocol isoiec_9798_3_1+where "isoiec_9798_3_1 = { isoiec_9798_3_1_A, isoiec_9798_3_1_B }"++locale restricted_isoiec_9798_3_1_state = isoiec_9798_3_1_state++type_invariant isoiec_9798_3_1_msc_typing for isoiec_9798_3_1+where "isoiec_9798_3_1_msc_typing = mk_typing+  [ ((isoiec_9798_3_1_B, ''A''), (KnownT isoiec_9798_3_1_B_1))+  , ((isoiec_9798_3_1_B, ''TNA''), (KnownT isoiec_9798_3_1_B_1))+  , ((isoiec_9798_3_1_A, ''Text1''), (KnownT isoiec_9798_3_1_A_text_1))+  , ((isoiec_9798_3_1_B, ''Text1''), (KnownT isoiec_9798_3_1_B_1))+  , ((isoiec_9798_3_1_A, ''Text2''), (KnownT isoiec_9798_3_1_A_text_1))+  , ((isoiec_9798_3_1_B, ''Text2''), (KnownT isoiec_9798_3_1_B_1))+  ]"++sublocale isoiec_9798_3_1_state < isoiec_9798_3_1_msc_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_3_1_msc_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_3_1_msc_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_3_1_A_text_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_1_A_text_1_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_1_B_1_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_1_B_1_TNA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_1_B_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_1_B_1_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_3_1_msc_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_3_1_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++lemma (in restricted_isoiec_9798_3_1_state) B_non_injective_agreement:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_3_1_B"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_3_1_B_1 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_3_1_A &+        ( tid1, isoiec_9798_3_1_A_1 ) : steps t &+        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,+           s(MV ''Text1'' tid1)+        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),+                s(MV ''Text1'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_3_1_sig_1'', s(MV ''TNA'' tid0),+                          s(AV ''B'' tid0), s(MV ''Text1'' tid0)+                       |}+                       ( SK ( s(MV ''A'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_3_1_A_1_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)?+qed++role isoiec_9798_3_2_A+where "isoiec_9798_3_2_A =+  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>+  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>+  , Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'',+                  PSign <| sC ''isoiec_9798_3_2_sig_2'', sN ''Ra'', sMV ''Rb'', sMV ''B'',+                           sMV ''Text2''+                        |>+                        ( sPK ''A'' )+               |>+  ]"++role isoiec_9798_3_2_B+where "isoiec_9798_3_2_B =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>+  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'',+                  PSign <| sC ''isoiec_9798_3_2_sig_2'', sMV ''Ra'', sN ''Rb'', sAV ''B'',+                           sMV ''Text2''+                        |>+                        ( sPK ''A'' )+               |>+  ]"++protocol isoiec_9798_3_2+where "isoiec_9798_3_2 = { isoiec_9798_3_2_A, isoiec_9798_3_2_B }"++locale restricted_isoiec_9798_3_2_state = isoiec_9798_3_2_state++type_invariant isoiec_9798_3_2_msc_typing for isoiec_9798_3_2+where "isoiec_9798_3_2_msc_typing = mk_typing+  [ ((isoiec_9798_3_2_A, ''B''), (KnownT isoiec_9798_3_2_A_1))+  , ((isoiec_9798_3_2_B, ''Ra''), (KnownT isoiec_9798_3_2_B_2))+  , ((isoiec_9798_3_2_A, ''Rb''), (KnownT isoiec_9798_3_2_A_1))+  , ((isoiec_9798_3_2_A, ''Text1''), (KnownT isoiec_9798_3_2_A_1))+  , ((isoiec_9798_3_2_B, ''Text1''), (KnownT isoiec_9798_3_2_B_text_1))+  , ((isoiec_9798_3_2_A, ''Text2''), (KnownT isoiec_9798_3_2_A_text_2))+  , ((isoiec_9798_3_2_B, ''Text2''), (KnownT isoiec_9798_3_2_B_2))+  , ((isoiec_9798_3_2_A, ''Text3''), (KnownT isoiec_9798_3_2_A_text_2))+  , ((isoiec_9798_3_2_B, ''Text3''), (KnownT isoiec_9798_3_2_B_2))+  ]"++sublocale isoiec_9798_3_2_state < isoiec_9798_3_2_msc_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_3_2_msc_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_3_2_msc_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_3_2_A_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_2_A_1_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_2_A_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_2_A_text_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_2_A_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_2_B_2_Ra t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_2_B_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_2_B_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_3_2_msc_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_3_2_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++lemma (in restricted_isoiec_9798_3_2_state) B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_2_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_2_B_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_2_A &+          ( tid1, isoiec_9798_3_2_A_2 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),+             s(MV ''Text2'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),+                  LN ''Rb'' tid0, s(MV ''Text2'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_2_sig_2'', s(MV ''Ra'' tid0), LN ''Rb'' tid0,+                              s(AV ''B'' tid0), s(MV ''Text2'' tid0)+                           |}+                           ( SK ( s(AV ''A'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_2_A_2_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++role isoiec_9798_3_3_A+where "isoiec_9798_3_3_A =+  [ Send ''leak_A'' ( sN ''TNA'' )+  , Recv ''text_1'' <| sMV ''Text1'', sMV ''Text2'' |>+  , Send ''1'' <| sAV ''A'', sAV ''B'', sMV ''Text2'',+                  PSign <| sC ''isoiec_9798_3_3_sig_1'', sN ''TNA'', sAV ''B'',+                           sMV ''Text1''+                        |>+                        ( sPK ''A'' )+               |>+  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text4'',+                  PSign <| sC ''isoiec_9798_3_3_sig_2'', sMV ''TNB'', sAV ''A'',+                           sMV ''Text3''+                        |>+                        ( sPK ''B'' )+               |>+  ]"++role isoiec_9798_3_3_B+where "isoiec_9798_3_3_B =+  [ Send ''leak_B'' ( sN ''TNB'' )+  , Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Text2'',+                  PSign <| sC ''isoiec_9798_3_3_sig_1'', sMV ''TNA'', sAV ''B'',+                           sMV ''Text1''+                        |>+                        ( PAsymPK ( sMV ''A'' ) )+               |>+  , Recv ''text_2'' <| sMV ''Text3'', sMV ''Text4'' |>+  , Send ''2'' <| sMV ''A'', sAV ''B'', sMV ''Text4'',+                  PSign <| sC ''isoiec_9798_3_3_sig_2'', sN ''TNB'', sMV ''A'',+                           sMV ''Text3''+                        |>+                        ( sPK ''B'' )+               |>+  ]"++protocol isoiec_9798_3_3+where "isoiec_9798_3_3 = { isoiec_9798_3_3_A, isoiec_9798_3_3_B }"++locale restricted_isoiec_9798_3_3_state = isoiec_9798_3_3_state++type_invariant isoiec_9798_3_3_msc_typing for isoiec_9798_3_3+where "isoiec_9798_3_3_msc_typing = mk_typing+  [ ((isoiec_9798_3_3_B, ''A''), (KnownT isoiec_9798_3_3_B_1))+  , ((isoiec_9798_3_3_B, ''TNA''), (KnownT isoiec_9798_3_3_B_1))+  , ((isoiec_9798_3_3_A, ''TNB''), (KnownT isoiec_9798_3_3_A_2))+  , ((isoiec_9798_3_3_A, ''Text1''), (KnownT isoiec_9798_3_3_A_text_1))+  , ((isoiec_9798_3_3_B, ''Text1''), (KnownT isoiec_9798_3_3_B_1))+  , ((isoiec_9798_3_3_A, ''Text2''), (KnownT isoiec_9798_3_3_A_text_1))+  , ((isoiec_9798_3_3_B, ''Text2''), (KnownT isoiec_9798_3_3_B_1))+  , ((isoiec_9798_3_3_A, ''Text3''), (KnownT isoiec_9798_3_3_A_2))+  , ((isoiec_9798_3_3_B, ''Text3''), (KnownT isoiec_9798_3_3_B_text_2))+  , ((isoiec_9798_3_3_A, ''Text4''), (KnownT isoiec_9798_3_3_A_2))+  , ((isoiec_9798_3_3_B, ''Text4''), (KnownT isoiec_9798_3_3_B_text_2))+  ]"++sublocale isoiec_9798_3_3_state < isoiec_9798_3_3_msc_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_3_3_msc_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_3_3_msc_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_3_3_A_text_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_3_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_3_A_text_1_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_3_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_3_A_2_TNB t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_3_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_3_A_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_3_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_3_A_2_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_3_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_3_B_1_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_3_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_3_B_1_TNA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_3_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_3_B_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_3_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_3_B_1_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_3_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_3_B_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_3_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_3_B_text_2_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_3_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_3_3_msc_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_3_3_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++lemma (in restricted_isoiec_9798_3_3_state) A_non_injective_agreement:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_3_3_A"+    "RLKR(s(AV ''B'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_3_3_A_2 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_3_3_B &+        ( tid1, isoiec_9798_3_3_B_2 ) : steps t &+        {| s(MV ''A'' tid1), s(AV ''B'' tid1), LN ''TNB'' tid1,+           s(MV ''Text3'' tid1)+        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNB'' tid0),+                s(MV ''Text3'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_3_3_sig_2'', s(MV ''TNB'' tid0),+                          s(AV ''A'' tid0), s(MV ''Text3'' tid0)+                       |}+                       ( SK ( s(AV ''B'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_3_3_B_2_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)?+qed++lemma (in restricted_isoiec_9798_3_3_state) B_non_injective_agreement:+  assumes facts:+    "roleMap r tid0 = Some isoiec_9798_3_3_B"+    "RLKR(s(MV ''A'' tid0)) ~: reveals t"+    "( tid0, isoiec_9798_3_3_B_1 ) : steps t"+  shows+    "(?  tid1.+        roleMap r tid1 = Some isoiec_9798_3_3_A &+        ( tid1, isoiec_9798_3_3_A_1 ) : steps t &+        {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''TNA'' tid1,+           s(MV ''Text1'' tid1)+        |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''TNA'' tid0),+                s(MV ''Text1'' tid0)+             |})"+proof -+  note_prefix_closed facts = facts+  thus ?thesis proof(sources! "+                   Enc {| LC ''isoiec_9798_3_3_sig_1'', s(MV ''TNA'' tid0),+                          s(AV ''B'' tid0), s(MV ''Text1'' tid0)+                       |}+                       ( SK ( s(MV ''A'' tid0) ) ) ")+    case fake note_unified facts = this facts+    thus ?thesis by (fastforce dest!: ltk_secrecy)+  next+    case (isoiec_9798_3_3_A_1_enc tid1) note_unified facts = this facts+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)?+qed++role isoiec_9798_3_4_A+where "isoiec_9798_3_4_A =+  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''RB'', sMV ''Text1'' |>+  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>+  , Send ''2'' <| sAV ''A'', sMV ''B'', sMV ''Text3'',+                  PSign <| sC ''isoiec_9798_3_4_sig_1'', sN ''RA'', sMV ''RB'', sMV ''B'',+                           sMV ''Text2''+                        |>+                        ( sPK ''A'' )+               |>+  , Recv ''3'' <| sMV ''B'', sAV ''A'', sMV ''Text5'',+                  PSign <| sC ''isoiec_9798_3_4_sig_2'', sMV ''RB'', sN ''RA'', sAV ''A'',+                           sMV ''Text4''+                        |>+                        ( PAsymPK ( sMV ''B'' ) )+               |>+  ]"++role isoiec_9798_3_4_B+where "isoiec_9798_3_4_B =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''RB'', sMV ''Text1'' |>+  , Recv ''2'' <| sAV ''A'', sAV ''B'', sMV ''Text3'',+                  PSign <| sC ''isoiec_9798_3_4_sig_1'', sMV ''RA'', sN ''RB'', sAV ''B'',+                           sMV ''Text2''+                        |>+                        ( sPK ''A'' )+               |>+  , Recv ''text_3'' <| sMV ''Text4'', sMV ''Text5'' |>+  , Send ''3'' <| sAV ''B'', sAV ''A'', sMV ''Text5'',+                  PSign <| sC ''isoiec_9798_3_4_sig_2'', sN ''RB'', sMV ''RA'', sAV ''A'',+                           sMV ''Text4''+                        |>+                        ( sPK ''B'' )+               |>+  ]"++protocol isoiec_9798_3_4+where "isoiec_9798_3_4 = { isoiec_9798_3_4_A, isoiec_9798_3_4_B }"++locale restricted_isoiec_9798_3_4_state = isoiec_9798_3_4_state++type_invariant isoiec_9798_3_4_msc_typing for isoiec_9798_3_4+where "isoiec_9798_3_4_msc_typing = mk_typing+  [ ((isoiec_9798_3_4_A, ''B''), (KnownT isoiec_9798_3_4_A_1))+  , ((isoiec_9798_3_4_B, ''RA''), (KnownT isoiec_9798_3_4_B_2))+  , ((isoiec_9798_3_4_A, ''RB''), (KnownT isoiec_9798_3_4_A_1))+  , ((isoiec_9798_3_4_A, ''Text1''), (KnownT isoiec_9798_3_4_A_1))+  , ((isoiec_9798_3_4_B, ''Text1''), (KnownT isoiec_9798_3_4_B_text_1))+  , ((isoiec_9798_3_4_A, ''Text2''), (KnownT isoiec_9798_3_4_A_text_2))+  , ((isoiec_9798_3_4_B, ''Text2''), (KnownT isoiec_9798_3_4_B_2))+  , ((isoiec_9798_3_4_A, ''Text3''), (KnownT isoiec_9798_3_4_A_text_2))+  , ((isoiec_9798_3_4_B, ''Text3''), (KnownT isoiec_9798_3_4_B_2))+  , ((isoiec_9798_3_4_A, ''Text4''), (KnownT isoiec_9798_3_4_A_3))+  , ((isoiec_9798_3_4_B, ''Text4''), (KnownT isoiec_9798_3_4_B_text_3))+  , ((isoiec_9798_3_4_A, ''Text5''), (KnownT isoiec_9798_3_4_A_3))+  , ((isoiec_9798_3_4_B, ''Text5''), (KnownT isoiec_9798_3_4_B_text_3))+  ]"++sublocale isoiec_9798_3_4_state < isoiec_9798_3_4_msc_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_3_4_msc_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_3_4_msc_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_3_4_A_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_4_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_4_A_1_RB t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_4_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_4_A_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_4_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_4_A_text_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_4_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_4_A_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_4_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_4_A_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_4_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_4_A_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_4_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_4_B_2_RA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_4_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_4_B_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_4_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_4_B_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_4_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_4_B_text_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_4_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_4_B_text_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_4_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_3_4_msc_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_3_4_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++lemma (in restricted_isoiec_9798_3_4_state) A_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_4_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_4_A_3 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_4_B &+          ( tid1, isoiec_9798_3_4_B_3 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''RA'' tid1), LN ''RB'' tid1,+             s(MV ''Text2'' tid1), s(MV ''Text4'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''RA'' tid0,+                  s(MV ''RB'' tid0), s(MV ''Text2'' tid0), s(MV ''Text4'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_4_sig_2'', s(MV ''RB'' tid0), LN ''RA'' tid0,+                              s(AV ''A'' tid0), s(MV ''Text4'' tid0)+                           |}+                           ( SK ( s(MV ''B'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_4_B_3_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_3_4_sig_1'', LN ''RA'' tid0, LN ''RB'' tid1,+                                s(AV ''B'' tid1), s(MV ''Text2'' tid1)+                             |}+                             ( SK ( s(AV ''A'' tid0) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_3_4_A_2_enc tid2) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_4_state) B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_4_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_4_B_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_4_A &+          ( tid1, isoiec_9798_3_4_A_2 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''RA'' tid1, s(MV ''RB'' tid1),+             s(MV ''Text2'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''RA'' tid0),+                  LN ''RB'' tid0, s(MV ''Text2'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_4_sig_1'', s(MV ''RA'' tid0), LN ''RB'' tid0,+                              s(AV ''B'' tid0), s(MV ''Text2'' tid0)+                           |}+                           ( SK ( s(AV ''A'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_4_A_2_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++role isoiec_9798_3_5_A+where "isoiec_9798_3_5_A =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''A'', sAV ''B'', sN ''RA'', sMV ''Text1'' |>+  , Recv ''2'' <| sAV ''B'', sAV ''A'', sMV ''RB'', sMV ''Text2'' |>+  , Recv ''3'' <| sAV ''B'', sAV ''A'', sMV ''Text6'',+                  PSign <| sC ''isoiec_9798_3_5_sig_1'', sMV ''RB'', sN ''RA'', sAV ''A'',+                           sMV ''Text5''+                        |>+                        ( sPK ''B'' )+               |>+  , Recv ''text_4'' <| sMV ''Text3'', sMV ''Text4'' |>+  , Send ''4'' <| sAV ''A'', sAV ''B'', sMV ''Text4'',+                  PSign <| sC ''isoiec_9798_3_5_sig_2'', sN ''RA'', sMV ''RB'', sAV ''B'',+                           sMV ''Text3''+                        |>+                        ( sPK ''A'' )+               |>+  ]"++role isoiec_9798_3_5_B+where "isoiec_9798_3_5_B =+  [ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''RA'', sMV ''Text1'' |>+  , Recv ''text_2'' ( sMV ''Text2'' )+  , Send ''2'' <| sAV ''B'', sMV ''A'', sN ''RB'', sMV ''Text2'' |>+  , Recv ''text_3'' <| sMV ''Text5'', sMV ''Text6'' |>+  , Send ''3'' <| sAV ''B'', sMV ''A'', sMV ''Text6'',+                  PSign <| sC ''isoiec_9798_3_5_sig_1'', sN ''RB'', sMV ''RA'', sMV ''A'',+                           sMV ''Text5''+                        |>+                        ( sPK ''B'' )+               |>+  , Recv ''4'' <| sMV ''A'', sAV ''B'', sMV ''Text4'',+                  PSign <| sC ''isoiec_9798_3_5_sig_2'', sMV ''RA'', sN ''RB'', sAV ''B'',+                           sMV ''Text3''+                        |>+                        ( PAsymPK ( sMV ''A'' ) )+               |>+  ]"++protocol isoiec_9798_3_5+where "isoiec_9798_3_5 = { isoiec_9798_3_5_A, isoiec_9798_3_5_B }"++locale restricted_isoiec_9798_3_5_state = isoiec_9798_3_5_state++type_invariant isoiec_9798_3_5_msc_typing for isoiec_9798_3_5+where "isoiec_9798_3_5_msc_typing = mk_typing+  [ ((isoiec_9798_3_5_B, ''A''), (KnownT isoiec_9798_3_5_B_1))+  , ((isoiec_9798_3_5_B, ''RA''), (KnownT isoiec_9798_3_5_B_1))+  , ((isoiec_9798_3_5_A, ''RB''), (KnownT isoiec_9798_3_5_A_2))+  , ((isoiec_9798_3_5_A, ''Text1''), (KnownT isoiec_9798_3_5_A_text_1))+  , ((isoiec_9798_3_5_B, ''Text1''), (KnownT isoiec_9798_3_5_B_1))+  , ((isoiec_9798_3_5_A, ''Text2''), (KnownT isoiec_9798_3_5_A_2))+  , ((isoiec_9798_3_5_B, ''Text2''), (KnownT isoiec_9798_3_5_B_text_2))+  , ((isoiec_9798_3_5_A, ''Text3''), (KnownT isoiec_9798_3_5_A_text_4))+  , ((isoiec_9798_3_5_B, ''Text3''), (KnownT isoiec_9798_3_5_B_4))+  , ((isoiec_9798_3_5_A, ''Text4''), (KnownT isoiec_9798_3_5_A_text_4))+  , ((isoiec_9798_3_5_B, ''Text4''), (KnownT isoiec_9798_3_5_B_4))+  , ((isoiec_9798_3_5_A, ''Text5''), (KnownT isoiec_9798_3_5_A_3))+  , ((isoiec_9798_3_5_B, ''Text5''), (KnownT isoiec_9798_3_5_B_text_3))+  , ((isoiec_9798_3_5_A, ''Text6''), (KnownT isoiec_9798_3_5_A_3))+  , ((isoiec_9798_3_5_B, ''Text6''), (KnownT isoiec_9798_3_5_B_text_3))+  ]"++sublocale isoiec_9798_3_5_state < isoiec_9798_3_5_msc_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_3_5_msc_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_3_5_msc_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_3_5_A_2_RB t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_5_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_A_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_5_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_A_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_5_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_A_3_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_5_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_A_text_4_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_5_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_A_text_4_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_5_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_B_1_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_5_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_B_1_RA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_5_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_B_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_5_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_B_text_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_5_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_B_text_3_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_5_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_B_4_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_5_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_5_B_4_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_5_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_3_5_msc_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_3_5_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++lemma (in restricted_isoiec_9798_3_5_state) A_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_5_A &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_5_A_3 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_5_B &+          ( tid1, isoiec_9798_3_5_B_3 ) : steps t &+          {| s(MV ''A'' tid1), s(AV ''B'' tid1), s(MV ''RA'' tid1), LN ''RB'' tid1,+             s(MV ''Text5'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''RA'' tid0,+                  s(MV ''RB'' tid0), s(MV ''Text5'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_5_sig_1'', s(MV ''RB'' tid0), LN ''RA'' tid0,+                              s(AV ''A'' tid0), s(MV ''Text5'' tid0)+                           |}+                           ( SK ( s(AV ''B'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_5_B_3_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_5_state) B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_5_B &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(MV ''A'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_5_B_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_5_A &+          ( tid1, isoiec_9798_3_5_A_4 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''RA'' tid1, s(MV ''RB'' tid1),+             s(MV ''Text3'' tid1), s(MV ''Text5'' tid1)+          |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''RA'' tid0),+                  LN ''RB'' tid0, s(MV ''Text3'' tid0), s(MV ''Text5'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_5_sig_2'', s(MV ''RA'' tid0), LN ''RB'' tid0,+                              s(AV ''B'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( SK ( s(MV ''A'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_5_A_4_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_3_5_sig_1'', LN ''RB'' tid0, LN ''RA'' tid1,+                                s(AV ''A'' tid1), s(MV ''Text5'' tid1)+                             |}+                             ( SK ( s(AV ''B'' tid0) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_3_5_B_3_enc tid2) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++role isoiec_9798_3_6_1_A+where "isoiec_9798_3_6_1_A =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''A'', sAV ''B'', sN ''Ra'', sMV ''Text1'' |>+  , Recv ''2'' <| sAV ''A'', sAV ''B'', sN ''Ra'', sMV ''Rb'',+                  sMV ''Text3'', sMV ''TokenBA''+               |>+  , Recv ''text_3'' ( sMV ''Text4'' )+  , Send ''3'' <| sAV ''A'', sAV ''T'', sN ''Rpa'', sMV ''Rb'', sAV ''B'',+                  sMV ''Text4''+               |>+  , Recv ''4'' <| sAV ''T'', sAV ''A'', sMV ''Text7'', sAV ''A'',+                  sPK ''A'', sAV ''B'', sMV ''pkB'',+                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_4_1'', sN ''Rpa'', sAV ''B'',+                           sMV ''pkB'', sMV ''Text6''+                        |>+                        ( sPK ''T'' ),+                  sMV ''TokenTA_for_B''+               |>+  , Send ''check_4_out'' ( PEnc <| sC ''check_4'', sMV ''TokenBA'' |>+                                ( sN ''check_nonce_4'' )+                         )+  , Recv ''check_4_in'' ( PEnc <| sC ''check_4'',+                                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_2'', sAV ''B'', sN ''Ra'',+                                           sMV ''Rb'', sAV ''A'', sMV ''Text2''+                                        |>+                                        ( sMV ''pkB'' )+                               |>+                               ( sN ''check_nonce_4'' )+                        )+  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>+  , Send ''5'' <| sAV ''A'', sAV ''B'', sMV ''Text9'', sAV ''T'',+                  sMV ''TokenTA_for_B'',+                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_5'', sMV ''Rb'', sN ''Ra'',+                           sAV ''B'', sAV ''A'', sMV ''Text8''+                        |>+                        ( sPK ''A'' )+               |>+  ]"++role isoiec_9798_3_6_1_B+where "isoiec_9798_3_6_1_B =+  [ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Ra'', sMV ''Text1'' |>+  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>+  , Send ''2'' <| sMV ''A'', sAV ''B'', sMV ''Ra'', sN ''Rb'',+                  sMV ''Text3'',+                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_2'', sAV ''B'', sMV ''Ra'',+                           sN ''Rb'', sMV ''A'', sMV ''Text2''+                        |>+                        ( sPK ''B'' )+               |>+  , Recv ''5'' <| sMV ''A'', sAV ''B'', sMV ''Text9'', sMV ''T'',+                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_4_2'', sN ''Rb'', sMV ''A'',+                           sMV ''pkA'', sMV ''Text5''+                        |>+                        ( PAsymPK ( sMV ''T'' ) ),+                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_5'', sN ''Rb'', sMV ''Ra'',+                           sAV ''B'', sMV ''A'', sMV ''Text8''+                        |>+                        ( sMV ''pkA'' )+               |>+  ]"++role isoiec_9798_3_6_1_T+where "isoiec_9798_3_6_1_T =+  [ Recv ''3'' <| sMV ''A'', sAV ''T'', sMV ''Rpa'', sMV ''Rb'', sMV ''B'',+                  sMV ''Text4''+               |>+  , Recv ''text_4'' <| sMV ''Text5'', sMV ''Text6'', sMV ''Text7'' |>+  , Send ''4'' <| sAV ''T'', sMV ''A'', sMV ''Text7'', sMV ''A'',+                  PAsymPK ( sMV ''A'' ), sMV ''B'', PAsymPK ( sMV ''B'' ),+                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_4_1'', sMV ''Rpa'', sMV ''B'',+                           PAsymPK ( sMV ''B'' ), sMV ''Text6''+                        |>+                        ( sPK ''T'' ),+                  PSign <| sC ''isoiec_9798_3_6_opt_1_sig_4_2'', sMV ''Rb'', sMV ''A'',+                           PAsymPK ( sMV ''A'' ), sMV ''Text5''+                        |>+                        ( sPK ''T'' )+               |>+  ]"++protocol isoiec_9798_3_6_1+where "isoiec_9798_3_6_1 =+{ isoiec_9798_3_6_1_A, isoiec_9798_3_6_1_B, isoiec_9798_3_6_1_T }"++locale restricted_isoiec_9798_3_6_1_state = isoiec_9798_3_6_1_state++type_invariant isoiec_9798_3_6_1_msc_typing for isoiec_9798_3_6_1+where "isoiec_9798_3_6_1_msc_typing = mk_typing+  [ ((isoiec_9798_3_6_1_B, ''A''), (KnownT isoiec_9798_3_6_1_B_1))+  , ((isoiec_9798_3_6_1_T, ''A''), (KnownT isoiec_9798_3_6_1_T_3))+  , ((isoiec_9798_3_6_1_T, ''B''), (KnownT isoiec_9798_3_6_1_T_3))+  , ((isoiec_9798_3_6_1_B, ''Ra''), (KnownT isoiec_9798_3_6_1_B_1))+  , ((isoiec_9798_3_6_1_A, ''Rb''), (KnownT isoiec_9798_3_6_1_A_2))+  , ((isoiec_9798_3_6_1_T, ''Rb''), (KnownT isoiec_9798_3_6_1_T_3))+  , ((isoiec_9798_3_6_1_T, ''Rpa''), (KnownT isoiec_9798_3_6_1_T_3))+  , ((isoiec_9798_3_6_1_B, ''T''), (KnownT isoiec_9798_3_6_1_B_5))+  , ((isoiec_9798_3_6_1_A, ''Text1''), (KnownT isoiec_9798_3_6_1_A_text_1))+  , ((isoiec_9798_3_6_1_B, ''Text1''), (KnownT isoiec_9798_3_6_1_B_1))+  , ((isoiec_9798_3_6_1_A, ''Text2''),+     (KnownT isoiec_9798_3_6_1_A_check_4_in))+  , ((isoiec_9798_3_6_1_B, ''Text2''), (KnownT isoiec_9798_3_6_1_B_text_2))+  , ((isoiec_9798_3_6_1_A, ''Text3''), (KnownT isoiec_9798_3_6_1_A_2))+  , ((isoiec_9798_3_6_1_B, ''Text3''), (KnownT isoiec_9798_3_6_1_B_text_2))+  , ((isoiec_9798_3_6_1_A, ''Text4''), (KnownT isoiec_9798_3_6_1_A_text_3))+  , ((isoiec_9798_3_6_1_T, ''Text4''), (KnownT isoiec_9798_3_6_1_T_3))+  , ((isoiec_9798_3_6_1_B, ''Text5''), (KnownT isoiec_9798_3_6_1_B_5))+  , ((isoiec_9798_3_6_1_T, ''Text5''), (KnownT isoiec_9798_3_6_1_T_text_4))+  , ((isoiec_9798_3_6_1_A, ''Text6''), (KnownT isoiec_9798_3_6_1_A_4))+  , ((isoiec_9798_3_6_1_T, ''Text6''), (KnownT isoiec_9798_3_6_1_T_text_4))+  , ((isoiec_9798_3_6_1_A, ''Text7''), (KnownT isoiec_9798_3_6_1_A_4))+  , ((isoiec_9798_3_6_1_T, ''Text7''), (KnownT isoiec_9798_3_6_1_T_text_4))+  , ((isoiec_9798_3_6_1_A, ''Text8''), (KnownT isoiec_9798_3_6_1_A_text_5))+  , ((isoiec_9798_3_6_1_B, ''Text8''), (KnownT isoiec_9798_3_6_1_B_5))+  , ((isoiec_9798_3_6_1_A, ''Text9''), (KnownT isoiec_9798_3_6_1_A_text_5))+  , ((isoiec_9798_3_6_1_B, ''Text9''), (KnownT isoiec_9798_3_6_1_B_5))+  , ((isoiec_9798_3_6_1_A, ''TokenBA''), (KnownT isoiec_9798_3_6_1_A_2))+  , ((isoiec_9798_3_6_1_A, ''TokenTA_for_B''),+     (KnownT isoiec_9798_3_6_1_A_4))+  , ((isoiec_9798_3_6_1_B, ''pkA''), (KnownT isoiec_9798_3_6_1_B_5))+  , ((isoiec_9798_3_6_1_A, ''pkB''), (KnownT isoiec_9798_3_6_1_A_4))+  ]"++sublocale isoiec_9798_3_6_1_state < isoiec_9798_3_6_1_msc_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_3_6_1_msc_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_3_6_1_msc_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_3_6_1_A_2_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_A_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_A_2_TokenBA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_A_4_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_A_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_A_4_TokenTA_for_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_A_4_pkB t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_A_check_4_in_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''check_4'',+               {| LC ''isoiec_9798_3_6_opt_1_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,+                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+               |},+               Enc {| LC ''isoiec_9798_3_6_opt_1_sig_2'', s(AV ''B'' tid0),+                      LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+                   |}+                   ( inv(s(MV ''pkB'' tid0)) )+            |}+            ( LN ''check_nonce_4'' tid0 ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_3_6_1_A_text_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_A_text_5_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_B_1_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_B_1_Ra t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_B_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_B_text_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_B_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_B_5_T t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_B_5_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_B_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_B_5_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_B_5_pkA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_T_3_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_T_3_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_T_3_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_T_3_Rpa t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_T_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_T_text_4_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_T_text_4_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_1_T_text_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_3_6_1_msc_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_3_6_1_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++lemma (in restricted_isoiec_9798_3_6_1_state) A_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_6_1_A &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(AV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_6_1_A_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_6_1_B &+          ( tid1, isoiec_9798_3_6_1_B_2 ) : steps t &+          {| s(MV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,+             s(MV ''Text2'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''Ra'' tid0,+                  s(MV ''Rb'' tid0), s(MV ''Text2'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''check_4'',+                              {| LC ''isoiec_9798_3_6_opt_1_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,+                                 s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+                              |},+                              Enc {| LC ''isoiec_9798_3_6_opt_1_sig_2'', s(AV ''B'' tid0),+                                     LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+                                  |}+                                  ( inv(s(MV ''pkB'' tid0)) )+                           |}+                           ( LN ''check_nonce_4'' tid0 ) ")+        case fake note_unified facts = this facts+        thus ?thesis proof(sources! " LN ''check_nonce_4'' tid0 ")+        qed (insert facts, fastforce+)?+      next+        case (isoiec_9798_3_6_1_A_check_4_out_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_3_6_opt_1_sig_2'', s(AV ''B'' tid0),+                                LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+                             |}+                             ( inv(s(MV ''pkB'' tid0)) ) ")+          case fake note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_3_6_opt_1_sig_4_1'', LN ''Rpa'' tid0,+                                  s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text6'' tid0)+                               |}+                               ( SK ( s(AV ''T'' tid0) ) ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest!: ltk_secrecy)+          next+            case (isoiec_9798_3_6_1_T_4_enc tid1) note_unified facts = this facts+            thus ?thesis by (fastforce dest!: ltk_secrecy)+          qed (insert facts, fastforce+)?+        next+          case (isoiec_9798_3_6_1_B_2_enc tid1) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_6_1_state) B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_6_1_B &+          RLKR(s(MV ''A'' tid0)) ~: reveals t &+          RLKR(s(MV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_6_1_B_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_6_1_A &+          ( tid1, isoiec_9798_3_6_1_A_5 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),+             s(MV ''Text8'' tid1)+          |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),+                  LN ''Rb'' tid0, s(MV ''Text8'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_6_opt_1_sig_4_2'', LN ''Rb'' tid0,+                              s(MV ''A'' tid0), s(MV ''pkA'' tid0), s(MV ''Text5'' tid0)+                           |}+                           ( SK ( s(MV ''T'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_6_1_T_4_enc_1 tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_3_6_opt_1_sig_5'', LN ''Rb'' tid0,+                                s(MV ''Ra'' tid0), s(AV ''B'' tid0), s(MV ''A'' tid0),+                                s(MV ''Text8'' tid0)+                             |}+                             ( SK ( s(MV ''A'' tid0) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_3_6_1_A_5_enc tid2) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_6_1_state) A_injective_agreement_T:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_6_1_A &+          RLKR(s(AV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_6_1_A_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_6_1_T &+          ( tid1, isoiec_9798_3_6_1_T_4 ) : steps t &+          {| s(MV ''B'' tid1), s(AV ''T'' tid1), s(MV ''Rpa'' tid1),+             PK ( s(MV ''B'' tid1) ), s(MV ''Text6'' tid1)+          |} = {| s(AV ''B'' tid0), s(AV ''T'' tid0), LN ''Rpa'' tid0,+                  s(MV ''pkB'' tid0), s(MV ''Text6'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_6_opt_1_sig_4_1'', LN ''Rpa'' tid0,+                              s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text6'' tid0)+                           |}+                           ( SK ( s(AV ''T'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_6_1_T_4_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_6_1_state) B_injective_agreement_T:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_6_1_B &+          RLKR(s(MV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_6_1_B_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_6_1_T &+          ( tid1, isoiec_9798_3_6_1_T_4 ) : steps t &+          {| s(MV ''A'' tid1), s(AV ''T'' tid1), s(MV ''Rb'' tid1),+             PK ( s(MV ''A'' tid1) ), s(MV ''Text5'' tid1)+          |} = {| s(MV ''A'' tid0), s(MV ''T'' tid0), LN ''Rb'' tid0,+                  s(MV ''pkA'' tid0), s(MV ''Text5'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_6_opt_1_sig_4_2'', LN ''Rb'' tid0,+                              s(MV ''A'' tid0), s(MV ''pkA'' tid0), s(MV ''Text5'' tid0)+                           |}+                           ( SK ( s(MV ''T'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_6_1_T_4_enc_1 tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++role isoiec_9798_3_6_2_A+where "isoiec_9798_3_6_2_A =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''A'', sAV ''B'', sN ''Ra'', sMV ''Text1'' |>+  , Recv ''2'' <| sAV ''A'', sAV ''B'', sN ''Ra'', sMV ''Rb'',+                  sMV ''Text3'', sMV ''TokenBA''+               |>+  , Recv ''text_3'' ( sMV ''Text4'' )+  , Send ''3'' <| sAV ''A'', sAV ''T'', sN ''Rpa'', sMV ''Rb'', sAV ''B'',+                  sMV ''Text4''+               |>+  , Recv ''4'' <| sAV ''T'', sAV ''A'', sMV ''Text7'', sAV ''A'',+                  sPK ''A'', sAV ''B'', sMV ''pkB'', sMV ''TokenTA''+               |>+  , Send ''check_4_out'' ( PEnc <| sC ''check_4'', sMV ''TokenTA'',+                                   sMV ''TokenBA''+                                |>+                                ( sN ''check_nonce_4'' )+                         )+  , Recv ''check_4_in'' ( PEnc <| sC ''check_4'',+                                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_4'', sN ''Rpa'', sMV ''Rb'',+                                           sAV ''A'', sMV ''pkA'', sAV ''B'', sMV ''pkB'', sMV ''Text5''+                                        |>+                                        ( sPK ''T'' ),+                                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_2'', sAV ''B'', sN ''Ra'',+                                           sMV ''Rb'', sAV ''A'', sMV ''Text2''+                                        |>+                                        ( sMV ''pkB'' )+                               |>+                               ( sN ''check_nonce_4'' )+                        )+  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>+  , Send ''5'' <| sAV ''A'', sAV ''B'', sN ''Rpa'', sMV ''Text9'',+                  sAV ''T'', sMV ''TokenTA'',+                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_5'', sMV ''Rb'', sN ''Ra'',+                           sAV ''B'', sAV ''A'', sMV ''Text8''+                        |>+                        ( sPK ''A'' )+               |>+  ]"++role isoiec_9798_3_6_2_B+where "isoiec_9798_3_6_2_B =+  [ Recv ''1'' <| sMV ''A'', sAV ''B'', sMV ''Ra'', sMV ''Text1'' |>+  , Recv ''text_2'' <| sMV ''Text2'', sMV ''Text3'' |>+  , Send ''2'' <| sMV ''A'', sAV ''B'', sMV ''Ra'', sN ''Rb'',+                  sMV ''Text3'',+                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_2'', sAV ''B'', sMV ''Ra'',+                           sN ''Rb'', sMV ''A'', sMV ''Text2''+                        |>+                        ( sPK ''B'' )+               |>+  , Recv ''5'' <| sMV ''A'', sAV ''B'', sMV ''Rpa'', sMV ''Text9'',+                  sMV ''T'',+                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_4'', sMV ''Rpa'', sN ''Rb'',+                           sMV ''A'', sMV ''pkA'', sAV ''B'', sMV ''pkB'', sMV ''Text5''+                        |>+                        ( PAsymPK ( sMV ''T'' ) ),+                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_5'', sN ''Rb'', sMV ''Ra'',+                           sAV ''B'', sMV ''A'', sMV ''Text8''+                        |>+                        ( sMV ''pkA'' )+               |>+  ]"++role isoiec_9798_3_6_2_T+where "isoiec_9798_3_6_2_T =+  [ Recv ''3'' <| sMV ''A'', sAV ''T'', sMV ''Rpa'', sMV ''Rb'', sMV ''B'',+                  sMV ''Text4''+               |>+  , Recv ''text_4'' <| sMV ''Text5'', sMV ''Text7'' |>+  , Send ''4'' <| sAV ''T'', sMV ''A'', sMV ''Text7'', sMV ''A'',+                  PAsymPK ( sMV ''A'' ), sMV ''B'', PAsymPK ( sMV ''B'' ),+                  PSign <| sC ''isoiec_9798_3_6_opt_2_sig_4'', sMV ''Rpa'', sMV ''Rb'',+                           sMV ''A'', PAsymPK ( sMV ''A'' ), sMV ''B'', PAsymPK ( sMV ''B'' ),+                           sMV ''Text5''+                        |>+                        ( sPK ''T'' )+               |>+  ]"++protocol isoiec_9798_3_6_2+where "isoiec_9798_3_6_2 =+{ isoiec_9798_3_6_2_A, isoiec_9798_3_6_2_B, isoiec_9798_3_6_2_T }"++locale restricted_isoiec_9798_3_6_2_state = isoiec_9798_3_6_2_state++type_invariant isoiec_9798_3_6_2_msc_typing for isoiec_9798_3_6_2+where "isoiec_9798_3_6_2_msc_typing = mk_typing+  [ ((isoiec_9798_3_6_2_B, ''A''), (KnownT isoiec_9798_3_6_2_B_1))+  , ((isoiec_9798_3_6_2_T, ''A''), (KnownT isoiec_9798_3_6_2_T_3))+  , ((isoiec_9798_3_6_2_T, ''B''), (KnownT isoiec_9798_3_6_2_T_3))+  , ((isoiec_9798_3_6_2_B, ''Ra''), (KnownT isoiec_9798_3_6_2_B_1))+  , ((isoiec_9798_3_6_2_A, ''Rb''), (KnownT isoiec_9798_3_6_2_A_2))+  , ((isoiec_9798_3_6_2_T, ''Rb''), (KnownT isoiec_9798_3_6_2_T_3))+  , ((isoiec_9798_3_6_2_B, ''Rpa''), (KnownT isoiec_9798_3_6_2_B_5))+  , ((isoiec_9798_3_6_2_T, ''Rpa''), (KnownT isoiec_9798_3_6_2_T_3))+  , ((isoiec_9798_3_6_2_B, ''T''), (KnownT isoiec_9798_3_6_2_B_5))+  , ((isoiec_9798_3_6_2_A, ''Text1''), (KnownT isoiec_9798_3_6_2_A_text_1))+  , ((isoiec_9798_3_6_2_B, ''Text1''), (KnownT isoiec_9798_3_6_2_B_1))+  , ((isoiec_9798_3_6_2_A, ''Text2''),+     (KnownT isoiec_9798_3_6_2_A_check_4_in))+  , ((isoiec_9798_3_6_2_B, ''Text2''), (KnownT isoiec_9798_3_6_2_B_text_2))+  , ((isoiec_9798_3_6_2_A, ''Text3''), (KnownT isoiec_9798_3_6_2_A_2))+  , ((isoiec_9798_3_6_2_B, ''Text3''), (KnownT isoiec_9798_3_6_2_B_text_2))+  , ((isoiec_9798_3_6_2_A, ''Text4''), (KnownT isoiec_9798_3_6_2_A_text_3))+  , ((isoiec_9798_3_6_2_T, ''Text4''), (KnownT isoiec_9798_3_6_2_T_3))+  , ((isoiec_9798_3_6_2_A, ''Text5''),+     (KnownT isoiec_9798_3_6_2_A_check_4_in))+  , ((isoiec_9798_3_6_2_B, ''Text5''), (KnownT isoiec_9798_3_6_2_B_5))+  , ((isoiec_9798_3_6_2_T, ''Text5''), (KnownT isoiec_9798_3_6_2_T_text_4))+  , ((isoiec_9798_3_6_2_A, ''Text7''), (KnownT isoiec_9798_3_6_2_A_4))+  , ((isoiec_9798_3_6_2_T, ''Text7''), (KnownT isoiec_9798_3_6_2_T_text_4))+  , ((isoiec_9798_3_6_2_A, ''Text8''), (KnownT isoiec_9798_3_6_2_A_text_5))+  , ((isoiec_9798_3_6_2_B, ''Text8''), (KnownT isoiec_9798_3_6_2_B_5))+  , ((isoiec_9798_3_6_2_A, ''Text9''), (KnownT isoiec_9798_3_6_2_A_text_5))+  , ((isoiec_9798_3_6_2_B, ''Text9''), (KnownT isoiec_9798_3_6_2_B_5))+  , ((isoiec_9798_3_6_2_A, ''TokenBA''), (KnownT isoiec_9798_3_6_2_A_2))+  , ((isoiec_9798_3_6_2_A, ''TokenTA''), (KnownT isoiec_9798_3_6_2_A_4))+  , ((isoiec_9798_3_6_2_A, ''pkA''),+     (KnownT isoiec_9798_3_6_2_A_check_4_in))+  , ((isoiec_9798_3_6_2_B, ''pkA''), (KnownT isoiec_9798_3_6_2_B_5))+  , ((isoiec_9798_3_6_2_A, ''pkB''), (KnownT isoiec_9798_3_6_2_A_4))+  , ((isoiec_9798_3_6_2_B, ''pkB''), (KnownT isoiec_9798_3_6_2_B_5))+  ]"++sublocale isoiec_9798_3_6_2_state < isoiec_9798_3_6_2_msc_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_3_6_2_msc_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_3_6_2_msc_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_3_6_2_A_2_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_A_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_A_2_TokenBA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_A_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_A_4_TokenTA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_A_4_pkB t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_A_check_4_in_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''check_4'',+               {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,+                     s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                     s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                  |},+                  Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,+                         s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                         s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                      |}+                      ( SK ( s(AV ''T'' tid0) ) )+               |},+               {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,+                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+               |},+               Enc {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0),+                      LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+                   |}+                   ( inv(s(MV ''pkB'' tid0)) )+            |}+            ( LN ''check_nonce_4'' tid0 ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_3_6_2_A_check_4_in_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''check_4'',+               {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,+                     s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                     s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                  |},+                  Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,+                         s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                         s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                      |}+                      ( SK ( s(AV ''T'' tid0) ) )+               |},+               {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,+                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+               |},+               Enc {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0),+                      LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+                   |}+                   ( inv(s(MV ''pkB'' tid0)) )+            |}+            ( LN ''check_nonce_4'' tid0 ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_3_6_2_A_check_4_in_pkA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''check_4'',+               {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,+                     s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                     s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                  |},+                  Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,+                         s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                         s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                      |}+                      ( SK ( s(AV ''T'' tid0) ) )+               |},+               {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,+                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+               |},+               Enc {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0),+                      LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+                   |}+                   ( inv(s(MV ''pkB'' tid0)) )+            |}+            ( LN ''check_nonce_4'' tid0 ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_3_6_2_A_text_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_A_text_5_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_B_1_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_B_1_Ra t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_B_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_B_text_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_B_text_2_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_B_5_Rpa t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_B_5_T t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_B_5_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_B_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_B_5_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_B_5_pkA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_B_5_pkB t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_T_3_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_T_3_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_T_3_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_T_3_Rpa t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_T_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_T_text_4_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_6_2_T_text_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_3_6_2_msc_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_3_6_2_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++lemma (in restricted_isoiec_9798_3_6_2_state) A_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_6_2_A &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          RLKR(s(AV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_6_2_A_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_6_2_B &+          ( tid1, isoiec_9798_3_6_2_B_2 ) : steps t &+          {| s(MV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,+             s(MV ''Text2'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''Ra'' tid0,+                  s(MV ''Rb'' tid0), s(MV ''Text2'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''check_4'',+                              {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,+                                    s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                                    s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                                 |},+                                 Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,+                                        s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                                        s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                                     |}+                                     ( SK ( s(AV ''T'' tid0) ) )+                              |},+                              {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,+                                 s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+                              |},+                              Enc {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0),+                                     LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+                                  |}+                                  ( inv(s(MV ''pkB'' tid0)) )+                           |}+                           ( LN ''check_nonce_4'' tid0 ) ")+        case fake note_unified facts = this facts+        thus ?thesis proof(sources! " LN ''check_nonce_4'' tid0 ")+        qed (insert facts, fastforce+)?+      next+        case (isoiec_9798_3_6_2_A_check_4_out_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0),+                                LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+                             |}+                             ( inv(s(MV ''pkB'' tid0)) ) ")+          case fake note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,+                                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                                  s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                               |}+                               ( SK ( s(AV ''T'' tid0) ) ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest!: ltk_secrecy)+          next+            case (isoiec_9798_3_6_2_T_4_enc tid1) note_unified facts = this facts+            thus ?thesis by (fastforce dest!: ltk_secrecy)+          qed (insert facts, fastforce+)?+        next+          case (isoiec_9798_3_6_2_B_2_enc tid1) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_6_2_state) B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_6_2_B &+          RLKR(s(MV ''A'' tid0)) ~: reveals t &+          RLKR(s(MV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_6_2_B_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_6_2_A &+          ( tid1, isoiec_9798_3_6_2_A_5 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),+             s(MV ''Text8'' tid1)+          |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),+                  LN ''Rb'' tid0, s(MV ''Text8'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', s(MV ''Rpa'' tid0),+                              LN ''Rb'' tid0, s(MV ''A'' tid0), s(MV ''pkA'' tid0), s(AV ''B'' tid0),+                              s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                           |}+                           ( SK ( s(MV ''T'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_6_2_T_4_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_3_6_opt_2_sig_5'', LN ''Rb'' tid0,+                                s(MV ''Ra'' tid0), s(AV ''B'' tid0), s(MV ''A'' tid0),+                                s(MV ''Text8'' tid0)+                             |}+                             ( SK ( s(MV ''A'' tid0) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_3_6_2_A_5_enc tid2) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_6_2_state) A_injective_agreement_T:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_6_2_A &+          RLKR(s(AV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_6_2_A_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_6_2_T &+          ( tid1, isoiec_9798_3_6_2_T_4 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''T'' tid1),+             s(MV ''Rpa'' tid1), s(MV ''Rb'' tid1), PK ( s(MV ''A'' tid1) ),+             PK ( s(MV ''B'' tid1) ), s(MV ''Text5'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(AV ''T'' tid0),+                  LN ''Rpa'' tid0, s(MV ''Rb'' tid0), s(MV ''pkA'' tid0),+                  s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''check_4'',+                              {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,+                                    s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                                    s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                                 |},+                                 Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,+                                        s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                                        s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                                     |}+                                     ( SK ( s(AV ''T'' tid0) ) )+                              |},+                              {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0,+                                 s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+                              |},+                              Enc {| LC ''isoiec_9798_3_6_opt_2_sig_2'', s(AV ''B'' tid0),+                                     LN ''Ra'' tid0, s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''Text2'' tid0)+                                  |}+                                  ( inv(s(MV ''pkB'' tid0)) )+                           |}+                           ( LN ''check_nonce_4'' tid0 ) ")+        case fake note_unified facts = this facts+        thus ?thesis proof(sources! " LN ''check_nonce_4'' tid0 ")+        qed (insert facts, fastforce+)?+      next+        case (isoiec_9798_3_6_2_A_check_4_out_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0,+                                s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                                s(AV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                             |}+                             ( SK ( s(AV ''T'' tid0) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_3_6_2_T_4_enc tid1) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_6_2_state) B_injective_agreement_T:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_6_2_B &+          RLKR(s(MV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_6_2_B_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_6_2_T &+          ( tid1, isoiec_9798_3_6_2_T_4 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''T'' tid1),+             s(MV ''Rpa'' tid1), s(MV ''Rb'' tid1), PK ( s(MV ''A'' tid1) ),+             PK ( s(MV ''B'' tid1) ), s(MV ''Text5'' tid1)+          |} = {| s(MV ''A'' tid0), s(AV ''B'' tid0), s(MV ''T'' tid0),+                  s(MV ''Rpa'' tid0), LN ''Rb'' tid0, s(MV ''pkA'' tid0),+                  s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_6_opt_2_sig_4'', s(MV ''Rpa'' tid0),+                              LN ''Rb'' tid0, s(MV ''A'' tid0), s(MV ''pkA'' tid0), s(AV ''B'' tid0),+                              s(MV ''pkB'' tid0), s(MV ''Text5'' tid0)+                           |}+                           ( SK ( s(MV ''T'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_6_2_T_4_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++role isoiec_9798_3_7_1_A+where "isoiec_9798_3_7_1_A =+  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>+  , Recv ''text_2'' ( sMV ''Text2'' )+  , Send ''2'' <| sAV ''A'', sAV ''T'', sN ''Rpa'', sMV ''Rb'', sAV ''A'',+                  sMV ''B'', sMV ''Text2''+               |>+  , Recv ''3'' <| sAV ''T'', sAV ''A'', sMV ''Text5'', sAV ''A'',+                  sPK ''A'', sMV ''B'', sMV ''pkB'',+                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_3_1'', sN ''Rpa'', sMV ''B'',+                           sMV ''pkB'', sMV ''Text4''+                        |>+                        ( sPK ''T'' ),+                  sMV ''TokenTA_for_B''+               |>+  , Recv ''text_4'' <| sMV ''Text6'', sMV ''Text7'' |>+  , Send ''4'' <| sAV ''A'', sMV ''B'', sN ''Rpa'', sMV ''Text7'',+                  sAV ''T'', sMV ''TokenTA_for_B'',+                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_4'', sMV ''Rb'', sN ''Ra'',+                           sMV ''B'', sAV ''A'', sMV ''Text6''+                        |>+                        ( sPK ''A'' )+               |>+  , Recv ''5'' <| sAV ''A'', sMV ''B'', sN ''Ra'', sMV ''Rb'',+                  sMV ''Text9'',+                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_5'', sN ''Ra'', sMV ''Rb'',+                           sAV ''A'', sMV ''B'', sMV ''Text8''+                        |>+                        ( sMV ''pkB'' )+               |>+  ]"++role isoiec_9798_3_7_1_B+where "isoiec_9798_3_7_1_B =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>+  , Recv ''4'' <| sAV ''A'', sAV ''B'', sMV ''Rpa'', sMV ''Text9'',+                  sMV ''T'',+                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_3_2'', sN ''Rb'', sAV ''A'',+                           sMV ''pkA'', sMV ''Text3''+                        |>+                        ( PAsymPK ( sMV ''T'' ) ),+                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_4'', sN ''Rb'', sMV ''Ra'',+                           sAV ''B'', sAV ''A'', sMV ''Text6''+                        |>+                        ( sMV ''pkA'' )+               |>+  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>+  , Send ''5'' <| sAV ''A'', sAV ''B'', sMV ''Ra'', sN ''Rb'',+                  sMV ''Text9'',+                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_5'', sMV ''Ra'', sN ''Rb'',+                           sAV ''A'', sAV ''B'', sMV ''Text8''+                        |>+                        ( sPK ''B'' )+               |>+  ]"++role isoiec_9798_3_7_1_T+where "isoiec_9798_3_7_1_T =+  [ Recv ''2'' <| sMV ''A'', sAV ''T'', sMV ''Rpa'', sMV ''Rb'', sMV ''A'',+                  sMV ''B'', sMV ''Text2''+               |>+  , Recv ''text_3'' <| sMV ''Text3'', sMV ''Text4'', sMV ''Text5'' |>+  , Send ''3'' <| sAV ''T'', sMV ''A'', sMV ''Text5'', sMV ''A'',+                  PAsymPK ( sMV ''A'' ), sMV ''B'', PAsymPK ( sMV ''B'' ),+                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_3_1'', sMV ''Rpa'', sMV ''B'',+                           PAsymPK ( sMV ''B'' ), sMV ''Text4''+                        |>+                        ( sPK ''T'' ),+                  PSign <| sC ''isoiec_9798_3_7_opt_1_sig_3_2'', sMV ''Rb'', sMV ''A'',+                           PAsymPK ( sMV ''A'' ), sMV ''Text3''+                        |>+                        ( sPK ''T'' )+               |>+  ]"++protocol isoiec_9798_3_7_1+where "isoiec_9798_3_7_1 =+{ isoiec_9798_3_7_1_A, isoiec_9798_3_7_1_B, isoiec_9798_3_7_1_T }"++locale restricted_isoiec_9798_3_7_1_state = isoiec_9798_3_7_1_state++type_invariant isoiec_9798_3_7_1_msc_typing for isoiec_9798_3_7_1+where "isoiec_9798_3_7_1_msc_typing = mk_typing+  [ ((isoiec_9798_3_7_1_T, ''A''), (KnownT isoiec_9798_3_7_1_T_2))+  , ((isoiec_9798_3_7_1_A, ''B''), (KnownT isoiec_9798_3_7_1_A_1))+  , ((isoiec_9798_3_7_1_T, ''B''), (KnownT isoiec_9798_3_7_1_T_2))+  , ((isoiec_9798_3_7_1_B, ''Ra''), (KnownT isoiec_9798_3_7_1_B_4))+  , ((isoiec_9798_3_7_1_A, ''Rb''), (KnownT isoiec_9798_3_7_1_A_1))+  , ((isoiec_9798_3_7_1_T, ''Rb''), (KnownT isoiec_9798_3_7_1_T_2))+  , ((isoiec_9798_3_7_1_B, ''Rpa''), (KnownT isoiec_9798_3_7_1_B_4))+  , ((isoiec_9798_3_7_1_T, ''Rpa''), (KnownT isoiec_9798_3_7_1_T_2))+  , ((isoiec_9798_3_7_1_B, ''T''), (KnownT isoiec_9798_3_7_1_B_4))+  , ((isoiec_9798_3_7_1_A, ''Text1''), (KnownT isoiec_9798_3_7_1_A_1))+  , ((isoiec_9798_3_7_1_B, ''Text1''), (KnownT isoiec_9798_3_7_1_B_text_1))+  , ((isoiec_9798_3_7_1_A, ''Text2''), (KnownT isoiec_9798_3_7_1_A_text_2))+  , ((isoiec_9798_3_7_1_T, ''Text2''), (KnownT isoiec_9798_3_7_1_T_2))+  , ((isoiec_9798_3_7_1_B, ''Text3''), (KnownT isoiec_9798_3_7_1_B_4))+  , ((isoiec_9798_3_7_1_T, ''Text3''), (KnownT isoiec_9798_3_7_1_T_text_3))+  , ((isoiec_9798_3_7_1_A, ''Text4''), (KnownT isoiec_9798_3_7_1_A_3))+  , ((isoiec_9798_3_7_1_T, ''Text4''), (KnownT isoiec_9798_3_7_1_T_text_3))+  , ((isoiec_9798_3_7_1_A, ''Text5''), (KnownT isoiec_9798_3_7_1_A_3))+  , ((isoiec_9798_3_7_1_T, ''Text5''), (KnownT isoiec_9798_3_7_1_T_text_3))+  , ((isoiec_9798_3_7_1_A, ''Text6''), (KnownT isoiec_9798_3_7_1_A_text_4))+  , ((isoiec_9798_3_7_1_B, ''Text6''), (KnownT isoiec_9798_3_7_1_B_4))+  , ((isoiec_9798_3_7_1_A, ''Text7''), (KnownT isoiec_9798_3_7_1_A_text_4))+  , ((isoiec_9798_3_7_1_A, ''Text8''), (KnownT isoiec_9798_3_7_1_A_5))+  , ((isoiec_9798_3_7_1_B, ''Text8''), (KnownT isoiec_9798_3_7_1_B_text_5))+  , ((isoiec_9798_3_7_1_A, ''Text9''), (KnownT isoiec_9798_3_7_1_A_5))+  , ((isoiec_9798_3_7_1_B, ''Text9''), (KnownT isoiec_9798_3_7_1_B_4))+  , ((isoiec_9798_3_7_1_A, ''TokenTA_for_B''),+     (KnownT isoiec_9798_3_7_1_A_3))+  , ((isoiec_9798_3_7_1_B, ''pkA''), (KnownT isoiec_9798_3_7_1_B_4))+  , ((isoiec_9798_3_7_1_A, ''pkB''), (KnownT isoiec_9798_3_7_1_A_3))+  ]"++sublocale isoiec_9798_3_7_1_state < isoiec_9798_3_7_1_msc_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_3_7_1_msc_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_3_7_1_msc_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_3_7_1_A_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_A_1_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_A_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_A_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_A_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_A_3_TokenTA_for_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_A_3_pkB t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_A_text_4_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_A_text_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_A_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_A_5_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_B_4_Ra t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_B_4_Rpa t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_B_4_T t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_B_4_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_B_4_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_B_4_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_B_4_pkA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_B_text_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_T_2_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_T_2_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_T_2_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_T_2_Rpa t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_T_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_T_text_3_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_T_text_3_Text4 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_1_T_text_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_3_7_1_msc_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_3_7_1_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++lemma (in restricted_isoiec_9798_3_7_1_state) A_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_7_1_A &+          RLKR(s(AV ''T'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_7_1_A_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_7_1_B &+          ( tid1, isoiec_9798_3_7_1_B_5 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,+             s(MV ''Text8'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''Ra'' tid0,+                  s(MV ''Rb'' tid0), s(MV ''Text8'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_7_opt_1_sig_3_1'', LN ''Rpa'' tid0,+                              s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text4'' tid0)+                           |}+                           ( SK ( s(AV ''T'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_7_1_T_3_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_3_7_opt_1_sig_5'', LN ''Ra'' tid0,+                                s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),+                                s(MV ''Text8'' tid0)+                             |}+                             ( SK ( s(MV ''B'' tid0) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_3_7_1_B_5_enc tid2) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_7_1_state) B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_7_1_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(MV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_7_1_B_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_7_1_A &+          ( tid1, isoiec_9798_3_7_1_A_4 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),+             s(MV ''Text6'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),+                  LN ''Rb'' tid0, s(MV ''Text6'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_7_opt_1_sig_3_2'', LN ''Rb'' tid0,+                              s(AV ''A'' tid0), s(MV ''pkA'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( SK ( s(MV ''T'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_7_1_T_3_enc_1 tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_3_7_opt_1_sig_4'', LN ''Rb'' tid0,+                                s(MV ''Ra'' tid0), s(AV ''B'' tid0), s(AV ''A'' tid0),+                                s(MV ''Text6'' tid0)+                             |}+                             ( SK ( s(AV ''A'' tid0) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_3_7_1_A_4_enc tid2) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_7_1_state) A_injective_agreement_T:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_7_1_A &+          RLKR(s(AV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_7_1_A_3 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_7_1_T &+          ( tid1, isoiec_9798_3_7_1_T_3 ) : steps t &+          {| s(MV ''B'' tid1), s(AV ''T'' tid1), s(MV ''Rpa'' tid1),+             PK ( s(MV ''B'' tid1) ), s(MV ''Text4'' tid1)+          |} = {| s(MV ''B'' tid0), s(AV ''T'' tid0), LN ''Rpa'' tid0,+                  s(MV ''pkB'' tid0), s(MV ''Text4'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_7_opt_1_sig_3_1'', LN ''Rpa'' tid0,+                              s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text4'' tid0)+                           |}+                           ( SK ( s(AV ''T'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_7_1_T_3_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_7_1_state) B_injective_agreement_T:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_7_1_B &+          RLKR(s(MV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_7_1_B_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_7_1_T &+          ( tid1, isoiec_9798_3_7_1_T_3 ) : steps t &+          {| s(MV ''A'' tid1), s(AV ''T'' tid1), s(MV ''Rb'' tid1),+             PK ( s(MV ''A'' tid1) ), s(MV ''Text3'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''T'' tid0), LN ''Rb'' tid0,+                  s(MV ''pkA'' tid0), s(MV ''Text3'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_7_opt_1_sig_3_2'', LN ''Rb'' tid0,+                              s(AV ''A'' tid0), s(MV ''pkA'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( SK ( s(MV ''T'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_7_1_T_3_enc_1 tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++role isoiec_9798_3_7_2_A+where "isoiec_9798_3_7_2_A =+  [ Recv ''1'' <| sMV ''B'', sAV ''A'', sMV ''Rb'', sMV ''Text1'' |>+  , Recv ''text_2'' ( sMV ''Text2'' )+  , Send ''2'' <| sAV ''A'', sAV ''T'', sN ''Rpa'', sMV ''Rb'', sAV ''A'',+                  sMV ''B'', sMV ''Text2''+               |>+  , Recv ''3'' <| sAV ''T'', sAV ''A'', sMV ''Text5'', sAV ''A'',+                  sPK ''A'', sMV ''B'', sMV ''pkB'', sMV ''TokenTA''+               |>+  , Send ''check_3_out'' ( PEnc <| sC ''check_4'', sMV ''TokenTA'' |>+                                ( sN ''check_nonce_4'' )+                         )+  , Recv ''check_3_in'' ( PEnc <| sC ''check_4'',+                                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_3'', sN ''Rpa'', sMV ''Rb'',+                                           sAV ''A'', sMV ''pkA'', sMV ''B'', sMV ''pkB'', sMV ''Text3''+                                        |>+                                        ( sPK ''T'' )+                               |>+                               ( sN ''check_nonce_4'' )+                        )+  , Recv ''text_4'' <| sMV ''Text6'', sMV ''Text7'' |>+  , Send ''4'' <| sAV ''A'', sMV ''B'', sN ''Rpa'', sMV ''Text7'',+                  sAV ''T'', sMV ''TokenTA'',+                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_4'', sMV ''Rb'', sN ''Ra'',+                           sMV ''B'', sAV ''A'', sMV ''Text6''+                        |>+                        ( sPK ''A'' )+               |>+  , Recv ''5'' <| sAV ''A'', sMV ''B'', sN ''Ra'', sMV ''Rb'',+                  sMV ''Text9'',+                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_5'', sN ''Ra'', sMV ''Rb'',+                           sAV ''A'', sMV ''B'', sMV ''Text8''+                        |>+                        ( sMV ''pkB'' )+               |>+  ]"++role isoiec_9798_3_7_2_B+where "isoiec_9798_3_7_2_B =+  [ Recv ''text_1'' ( sMV ''Text1'' )+  , Send ''1'' <| sAV ''B'', sAV ''A'', sN ''Rb'', sMV ''Text1'' |>+  , Recv ''4'' <| sAV ''A'', sAV ''B'', sMV ''Rpa'', sMV ''Text9'',+                  sMV ''T'',+                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_3'', sMV ''Rpa'', sN ''Rb'',+                           sAV ''A'', sMV ''pkA'', sAV ''B'', sMV ''pkB'', sMV ''Text3''+                        |>+                        ( PAsymPK ( sMV ''T'' ) ),+                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_4'', sN ''Rb'', sMV ''Ra'',+                           sAV ''B'', sAV ''A'', sMV ''Text6''+                        |>+                        ( sMV ''pkA'' )+               |>+  , Recv ''text_5'' <| sMV ''Text8'', sMV ''Text9'' |>+  , Send ''5'' <| sAV ''A'', sAV ''B'', sMV ''Ra'', sN ''Rb'',+                  sMV ''Text9'',+                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_5'', sMV ''Ra'', sN ''Rb'',+                           sAV ''A'', sAV ''B'', sMV ''Text8''+                        |>+                        ( sPK ''B'' )+               |>+  ]"++role isoiec_9798_3_7_2_T+where "isoiec_9798_3_7_2_T =+  [ Recv ''2'' <| sMV ''A'', sAV ''T'', sMV ''Rpa'', sMV ''Rb'', sMV ''A'',+                  sMV ''B'', sMV ''Text2''+               |>+  , Recv ''text_3'' <| sMV ''Text3'', sMV ''Text5'' |>+  , Send ''3'' <| sAV ''T'', sMV ''A'', sMV ''Text5'', sMV ''A'',+                  PAsymPK ( sMV ''A'' ), sMV ''B'', PAsymPK ( sMV ''B'' ),+                  PSign <| sC ''isoiec_9798_3_7_opt_2_sig_3'', sMV ''Rpa'', sMV ''Rb'',+                           sMV ''A'', PAsymPK ( sMV ''A'' ), sMV ''B'', PAsymPK ( sMV ''B'' ),+                           sMV ''Text3''+                        |>+                        ( sPK ''T'' )+               |>+  ]"++protocol isoiec_9798_3_7_2+where "isoiec_9798_3_7_2 =+{ isoiec_9798_3_7_2_A, isoiec_9798_3_7_2_B, isoiec_9798_3_7_2_T }"++locale restricted_isoiec_9798_3_7_2_state = isoiec_9798_3_7_2_state++type_invariant isoiec_9798_3_7_2_msc_typing for isoiec_9798_3_7_2+where "isoiec_9798_3_7_2_msc_typing = mk_typing+  [ ((isoiec_9798_3_7_2_T, ''A''), (KnownT isoiec_9798_3_7_2_T_2))+  , ((isoiec_9798_3_7_2_A, ''B''), (KnownT isoiec_9798_3_7_2_A_1))+  , ((isoiec_9798_3_7_2_T, ''B''), (KnownT isoiec_9798_3_7_2_T_2))+  , ((isoiec_9798_3_7_2_B, ''Ra''), (KnownT isoiec_9798_3_7_2_B_4))+  , ((isoiec_9798_3_7_2_A, ''Rb''), (KnownT isoiec_9798_3_7_2_A_1))+  , ((isoiec_9798_3_7_2_T, ''Rb''), (KnownT isoiec_9798_3_7_2_T_2))+  , ((isoiec_9798_3_7_2_B, ''Rpa''), (KnownT isoiec_9798_3_7_2_B_4))+  , ((isoiec_9798_3_7_2_T, ''Rpa''), (KnownT isoiec_9798_3_7_2_T_2))+  , ((isoiec_9798_3_7_2_B, ''T''), (KnownT isoiec_9798_3_7_2_B_4))+  , ((isoiec_9798_3_7_2_A, ''Text1''), (KnownT isoiec_9798_3_7_2_A_1))+  , ((isoiec_9798_3_7_2_B, ''Text1''), (KnownT isoiec_9798_3_7_2_B_text_1))+  , ((isoiec_9798_3_7_2_A, ''Text2''), (KnownT isoiec_9798_3_7_2_A_text_2))+  , ((isoiec_9798_3_7_2_T, ''Text2''), (KnownT isoiec_9798_3_7_2_T_2))+  , ((isoiec_9798_3_7_2_A, ''Text3''),+     (KnownT isoiec_9798_3_7_2_A_check_3_in))+  , ((isoiec_9798_3_7_2_B, ''Text3''), (KnownT isoiec_9798_3_7_2_B_4))+  , ((isoiec_9798_3_7_2_T, ''Text3''), (KnownT isoiec_9798_3_7_2_T_text_3))+  , ((isoiec_9798_3_7_2_A, ''Text5''), (KnownT isoiec_9798_3_7_2_A_3))+  , ((isoiec_9798_3_7_2_T, ''Text5''), (KnownT isoiec_9798_3_7_2_T_text_3))+  , ((isoiec_9798_3_7_2_A, ''Text6''), (KnownT isoiec_9798_3_7_2_A_text_4))+  , ((isoiec_9798_3_7_2_B, ''Text6''), (KnownT isoiec_9798_3_7_2_B_4))+  , ((isoiec_9798_3_7_2_A, ''Text7''), (KnownT isoiec_9798_3_7_2_A_text_4))+  , ((isoiec_9798_3_7_2_A, ''Text8''), (KnownT isoiec_9798_3_7_2_A_5))+  , ((isoiec_9798_3_7_2_B, ''Text8''), (KnownT isoiec_9798_3_7_2_B_text_5))+  , ((isoiec_9798_3_7_2_A, ''Text9''), (KnownT isoiec_9798_3_7_2_A_5))+  , ((isoiec_9798_3_7_2_B, ''Text9''), (KnownT isoiec_9798_3_7_2_B_4))+  , ((isoiec_9798_3_7_2_A, ''TokenTA''), (KnownT isoiec_9798_3_7_2_A_3))+  , ((isoiec_9798_3_7_2_A, ''pkA''),+     (KnownT isoiec_9798_3_7_2_A_check_3_in))+  , ((isoiec_9798_3_7_2_B, ''pkA''), (KnownT isoiec_9798_3_7_2_B_4))+  , ((isoiec_9798_3_7_2_A, ''pkB''), (KnownT isoiec_9798_3_7_2_A_3))+  , ((isoiec_9798_3_7_2_B, ''pkB''), (KnownT isoiec_9798_3_7_2_B_4))+  ]"++sublocale isoiec_9798_3_7_2_state < isoiec_9798_3_7_2_msc_typing_state+proof -+  have "(t,r,s) : approx isoiec_9798_3_7_2_msc_typing"+  proof(cases rule: reachable_in_approxI_ext+        [OF isoiec_9798_3_7_2_msc_typing.monoTyp, completeness_cases_rule])+    case (isoiec_9798_3_7_2_A_1_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_A_1_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_A_1_Text1 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_A_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_A_3_TokenTA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_A_3_pkB t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_A_check_3_in_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''check_4'',+               {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,+                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                  s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+               |},+               Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,+                      s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                      s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+                   |}+                   ( SK ( s(AV ''T'' tid0) ) )+            |}+            ( LN ''check_nonce_4'' tid0 ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_3_7_2_A_check_3_in_pkA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    proof(sources! "+        Enc {| LC ''check_4'',+               {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,+                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                  s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+               |},+               Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,+                      s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                      s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+                   |}+                   ( SK ( s(AV ''T'' tid0) ) )+            |}+            ( LN ''check_nonce_4'' tid0 ) ")+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?+  next+    case (isoiec_9798_3_7_2_A_text_4_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_A_text_4_Text7 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_A_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_A_5_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_B_4_Ra t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_B_4_Rpa t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_B_4_T t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_B_4_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_B_4_Text6 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_B_4_Text9 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_B_4_pkA t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_B_4_pkB t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_B_text_5_Text8 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_T_2_A t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_T_2_B t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_T_2_Rb t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_T_2_Rpa t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_T_2_Text2 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_T_text_3_Text3 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  next+    case (isoiec_9798_3_7_2_T_text_3_Text5 t r s tid0) note facts = this+    then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s+      by unfold_locales auto+    show ?case using facts+    by (fastforce intro: event_predOrdI split: if_splits)+  qed+  thus "isoiec_9798_3_7_2_msc_typing_state t r s" by unfold_locales auto+qed++text{* Prove secrecy of long-term keys. *}+context isoiec_9798_3_7_2_state begin++  (* This rule is unsafe in general, but OK here, +     as we are only reasoning about static compromise. +  *)+  lemma static_longterm_key_reveal[dest!]:+    "predOrd t (LKR a) e ==> RLKR a : reveals t"+    by (auto intro: compr_predOrdI)++  lemma longterm_private_key_secrecy:+    assumes facts:+      "SK m : knows t"+      "RLKR m ~: reveals t"+    shows "False"+  using facts by (sources "SK m")++  lemma longterm_sym_ud_key_secrecy:+    assumes facts:+      "K m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+    shows "False"+  using facts by (sources "K m1 m2")++  lemma longterm_sym_bd_key_secrecy:+    assumes facts:+      "Kbd m1 m2 : knows t"+      "RLKR m1 ~: reveals t"+      "RLKR m2 ~: reveals t"+      "m1 : Agent"+      "m2 : Agent"+    shows "False"+  proof -+    from facts +    have "KShr (agents {m1, m2}) : knows t"+      by (auto simp: Kbd_def)+    thus ?thesis using facts+    proof (sources "KShr (agents {m1, m2})")+    qed (auto simp: agents_def Agent_def)+  qed++  lemmas ltk_secrecy =+    longterm_sym_ud_key_secrecy+    longterm_sym_ud_key_secrecy[OF in_knows_predOrd1]+    longterm_sym_bd_key_secrecy+    longterm_sym_bd_key_secrecy[OF in_knows_predOrd1]+    longterm_private_key_secrecy+    longterm_private_key_secrecy[OF in_knows_predOrd1]++end++lemma (in restricted_isoiec_9798_3_7_2_state) A_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_7_2_A &+          RLKR(s(AV ''T'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_7_2_A_5 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_7_2_B &+          ( tid1, isoiec_9798_3_7_2_B_5 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,+             s(MV ''Text8'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''Ra'' tid0,+                  s(MV ''Rb'' tid0), s(MV ''Text8'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''check_4'',+                              {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,+                                 s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                                 s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+                              |},+                              Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,+                                     s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                                     s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+                                  |}+                                  ( SK ( s(AV ''T'' tid0) ) )+                           |}+                           ( LN ''check_nonce_4'' tid0 ) ")+        case fake note_unified facts = this facts+        thus ?thesis proof(sources! " LN ''check_nonce_4'' tid0 ")+        qed (insert facts, fastforce+)?+      next+        case (isoiec_9798_3_7_2_A_check_3_out_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,+                                s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                                s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+                             |}+                             ( SK ( s(AV ''T'' tid0) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_3_7_2_T_3_enc tid1) note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Enc {| LC ''isoiec_9798_3_7_opt_2_sig_5'', LN ''Ra'' tid0,+                                  s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''B'' tid0),+                                  s(MV ''Text8'' tid0)+                               |}+                               ( SK ( s(MV ''B'' tid0) ) ) ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest!: ltk_secrecy)+          next+            case (isoiec_9798_3_7_2_B_5_enc tid2) note_unified facts = this facts+            thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+          qed (insert facts, fastforce+)?+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_7_2_state) B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_7_2_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(MV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_7_2_B_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_7_2_A &+          ( tid1, isoiec_9798_3_7_2_A_4 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),+             s(MV ''Text6'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),+                  LN ''Rb'' tid0, s(MV ''Text6'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', s(MV ''Rpa'' tid0),+                              LN ''Rb'' tid0, s(AV ''A'' tid0), s(MV ''pkA'' tid0), s(AV ''B'' tid0),+                              s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( SK ( s(MV ''T'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_7_2_T_3_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_3_7_opt_2_sig_4'', LN ''Rb'' tid0,+                                s(MV ''Ra'' tid0), s(AV ''B'' tid0), s(AV ''A'' tid0),+                                s(MV ''Text6'' tid0)+                             |}+                             ( SK ( s(AV ''A'' tid0) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_3_7_2_A_4_enc tid2) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_7_2_state) A_injective_agreement_T:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_7_2_A &+          RLKR(s(AV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_7_2_A_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_7_2_T &+          ( tid1, isoiec_9798_3_7_2_T_3 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''T'' tid1),+             s(MV ''Rpa'' tid1), s(MV ''Rb'' tid1), PK ( s(MV ''A'' tid1) ),+             PK ( s(MV ''B'' tid1) ), s(MV ''Text3'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), s(AV ''T'' tid0),+                  LN ''Rpa'' tid0, s(MV ''Rb'' tid0), s(MV ''pkA'' tid0),+                  s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''check_4'',+                              {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,+                                 s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                                 s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+                              |},+                              Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,+                                     s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                                     s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+                                  |}+                                  ( SK ( s(AV ''T'' tid0) ) )+                           |}+                           ( LN ''check_nonce_4'' tid0 ) ")+        case fake note_unified facts = this facts+        thus ?thesis proof(sources! " LN ''check_nonce_4'' tid0 ")+        qed (insert facts, fastforce+)?+      next+        case (isoiec_9798_3_7_2_A_check_3_out_enc tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0,+                                s(MV ''Rb'' tid0), s(AV ''A'' tid0), s(MV ''pkA'' tid0),+                                s(MV ''B'' tid0), s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+                             |}+                             ( SK ( s(AV ''T'' tid0) ) ) ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_3_7_2_T_3_enc tid1) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_3_7_2_state) B_injective_agreement_T:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_3_7_2_B &+          RLKR(s(MV ''T'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_3_7_2_B_4 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_3_7_2_T &+          ( tid1, isoiec_9798_3_7_2_T_3 ) : steps t &+          {| s(MV ''A'' tid1), s(MV ''B'' tid1), s(AV ''T'' tid1),+             s(MV ''Rpa'' tid1), s(MV ''Rb'' tid1), PK ( s(MV ''A'' tid1) ),+             PK ( s(MV ''B'' tid1) ), s(MV ''Text3'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''T'' tid0),+                  s(MV ''Rpa'' tid0), LN ''Rb'' tid0, s(MV ''pkA'' tid0),+                  s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Enc {| LC ''isoiec_9798_3_7_opt_2_sig_3'', s(MV ''Rpa'' tid0),+                              LN ''Rb'' tid0, s(AV ''A'' tid0), s(MV ''pkA'' tid0), s(AV ''B'' tid0),+                              s(MV ''pkB'' tid0), s(MV ''Text3'' tid0)+                           |}+                           ( SK ( s(MV ''T'' tid0) ) ) ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_3_7_2_T_3_enc tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj) qed  end
data/examples/iso9798/isabelle-proofs/isoiec-9798-4-bdkey_cert_auto.thy view
@@ -1,6 +1,6 @@ theory "isoiec-9798-4-bdkey_cert_auto" imports-  "../ESPLogic"+  "ESPLogic" begin  role isoiec_9798_4_1_bdkey_A@@ -55,37 +55,37 @@     then interpret state: isoiec_9798_4_1_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_1_bdkey_A_text_1_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_1_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_1_bdkey_B_1_A t r s tid0) note facts = this     then interpret state: isoiec_9798_4_1_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_1_bdkey_B_1_TNA t r s tid0) note facts = this     then interpret state: isoiec_9798_4_1_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_1_bdkey_B_1_Text1 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_1_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_1_bdkey_B_1_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_1_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   qed   thus "isoiec_9798_4_1_bdkey_msc_typing_state t r s" by unfold_locales auto qed@@ -165,11 +165,11 @@                            s(MV ''Text1'' tid0)                         |} ")     case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)+    thus ?thesis by (fastforce dest!: ltk_secrecy)   next     case (isoiec_9798_4_1_bdkey_A_1_hash tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)? qed  role isoiec_9798_4_2_bdkey_A@@ -229,43 +229,43 @@     then interpret state: isoiec_9798_4_2_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_bdkey_A_1_Rb t r s tid0) note facts = this     then interpret state: isoiec_9798_4_2_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_bdkey_A_1_Text1 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_2_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_bdkey_A_text_2_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_2_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_bdkey_A_text_2_Text3 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_2_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_bdkey_B_2_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_2_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_bdkey_B_2_Text3 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_2_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   qed   thus "isoiec_9798_4_2_bdkey_msc_typing_state t r s" by unfold_locales auto qed@@ -322,34 +322,54 @@  end -lemma (in restricted_isoiec_9798_4_2_bdkey_state) B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_4_2_bdkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_4_2_bdkey_B_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_4_2_bdkey_A &-        ( tid1, isoiec_9798_4_2_bdkey_A_2 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(MV ''Rb'' tid1),-           s(MV ''Text2'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''Rb'' tid0,-                s(MV ''Text2'' tid0)-             |})"+lemma (in restricted_isoiec_9798_4_2_bdkey_state) B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_4_2_bdkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_4_2_bdkey_B_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_4_2_bdkey_A &+          ( tid1, isoiec_9798_4_2_bdkey_A_2 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(MV ''Rb'' tid1),+             s(MV ''Text2'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''Rb'' tid0,+                  s(MV ''Text2'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs") proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) |},-                           LC ''isoiec_9798_4_2_ccf_2'', LN ''Rb'' tid0, s(AV ''B'' tid0),-                           s(MV ''Text2'' tid0)-                        |} ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_4_2_bdkey_A_2_hash tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) |},+                               LC ''isoiec_9798_4_2_ccf_2'', LN ''Rb'' tid0, s(AV ''B'' tid0),+                               s(MV ''Text2'' tid0)+                            |} ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_4_2_bdkey_A_2_hash tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj) qed  role isoiec_9798_4_3_bdkey_A@@ -428,67 +448,67 @@     then interpret state: isoiec_9798_4_3_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_bdkey_A_text_1_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_3_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_bdkey_A_2_TNb t r s tid0) note facts = this     then interpret state: isoiec_9798_4_3_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_bdkey_A_2_Text3 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_3_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_bdkey_A_2_Text4 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_3_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_bdkey_B_1_A t r s tid0) note facts = this     then interpret state: isoiec_9798_4_3_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_bdkey_B_1_TNa t r s tid0) note facts = this     then interpret state: isoiec_9798_4_3_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_bdkey_B_1_Text1 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_3_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_bdkey_B_1_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_3_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_bdkey_B_text_2_Text3 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_3_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_bdkey_B_text_2_Text4 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_3_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   qed   thus "isoiec_9798_4_3_bdkey_msc_typing_state t r s" by unfold_locales auto qed@@ -568,11 +588,11 @@                            s(MV ''Text3'' tid0)                         |} ")     case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)+    thus ?thesis by (fastforce dest!: ltk_secrecy)   next     case (isoiec_9798_4_3_bdkey_B_2_hash tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)? qed  lemma (in restricted_isoiec_9798_4_3_bdkey_state) B_non_injective_agreement:@@ -598,11 +618,11 @@                            s(MV ''Text1'' tid0)                         |} ")     case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)+    thus ?thesis by (fastforce dest!: ltk_secrecy)   next     case (isoiec_9798_4_3_bdkey_A_1_hash tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)? qed  role isoiec_9798_4_4_bdkey_A@@ -684,73 +704,73 @@     then interpret state: isoiec_9798_4_4_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_bdkey_A_1_Rb t r s tid0) note facts = this     then interpret state: isoiec_9798_4_4_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_bdkey_A_1_Text1 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_4_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_bdkey_A_text_2_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_4_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_bdkey_A_text_2_Text3 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_4_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_bdkey_A_3_Text4 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_4_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_bdkey_A_3_Text5 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_4_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_bdkey_B_2_Ra t r s tid0) note facts = this     then interpret state: isoiec_9798_4_4_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_bdkey_B_2_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_4_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_bdkey_B_2_Text3 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_4_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_bdkey_B_text_3_Text4 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_4_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_bdkey_B_text_3_Text5 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_4_bdkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   qed   thus "isoiec_9798_4_4_bdkey_msc_typing_state t r s" by unfold_locales auto qed@@ -807,93 +827,133 @@  end -lemma (in restricted_isoiec_9798_4_4_bdkey_state) A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_4_4_bdkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_4_4_bdkey_A_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_4_4_bdkey_B &-        ( tid1, isoiec_9798_4_4_bdkey_B_3 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,-           s(MV ''Text2'' tid1), s(MV ''Text4'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''Ra'' tid0,-                s(MV ''Rb'' tid0), s(MV ''Text2'' tid0), s(MV ''Text4'' tid0)-             |})"+lemma (in restricted_isoiec_9798_4_4_bdkey_state) A_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_4_4_bdkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_4_4_bdkey_A_3 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_4_4_bdkey_B &+          ( tid1, isoiec_9798_4_4_bdkey_B_3 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,+             s(MV ''Text2'' tid1), s(MV ''Text4'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''Ra'' tid0,+                  s(MV ''Rb'' tid0), s(MV ''Text2'' tid0), s(MV ''Text4'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs") proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) ) |},-                           LC ''isoiec_9798_4_4_ccf_3'', s(MV ''Rb'' tid0), LN ''Ra'' tid0,-                           s(MV ''Text4'' tid0)-                        |} ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_4_4_bdkey_B_3_hash tid1) note_unified facts = this facts-    hence "Kbd ( s(AV ''A'' tid1) )-               ( s(AV ''B'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) )"-      by simp note facts = this facts-    thus ?thesis proof(cases rule: Kbd_cases)-      case noswap note_unified facts = this facts+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts       thus ?thesis proof(sources! "-                       Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid1) ) |},-                               LC ''isoiec_9798_4_4_ccf_2'', LN ''Ra'' tid0, LN ''Rb'' tid1,-                               s(AV ''B'' tid1), s(MV ''Text2'' tid1)+                       Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) ) |},+                               LC ''isoiec_9798_4_4_ccf_3'', s(MV ''Rb'' tid0), LN ''Ra'' tid0,+                               s(MV ''Text4'' tid0)                             |} ")         case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest!: ltk_secrecy)+        thus ?thesis by (fastforce dest!: ltk_secrecy)       next-        case (isoiec_9798_4_4_bdkey_A_2_hash tid2) note_unified facts = this facts-        thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-      qed (insert facts, fastsimp+)?-    next-      case swapped note_unified facts = this facts+        case (isoiec_9798_4_4_bdkey_B_3_hash tid1) note_unified facts = this facts+        hence "Kbd ( s(AV ''A'' tid1) )+                   ( s(AV ''B'' tid1) ) = Kbd ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) )"+          by simp note facts = this facts+        thus ?thesis proof(cases rule: Kbd_cases)+          case noswap note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid1) ) |},+                                   LC ''isoiec_9798_4_4_ccf_2'', LN ''Ra'' tid0, LN ''Rb'' tid1,+                                   s(AV ''B'' tid1), s(MV ''Text2'' tid1)+                                |} ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest!: ltk_secrecy)+          next+            case (isoiec_9798_4_4_bdkey_A_2_hash tid2) note_unified facts = this facts+            thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+          qed (insert facts, fastforce+)?+        next+          case swapped note_unified facts = this facts+          thus ?thesis proof(sources! "+                           Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(AV ''A'' tid1) ) |},+                                   LC ''isoiec_9798_4_4_ccf_2'', LN ''Ra'' tid0, LN ''Rb'' tid1,+                                   s(AV ''A'' tid0), s(MV ''Text2'' tid1)+                                |} ")+            case fake note_unified facts = this facts+            thus ?thesis by (fastforce dest!: ltk_secrecy)+          next+            case (isoiec_9798_4_4_bdkey_A_2_hash tid2) note_unified facts = this facts+            thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+          qed (insert facts, fastforce+)?+        qed (fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj)+qed++lemma (in restricted_isoiec_9798_4_4_bdkey_state) B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_4_4_bdkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_4_4_bdkey_B_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_4_4_bdkey_A &+          ( tid1, isoiec_9798_4_4_bdkey_A_2 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),+             s(MV ''Text2'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),+                  LN ''Rb'' tid0, s(MV ''Text2'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs")+proof -+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts       thus ?thesis proof(sources! "-                       Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(AV ''A'' tid1) ) |},-                               LC ''isoiec_9798_4_4_ccf_2'', LN ''Ra'' tid0, LN ''Rb'' tid1,-                               s(AV ''A'' tid0), s(MV ''Text2'' tid1)+                       Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) |},+                               LC ''isoiec_9798_4_4_ccf_2'', s(MV ''Ra'' tid0), LN ''Rb'' tid0,+                               s(AV ''B'' tid0), s(MV ''Text2'' tid0)                             |} ")         case fake note_unified facts = this facts-        thus ?thesis by (fastsimp dest!: ltk_secrecy)+        thus ?thesis by (fastforce dest!: ltk_secrecy)       next-        case (isoiec_9798_4_4_bdkey_A_2_hash tid2) note_unified facts = this facts-        thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-      qed (insert facts, fastsimp+)?-    qed (fastsimp+)?-  qed (insert facts, fastsimp+)?-qed--lemma (in restricted_isoiec_9798_4_4_bdkey_state) B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_4_4_bdkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_4_4_bdkey_B_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_4_4_bdkey_A &-        ( tid1, isoiec_9798_4_4_bdkey_A_2 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),-           s(MV ''Text2'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),-                LN ''Rb'' tid0, s(MV ''Text2'' tid0)-             |})"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Hash {| {| LC ''CCF'', Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) |},-                           LC ''isoiec_9798_4_4_ccf_2'', s(MV ''Ra'' tid0), LN ''Rb'' tid0,-                           s(AV ''B'' tid0), s(MV ''Text2'' tid0)-                        |} ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_4_4_bdkey_A_2_hash tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?+        case (isoiec_9798_4_4_bdkey_A_2_hash tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj) qed  end
data/examples/iso9798/isabelle-proofs/isoiec-9798-4-udkey_cert_auto.thy view
@@ -1,6 +1,6 @@ theory "isoiec-9798-4-udkey_cert_auto" imports-  "../ESPLogic"+  "ESPLogic" begin  role isoiec_9798_4_1_udkey_A@@ -55,37 +55,37 @@     then interpret state: isoiec_9798_4_1_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_1_udkey_A_text_1_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_1_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_1_udkey_B_1_A t r s tid0) note facts = this     then interpret state: isoiec_9798_4_1_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_1_udkey_B_1_TNA t r s tid0) note facts = this     then interpret state: isoiec_9798_4_1_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_1_udkey_B_1_Text1 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_1_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_1_udkey_B_1_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_1_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   qed   thus "isoiec_9798_4_1_udkey_msc_typing_state t r s" by unfold_locales auto qed@@ -164,11 +164,11 @@                            LC ''isoiec_9798_4_1_ccf_1'', s(MV ''TNA'' tid0), s(MV ''Text1'' tid0)                         |} ")     case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)+    thus ?thesis by (fastforce dest!: ltk_secrecy)   next     case (isoiec_9798_4_1_udkey_A_1_hash tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)? qed  role isoiec_9798_4_2_udkey_A@@ -228,43 +228,43 @@     then interpret state: isoiec_9798_4_2_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_udkey_A_1_Rb t r s tid0) note facts = this     then interpret state: isoiec_9798_4_2_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_udkey_A_1_Text1 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_2_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_udkey_A_text_2_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_2_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_udkey_A_text_2_Text3 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_2_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_udkey_B_2_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_2_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_2_udkey_B_2_Text3 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_2_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   qed   thus "isoiec_9798_4_2_udkey_msc_typing_state t r s" by unfold_locales auto qed@@ -321,33 +321,53 @@  end -lemma (in restricted_isoiec_9798_4_2_udkey_state) B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_4_2_udkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_4_2_udkey_B_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_4_2_udkey_A &-        ( tid1, isoiec_9798_4_2_udkey_A_2 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(MV ''Rb'' tid1),-           s(MV ''Text2'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''Rb'' tid0,-                s(MV ''Text2'' tid0)-             |})"+lemma (in restricted_isoiec_9798_4_2_udkey_state) B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_4_2_udkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_4_2_udkey_B_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_4_2_udkey_A &+          ( tid1, isoiec_9798_4_2_udkey_A_2 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), s(MV ''Rb'' tid1),+             s(MV ''Text2'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), LN ''Rb'' tid0,+                  s(MV ''Text2'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs") proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Hash {| {| LC ''CCF'', K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) |},-                           LC ''isoiec_9798_4_2_ccf_2'', LN ''Rb'' tid0, s(MV ''Text2'' tid0)-                        |} ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_4_2_udkey_A_2_hash tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Hash {| {| LC ''CCF'', K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) |},+                               LC ''isoiec_9798_4_2_ccf_2'', LN ''Rb'' tid0, s(MV ''Text2'' tid0)+                            |} ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_4_2_udkey_A_2_hash tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj) qed  role isoiec_9798_4_3_udkey_A@@ -426,67 +446,67 @@     then interpret state: isoiec_9798_4_3_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_udkey_A_text_1_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_3_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_udkey_A_2_TNb t r s tid0) note facts = this     then interpret state: isoiec_9798_4_3_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_udkey_A_2_Text3 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_3_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_udkey_A_2_Text4 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_3_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_udkey_B_1_A t r s tid0) note facts = this     then interpret state: isoiec_9798_4_3_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_udkey_B_1_TNa t r s tid0) note facts = this     then interpret state: isoiec_9798_4_3_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_udkey_B_1_Text1 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_3_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_udkey_B_1_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_3_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_udkey_B_text_2_Text3 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_3_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_3_udkey_B_text_2_Text4 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_3_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   qed   thus "isoiec_9798_4_3_udkey_msc_typing_state t r s" by unfold_locales auto qed@@ -565,11 +585,11 @@                            LC ''isoiec_9798_4_3_ccf_2'', s(MV ''TNb'' tid0), s(MV ''Text3'' tid0)                         |} ")     case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)+    thus ?thesis by (fastforce dest!: ltk_secrecy)   next     case (isoiec_9798_4_3_udkey_B_2_hash tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)? qed  lemma (in restricted_isoiec_9798_4_3_udkey_state) B_non_injective_agreement:@@ -594,11 +614,11 @@                            LC ''isoiec_9798_4_3_ccf_1'', s(MV ''TNa'' tid0), s(MV ''Text1'' tid0)                         |} ")     case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)+    thus ?thesis by (fastforce dest!: ltk_secrecy)   next     case (isoiec_9798_4_3_udkey_A_1_hash tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?+    thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+  qed (insert facts, fastforce+)? qed  role isoiec_9798_4_4_udkey_A@@ -678,73 +698,73 @@     then interpret state: isoiec_9798_4_4_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_udkey_A_1_Rb t r s tid0) note facts = this     then interpret state: isoiec_9798_4_4_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_udkey_A_1_Text1 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_4_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_udkey_A_text_2_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_4_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_udkey_A_text_2_Text3 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_4_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_udkey_A_3_Text4 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_4_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_udkey_A_3_Text5 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_4_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_udkey_B_2_Ra t r s tid0) note facts = this     then interpret state: isoiec_9798_4_4_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_udkey_B_2_Text2 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_4_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_udkey_B_2_Text3 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_4_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_udkey_B_text_3_Text4 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_4_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (isoiec_9798_4_4_udkey_B_text_3_Text5 t r s tid0) note facts = this     then interpret state: isoiec_9798_4_4_udkey_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   qed   thus "isoiec_9798_4_4_udkey_msc_typing_state t r s" by unfold_locales auto qed@@ -801,74 +821,114 @@  end -lemma (in restricted_isoiec_9798_4_4_udkey_state) A_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_4_4_udkey_A"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(MV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_4_4_udkey_A_3 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_4_4_udkey_B &-        ( tid1, isoiec_9798_4_4_udkey_B_3 ) : steps t &-        {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,-           s(MV ''Text2'' tid1), s(MV ''Text4'' tid1)-        |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''Ra'' tid0,-                s(MV ''Rb'' tid0), s(MV ''Text2'' tid0), s(MV ''Text4'' tid0)-             |})"+lemma (in restricted_isoiec_9798_4_4_udkey_state) A_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_4_4_udkey_A &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(MV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_4_4_udkey_A_3 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_4_4_udkey_B &+          ( tid1, isoiec_9798_4_4_udkey_B_3 ) : steps t &+          {| s(AV ''A'' tid1), s(AV ''B'' tid1), s(MV ''Ra'' tid1), LN ''Rb'' tid1,+             s(MV ''Text2'' tid1), s(MV ''Text4'' tid1)+          |} = {| s(AV ''A'' tid0), s(MV ''B'' tid0), LN ''Ra'' tid0,+                  s(MV ''Rb'' tid0), s(MV ''Text2'' tid0), s(MV ''Text4'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs") proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Hash {| {| LC ''CCF'', K ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) ) |},-                           LC ''isoiec_9798_4_4_ccf_3'', s(MV ''Rb'' tid0), LN ''Ra'' tid0,-                           s(MV ''Text4'' tid0)-                        |} ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_4_4_udkey_B_3_hash tid1) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Hash {| {| LC ''CCF'', K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid1) ) |},-                             LC ''isoiec_9798_4_4_ccf_2'', LN ''Ra'' tid0, LN ''Rb'' tid1,-                             s(MV ''Text2'' tid1)-                          |} ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest!: ltk_secrecy)-    next-      case (isoiec_9798_4_4_udkey_A_2_hash tid2) note_unified facts = this facts-      thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-    qed (insert facts, fastsimp+)?-  qed (insert facts, fastsimp+)?+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Hash {| {| LC ''CCF'', K ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) ) |},+                               LC ''isoiec_9798_4_4_ccf_3'', s(MV ''Rb'' tid0), LN ''Ra'' tid0,+                               s(MV ''Text4'' tid0)+                            |} ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_4_4_udkey_B_3_hash tid1) note_unified facts = this facts+        thus ?thesis proof(sources! "+                         Hash {| {| LC ''CCF'', K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid1) ) |},+                                 LC ''isoiec_9798_4_4_ccf_2'', LN ''Ra'' tid0, LN ''Rb'' tid1,+                                 s(MV ''Text2'' tid1)+                              |} ")+          case fake note_unified facts = this facts+          thus ?thesis by (fastforce dest!: ltk_secrecy)+        next+          case (isoiec_9798_4_4_udkey_A_2_hash tid2) note_unified facts = this facts+          thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+        qed (insert facts, fastforce+)?+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj) qed -lemma (in restricted_isoiec_9798_4_4_udkey_state) B_non_injective_agreement:-  assumes facts:-    "roleMap r tid0 = Some isoiec_9798_4_4_udkey_B"-    "RLKR(s(AV ''A'' tid0)) ~: reveals t"-    "RLKR(s(AV ''B'' tid0)) ~: reveals t"-    "( tid0, isoiec_9798_4_4_udkey_B_2 ) : steps t"-  shows-    "(?  tid1.-        roleMap r tid1 = Some isoiec_9798_4_4_udkey_A &-        ( tid1, isoiec_9798_4_4_udkey_A_2 ) : steps t &-        {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),-           s(MV ''Text2'' tid1)-        |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),-                LN ''Rb'' tid0, s(MV ''Text2'' tid0)-             |})"+lemma (in restricted_isoiec_9798_4_4_udkey_state) B_injective_agreement:+  "let+     prems =+       (% tid0.+          roleMap r tid0 = Some isoiec_9798_4_4_udkey_B &+          RLKR(s(AV ''A'' tid0)) ~: reveals t &+          RLKR(s(AV ''B'' tid0)) ~: reveals t &+          ( tid0, isoiec_9798_4_4_udkey_B_2 ) : steps t);+     concs =+       (% tid0 tid1.+          roleMap r tid1 = Some isoiec_9798_4_4_udkey_A &+          ( tid1, isoiec_9798_4_4_udkey_A_2 ) : steps t &+          {| s(AV ''A'' tid1), s(MV ''B'' tid1), LN ''Ra'' tid1, s(MV ''Rb'' tid1),+             s(MV ''Text2'' tid1)+          |} = {| s(AV ''A'' tid0), s(AV ''B'' tid0), s(MV ''Ra'' tid0),+                  LN ''Rb'' tid0, s(MV ''Text2'' tid0)+               |})+   in ? f. inj_on f (Collect prems) & (! i. prems i --> concs i (f i))"+  (is "let prems = ?prems; concs = ?concs in ?P prems concs") proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! "-                   Hash {| {| LC ''CCF'', K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) |},-                           LC ''isoiec_9798_4_4_ccf_2'', s(MV ''Ra'' tid0), LN ''Rb'' tid0,-                           s(MV ''Text2'' tid0)-                        |} ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest!: ltk_secrecy)-  next-    case (isoiec_9798_4_4_udkey_A_2_hash tid1) note_unified facts = this facts-    thus ?thesis by (fastsimp intro: event_predOrdI split: if_splits)-  qed (insert facts, fastsimp+)?+  { fix tid0 tid1+    assume facts: "?prems tid0"+    have " ? tid1. ?concs tid0 tid1"+    proof -+      note_unified facts = facts+      note_prefix_closed facts = facts+      thus ?thesis proof(sources! "+                       Hash {| {| LC ''CCF'', K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) |},+                               LC ''isoiec_9798_4_4_ccf_2'', s(MV ''Ra'' tid0), LN ''Rb'' tid0,+                               s(MV ''Text2'' tid0)+                            |} ")+        case fake note_unified facts = this facts+        thus ?thesis by (fastforce dest!: ltk_secrecy)+      next+        case (isoiec_9798_4_4_udkey_A_2_hash tid1) note_unified facts = this facts+        thus ?thesis by (fastforce intro: event_predOrdI split: if_splits)+      qed (insert facts, fastforce+)?+    qed+  }+  note niagree = this+  { fix i1 i2 j+    assume "?concs i1 j & ?concs i2 j"+    note_unified facts = this+    have "i1 = i2" using facts by simp+  }+  note conc_inj = this+  show ?thesis+    by (fast intro!: iagree_to_niagree elim!: niagree conc_inj) qed  end
data/isabelle/AUTHORS view
@@ -1,4 +1,8 @@-Simon Meier <meiersi@inf.ethz.ch>+Simon Meier <iridcode@gmail.com>++Port to Isabelle 2013:+----------------------+Andreas Lochbihler <andreas.lochbihler@inf.ethz.ch>  Student contributor: ---------------------
− data/isabelle/IsaMakefile 
@@ -1,31 +0,0 @@--## targets--default: ESPL-images: ESPL-test: --all: images test---## global settings--SRC = $(ISABELLE_HOME)/src-OUT = $(ISABELLE_OUTPUT)-LOG = $(OUT)/log--USEDIR = $(ISABELLE_TOOL) usedir -v true -i true ## -d pdf  ## -D generated---## ESPL--ESPL: $(OUT)/ESPL--$(OUT)/ESPL: ## ROOT.ML document/root.tex src/*.thy src/ESPLogic/*.thy src/ESPLogic/*.ML-	@$(USEDIR) -b -P http://isabelle.in.tum.de/library HOL ESPL---## clean--clean:-	@rm -f $(OUT)/ESPL
data/isabelle/Makefile view
@@ -26,12 +26,11 @@  # The following commands require #-#   a working installation of Isabelle2009-1+#   a working installation of Isabelle2013 #   (http://www.cl.cam.ac.uk/research/hvg/Isabelle/). #  # build an image of the ESPL formalization in Isabelle. This is required for # the 'scyther-proof --isabelle' switch to work. espl-image:-	isabelle make clean-	isabelle make+	isabelle build -cb -d . ESPL
data/isabelle/README view
@@ -1,10 +1,9 @@ README: The scyther-proof security protocol verification tool ============================================================= -Author: Simon Meier <simon.meier@inf.ethz.ch>--Creation Date: 13/05/2011  --  Last Updated:  28/06/2012-+Authors: Simon Meier <iridcode@gmail.com>+Creation Date: 2011-05-13+Last Updated:  2013-02-27 by Andreas Lochbihler <andreas.lochbihler@inf.ethz.ch>  1. Introduction ===============@@ -56,42 +55,48 @@ 2.2 Installing the Isabelle/HOL theories ---------------------------------------- -Download and install full Isabelle2009-1 according to the installation+Download and install full Isabelle2013 according to the installation instructions at -    http://isabelle.in.tum.de/website-Isabelle2009-1/download_x86-linux.html+    http://isabelle.in.tum.de/website-Isabelle2013/download_x86-linux.html  The first time you call `scyther-proof` with the `--isabelle` flag it will build the logic image of the Isabelle/HOL theories formalizing the security protocol verification theory underlying `scyther-proof`. -For enabling interactive processing of theory files based using our-extensions to Isabelle's ISAR proof language use one of the following two-variants.+If you wish to use ProofGeneral to interactively process the theory files+using our extensions to Isabelle's ISAR proof language, use one of the+following two variants. This is needed in order to make the new ISAR keywords+`role`, `protocol`, `sources`, and `prefix_close` available in the Emacs+frontend. If you are using the Isabelle/jEdit Prover IDE, the keywords are+automatically registered. + Variant a: Brute Force ---------------------- -Overwrite the standard Emacs keywords file+Copy the Emacs keywords file provided with the ESPL distribution at -    $ISABELLE_HOME/etc/isar-keywords.el+    $SCYTHER_PROOF_HOME/data/isabelle/src/isar-keywords.el -with the Emacs keywords file provided with the ESPL distribution.+to your local Isabelle configuration in -    $SCYTHER_PROOF_HOME/isabelle/src/isar-keywords.el+    $ISABELLE_HOME_USER/etc -This is needed in order to make the new ISAR keywords `role`,-`protocol`, `sources`, and `prefix_close` available in the Emacs-frontend.+This will replace any custom keyword file that you have already+installed in that way. You can find out about $ISABELLE_HOME_USER+by running +    isabelle getenv ISABELLE_HOME_USER + Variant b: Elegance -------------------  A more elegant way is to copy the keywords file provided with our distribution to -    $ISABELLE_HOME/etc/isar-keywords-ESPL.el+    $ISABELLE_HOME_USER/etc/isar-keywords-ESPL.el  and start Isabelle using the -k switch as follows. @@ -104,7 +109,7 @@   3.1 scyther-proof-------------+-----------------     Usage Example@@ -120,15 +125,13 @@   all specified security properties together with the proof with the fewest   number of chain rule applications to stdout. -  In order to generate an Isabelle proof script two additional options need to-  be added+  To generate an Isabelle proof script, two additional options are required.      scyther-proof $EXAMPLE_DIR/classic/NS_Public.spthy --shortest --output=nsl_cert.thy --ASCII    The first one specifies the output file and the second one instructs   scyther-proof to use Isabelle's ASCII notation as the output format. -   To build the source code documentation you can use the call      cabal configure; cabal haddock@@ -141,25 +144,40 @@ 3.2 The Isabelle/HOL theories ----------------------------- +   Note that in many case the easiest way to start with constructing+   machine-checked proofs interactively is to use a proof script generated by+   scyther-proof.++   Using ProofGeneral+   ------------------+    In the directory output by scyther-proof, load the Tutorial on interactive    proof construction using the following commands          cd <theory-dir-output-by-scytherproof>/src         isabelle emacs Tutorial.thy -    or if you've chosen the elegant variant+    or if you've chosen the elegant variant for the keywords file          isabelle emacs -k ESPL Tutorial.thy -   Note that in many case the easiest way to start with constructing-   machine-checked proofs interactively is to use a proof script generated by-   scyther-proof. +   Using the Isabelle/jEdit Prover IDE+   ----------------------------------- +   In the directory output by scyther-proof, load the Tutorial on interactive+   proof construction using the following commands++        cd <theory-dir-output-by-scytherproof>/src+        isabelle jedit -d $SCYTHER_PROOF_HOME/data/isabelle -l ESPL Tutorial.thy++   where $SCYTHER_PROOF_HOME expands to the home directory of scyther-proof.++ ***  `Happy Proving :)` -In case of questions do not hesistate to contact me at+In case of questions do not hesistate to contact Simon Meier at iridcode@gmail.com.
+ data/isabelle/ROOT view
@@ -0,0 +1,2 @@+session ESPL = HOL ++  theories "src/ESPLogic"
− data/isabelle/ROOT.ML 
@@ -1,1 +0,0 @@-use_thy "src/ESPLogic"
data/isabelle/src/ESPLogic/Automation.thy view
@@ -15,11 +15,13 @@   Syntax   InferenceRules   WeakTyping-uses-  espl_definitions-  espl_methods+keywords "role" "protocol" "type_invariant" :: thy_decl+  and "prefix_close" :: prf_decl begin +ML_file "espl_definitions.ML"+ML_file "espl_methods.ML"+ section{* Automation *}  subsection{* Setup of ISAR commands *}@@ -153,235 +155,5 @@     "(LKR (Lit (EveNonce i))) \<prec> e \<Longrightarrow> False"   "e \<prec> (LKR (Lit (EveNonce i))) \<Longrightarrow> False" by(auto dest: predOrd_LKR_agent1 predOrd_LKR_agent2)---subsection{* Testing the Infrastructure *}---(*-text{*-  Commented out because new ISAR syntax comes only active after-  the theory file that defines them.-*}--role C-where "C =-  [ Send ''1'' ( PEnc ( sN ''k'' ) ( sPK ''S'' ) )-  , Recv ''2'' ( PHash ( sN ''k'' ) )-  , Note ''3'' SessKey (sN ''k'')-  ]"--role S-where "S =-  [ Recv ''1'' ( PEnc ( sMV ''k'' ) ( sPK ''S'' ) )-  , Send ''2'' ( PHash ( sMV ''k'' ) )-  ]"--protocol CR-where "CR = { C, S }"--locale restricted_CR_state = CR_state--type_invariant auto_msc_typing for CR-where "auto_msc_typing = mk_typing-  [ ((S, ''k''), (SumT (KnownT S_1) (NonceT C ''k'')))-  ]"---lemma additional_reveal_order:-  assumes facts:-    "predOrd t (LKR a) c"-  shows -    "a \<in> lkreveals t \<and> predOrd t (LKR a) c"-using facts-by(auto intro: event_predOrdI)--sublocale CR_state < auto_msc_typing_state-proof --  have "(t,r,s) : approx auto_msc_typing"-  proof(cases rule: reachable_in_approxI_ext-        [OF auto_msc_typing.monoTyp, completeness_cases_rule])-    case (S_1_k t r s tid0) note facts = this-    then interpret state: auto_msc_typing_state t r s-      by unfold_locales auto-    show ?case using facts-    proof(sources! "-        Enc ( s(MV ''k'' tid0) ) ( PK ( s(AV ''S'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits) | (fastsimp intro: event_predOrdI split: if_splits))+)?-  qed-  thus "auto_msc_typing_state t r s" by unfold_locales auto-qed--lemma (in restricted_CR_state) C_k_order_raw:-   assumes facts:-     "roleMap r tid0 = Some C"-   shows-     "LN ''k'' tid0 \<in> knows t \<longrightarrow>-     (LKR (s(AV ''S'' tid0))) \<prec> (Ln (LN ''k'' tid0)) \<or> -     (St (tid0, C_3) \<prec> (Ln (LN ''k'' tid0)))" -     (is "?knows \<longrightarrow> ?order")-proof-  assume "?knows"-  thus "?order" using facts-  proof (sources "LN ''k'' tid0")-    case C_1_k-    thus ?thesis-      by (sources "SK (s (AV ''S'' tid0))")  (fastsimp intro: event_predOrdI)+-  qed auto-qed--(*-lemmas (in restricted_CR_state) C_k_order = C_k_order_raw[rule_format, THEN additional_reveal_order]-*)--lemma (in restricted_CR_state) C_k_secrecy:-  assumes facts:-    "roleMap r tid0 = Some C"-    "s(AV ''S'' tid0) ~: lkreveals t"-    "(tid0, C_3) \<notin> steps t"-    "LN ''k'' tid0 : knows t"-  shows "False"-using facts -by(fastsimp dest: C_k_order_raw[rule_format] -           intro: event_predOrdI)---*)---(*-text{*-  Commented out because new ISAR syntax comes only active after-  the theory file that defines them.-*}--text{* Testing the role definition command *}-role I-where "I \<equiv> -  [ Send ''0'' (PEnc \<langle>sLC ''0'', sAV ''I'', sN ''ni''\<rangle> (sPK ''R''))-  , Recv ''1'' (PEnc \<langle>sLC ''1'', sAV ''R'', sN ''ni'', sMV ''nr''\<rangle> (sPK ''I''))-  , Send ''2'' (PEnc \<langle>sLC ''2'', sMV ''nr''\<rangle> (sPK ''R''))-  ]"--text{* A few of the proven theorems: *}-thm I.weakly_atomic_convs-thm I_def-thm I.unfold-thm I.wf_role-thm I.distinct_steps-thm I.in_set_conv-thm I.zip_conv-thm I.prefixClose_convs--thm I_1_def-thm I_1.unfold-thm I_1_pt_def-thm I_1.inst_conv-thm I_1.sendStep_conv-thm I_1.stepPat_conv-thm I_1.FV_conv-thm I_1.FMV_conv--text{* -  Note that you should not need to use these theorems manually as the -  simplifier and the classical reasoner are already setup such that-  they are used when appropriate.--  The general design idea behind the rules is such that wherever possible-  constants are not unfolded, as this simplifies proof states.-*}--text{* An additional role for testing purposes. *}-role R-where "R \<equiv>-  [ Recv ''0'' (PEnc \<langle>sLC ''0'', sLAV ''I'', sLMV ''ni''\<rangle> (sPK ''R''))-  , Send ''1'' (PEnc \<langle>sLC ''1'', sLAV ''R'', sLMV ''ni'', sLN ''nr''\<rangle> (sPK ''I''))-  , Recv ''2'' (PEnc \<langle>sLC ''2'', sLN ''nr''\<rangle> (sPK ''R''))-  ]"--thm R.weakly_atomic_convs--protocol nsl-where "nsl = {I, R}"--text{* Testing the protocol definition command; the generated theorems: *}-thm nsl_def-thm nsl.unfold-thm nsl.wf_proto-thm nsl.distinct_roles-thm nsl.in_set_conv--type_invariant typed_nsl for nsl-where "typed_nsl = mk_typing-   [ ((R, ''ni''), (SumT (KnownT R_0) (NonceT I ''ni'')))-   , ((I, ''nr''), (SumT (KnownT I_1) (NonceT R ''nr'')))-   ]"---sublocale nsl_state \<subseteq> typed_nsl_state-proof --  have "(t,r,s) \<in> approx typed_nsl"-  proof(cases rule: reachable_in_approxI_ext-                    [OF typed_nsl.monoTyp, completeness_cases_rule])-    case (I_1_nr t r s i)-    then interpret state: typed_nsl_state t r s-      by unfold_locales auto-    show ?case using I_1_nr-    proof(sources "inst s i I_1_pt")-    qed (fastsimp intro: event_predOrdI split: if_splits)+-  next-    case (R_0_ni t r s i)-    then interpret state: typed_nsl_state t r s-      by unfold_locales auto-    show ?case using R_0_ni-    proof(sources "inst s i R_0_pt")-    qed (fastsimp intro: event_predOrdI split: if_splits)+-  qed-  thus "typed_nsl_state t r s" by unfold_locales auto-qed--context nsl_state begin-  lemma longterm_private_key_secrecy:-    assumes facts:-      "SK m : knows t"-      "m ~: Compromised"-    shows "False"-  using facts by (sources "SK m")--  lemma longterm_shared_key_secrecy:-    assumes facts:-      "K m1 m2 : knows t"-      "m1 ~: Compromised"-      "m2 ~: Compromised"-    shows "False"-  using facts by (sources "K m1 m2")--  lemmas ltk_secrecy =-    longterm_shared_key_secrecy-    longterm_shared_key_secrecy[OF in_knows_predOrd1]-    longterm_private_key_secrecy-    longterm_private_key_secrecy[OF in_knows_predOrd1]-end--lemma (in nsl_state) I_ni_secrecy:-  assumes facts:-    "roleMap r i = Some I"-    "LN ''ni'' i \<in> knows t"-    "s (AV ''I'' i) \<notin> lkreveals t"-    "s (AV ''R'' i) \<notin> lkreveals t"   -  shows "False"-using facts proof(sources " LN ''ni'' tid0 ")-  case I_0_ni thus ?thesis by (fastsimp dest!: ltk_secrecy)-next-  case (R_1_ni tid1) thus ?thesis -  proof(sources "inst s tid1 R_0_pt")-    case I_0_enc thus ?thesis -      by (fastsimp dest!: ltk_secrecy)-  qed (insert facts, (((clarsimp, order?) | order))+)?-qed---*)-  end
data/isabelle/src/ESPLogic/Capabilities.thy view
@@ -19,7 +19,7 @@ chapter{* Compromising Adversary Capability *}  section{* Partnering *}-types partnering = "state \<Rightarrow> (tid \<times> tid) set"+type_synonym partnering = "state \<Rightarrow> (tid \<times> tid) set"   definition unionPart :: "partnering \<Rightarrow> partnering \<Rightarrow> partnering" (infix "UNP" 65)@@ -31,7 +31,7 @@  lemma union_unionPart_conv:   "(a \<in> ((P1 \<union>\<^isub>P P2) q)) = (a \<in> (P1 q \<union> P2 q))"-by (fastsimp simp add: unionPart_def)+by (fastforce simp add: unionPart_def)   definition mk_partnering :: "role \<Rightarrow> role \<Rightarrow> (pattern \<times> pattern \<times> rolestep) set \<Rightarrow> partnering"@@ -44,10 +44,10 @@  "((i,j) \<in> mk_partnering R1 R2 conds (t,r,s)) =     (roleMap r i = Some R1 \<and> roleMap r j = Some R2 \<and>     (\<forall> (p1,p2,st) \<in> conds. (j,st) \<in> steps t \<longrightarrow> (inst s i p1) = (inst s j p2)))"-by (fastsimp simp add: mk_partnering_def)+by (fastforce simp add: mk_partnering_def)  lemma setEqImpTupleIn: "(X = Y) \<Longrightarrow> ((i,j) \<in> X) = ((i,j) \<in> Y)"-by fastsimp+by fastforce  lemma uniquePartner:    assumes facts:@@ -59,15 +59,15 @@     "\<forall> j'. (i,j') \<in> mk_partnering R1 R2 conds (t,r,s) \<and> (j',st) \<in> steps t \<longrightarrow> j' = j" proof -   have "inst s i pt1 = inst s j pt2"-    using facts by (fastsimp simp add: mk_partnering_conv)+    using facts by (fastforce simp add: mk_partnering_conv)   moreover    hence "\<forall> j'. j' \<noteq> j \<longrightarrow> inst s j pt2 \<noteq> inst s j' pt2"-    using facts by fastsimp+    using facts by fastforce   ultimately    have "\<forall> j'. j' \<noteq> j \<longrightarrow> inst s i pt1 \<noteq> inst s j' pt2"-    by fastsimp+    by fastforce   hence "\<forall> j'. (j' \<noteq> j \<and> (j',st) \<in> steps t) \<longrightarrow>  (i,j') \<notin> mk_partnering R1 R2 conds (t,r,s)"-    using facts by (fastsimp simp add: mk_partnering_conv)+    using facts by (fastforce simp add: mk_partnering_conv)   thus ?thesis     by auto qed@@ -78,11 +78,11 @@   shows    "roleMap r i = Some R1 \<and> roleMap r j = Some R2" using facts-by (fastsimp simp add: mk_partnering_conv)+by (fastforce simp add: mk_partnering_conv)  section{* Capabilities *} -types capability = "state \<Rightarrow> reveal set"+type_synonym capability = "state \<Rightarrow> reveal set"  subsection{* Helper Functions *} definition interCap :: "capability \<Rightarrow> capability \<Rightarrow> capability" (infix "INC" 65)@@ -101,11 +101,11 @@  lemma union_unionCap_conv:   "(a \<in> ((C1 \<union>\<^isub>C C2) q)) = (a \<in> (C1 q \<union> C2 q))"-by (fastsimp simp add: unionCap_def)+by (fastforce simp add: unionCap_def)  lemma inter_interCap_conv:   "(a \<in> ((C1 \<inter>\<^isub>C C2) q)) = (a \<in> (C1 q \<inter> C2 q))"-by (fastsimp simp add: interCap_def)+by (fastforce simp add: interCap_def)   subsection{* Adversary-Compromise Model *}@@ -119,13 +119,13 @@   (t,r,s) \<in> acm caps ;    reveal \<in> reveals t   \<rbrakk> \<Longrightarrow> \<exists> cap \<in> caps. reveal \<in> cap (t,r,s)"-by(fastsimp simp add: acm_def)+by(fastforce simp add: acm_def)   lemma acm_monotone: "\<lbrakk> (t,r,s) \<in> acm caps \<rbrakk>   \<Longrightarrow> (t,r,s) \<in> acm (caps \<union> caps')"-by(fastsimp simp add: acm_def)+by(fastforce simp add: acm_def)  subsection{* Implementation of Capabilities and Dot-Mapping *} @@ -183,7 +183,7 @@   "RCompr a b \<notin> LKRactor i c (t,r,s)"   "RCompr a b \<notin> LKRafter i (t,r,s)"   "RCompr a b \<notin> LKRafterCorrect i ps(t,r,s)"-by(fastsimp)++by(fastforce)+   subsubsection{* Compromises *}@@ -230,20 +230,20 @@   "RCompr RandGen j \<notin> SkR i ps q"   "RCompr State j \<notin> RNR q"   "RCompr SessKey j \<notin> RNR q"-by(fastsimp simp add: StR_def SkR_def RNR_def)++by(fastforce simp add: StR_def SkR_def RNR_def)+   lemma SkR_conv[simp]:   "c \<in> SkR i ps (t,r,s) = (\<exists> j. (c = RCompr SessKey j) \<and> (i,j) \<notin> ps (t,r,s) \<and> j \<noteq> i )"-by(fastsimp simp add: SkR_def)+by(fastforce simp add: SkR_def)  lemma RNR_conv[simp]:   "c \<in> RNR (t,r,s) = (\<exists> j. (c = RCompr RandGen j))"-by(fastsimp simp add: RNR_def)+by(fastforce simp add: RNR_def)  lemma StR_conv[simp]:   "c \<in> StR i ps (t,r,s) = (\<exists> j. (c = RCompr State j) \<and> (i,j) \<notin> ps (t,r,s) \<and> j \<noteq> i )"-by(fastsimp simp add: StR_def)+by(fastforce simp add: StR_def)   lemma (in reachable_state) LKRafterTrans:@@ -253,6 +253,6 @@     RLKR a \<in> LKRafter i (t,r,s);     LKR a \<prec> St (i,st)    \<rbrakk> \<Longrightarrow> False"-by(fastsimp)+by(fastforce)  end
data/isabelle/src/ESPLogic/DistinctList.thy view
@@ -210,10 +210,10 @@   by(auto dest: next_imp_less)  lemma in_set_less1: "x \<prec> y \<Longrightarrow> x \<in> set xs"-  by(simp add: pred_def in_set_listOrd1)+  by(simp add: in_set_listOrd1)  lemma in_set_less2: "x \<prec> y \<Longrightarrow> y \<in> set xs"-  by(simp add: pred_def in_set_listOrd2)+  by(simp add: in_set_listOrd2)  lemmas in_set_next1 = in_set_less1[OF next_imp_less, rule_format] lemmas in_set_next2 = in_set_less2[OF next_imp_less, rule_format]
data/isabelle/src/ESPLogic/ExecMessage.thy view
@@ -43,7 +43,7 @@  translations   "{|x, y, z|}"   == "{|x, {|y, z|}|}"-  "{|x, y|}"      == "Tup x y"+  "{|x, y|}"      == "(CONST Tup) x y"   text{* @@ -85,7 +85,7 @@ lemma Kbd_split_inj:   "\<lbrakk> a \<in> Agent; b \<in> Agent; x \<in> Agent; y \<in> Agent \<rbrakk> \<Longrightarrow>    (Kbd a b = Kbd x y) = (a = x \<and> b = y \<or> a = y \<and> b = x)"-  apply(clarsimp simp: Kbd_def Agent_def agents_def expand_set_eq) +  apply(clarsimp simp: Kbd_def Agent_def agents_def set_eq_iff)    apply(rule iffI)   apply(rename_tac a b x y)   apply(safe)@@ -126,7 +126,7 @@  subsection{* Operations *} -types store = "varid \<times> tid \<Rightarrow> execmsg"+type_synonym store = "varid \<times> tid \<Rightarrow> execmsg"  fun inv :: "execmsg \<Rightarrow> execmsg" where
data/isabelle/src/ESPLogic/ExplicitModel.thy view
@@ -34,9 +34,9 @@   RCompr notetype tid | RLKR execmsg -types explicit_trace = "rawevent list"-types execstep = "tid \<times> rolestep"-types threadpool = "tid \<rightharpoonup> (rolestep list \<times> rolestep list \<times> rolestep set)"+type_synonym explicit_trace = "rawevent list"+type_synonym execstep = "tid \<times> rolestep"+type_synonym threadpool = "tid \<rightharpoonup> (rolestep list \<times> rolestep list \<times> rolestep set)"  fun knows :: "explicit_trace \<Rightarrow> execmsg set" where@@ -109,7 +109,7 @@   by (auto simp: longTermKeys_def)  -types state = "explicit_trace \<times> threadpool \<times> store"+type_synonym state = "explicit_trace \<times> threadpool \<times> store"  inductive_set    reachable :: "proto \<Rightarrow> state set" @@ -208,7 +208,7 @@ lemma role_in_P:  "done @ todo \<in> P" using thread_exists proof (induct arbitrary: i "done" todo skipped rule: reachable_induct)-qed (fastsimp split: if_splits)++qed (fastforce split: if_splits)+  end @@ -297,7 +297,7 @@  lemma RCompr_steps_conv:   "RCompr ty i \<in> reveals t = (\<exists> l pt. (i, Note l ty pt) \<in> steps t)"-by (fastsimp intro: reveals_to_steps steps_to_reveals)+by (fastforce intro: reveals_to_steps steps_to_reveals)  context reachable_thread begin@@ -330,7 +330,7 @@ using thread_exists proof(induct arbitrary: i "done" todo skipped rule: reachable_induct)   case init-  thus "?case" by fastsimp+  thus "?case" by fastforce qed( auto split: if_splits)  @@ -348,7 +348,7 @@ using thread_exists using distinct proof(induct arbitrary: i "done" todo skipped rule: reachable_induct)-  case init thus ?case by fastsimp+  case init thus ?case by fastforce next    case (send t r s i "done" l pt todo skipped m i' done' todo' skipped')   thus ?case@@ -357,8 +357,8 @@     then interpret thread:        reachable_thread P t r s i "done" "Send l pt # todo" skipped'       using send by unfold_locales auto-    thus ?thesis -      using send `i = i'` by fastsimp +    show ?thesis +      using send `i = i'` by fastforce    qed auto next   case (recv t r s i "done" l pt todo skipped m i' done' todo' skipped')@@ -368,8 +368,8 @@     then interpret thread:        reachable_thread P t r s i "done" "Recv l pt # todo" skipped'       using recv by unfold_locales auto-    thus ?thesis -      using recv `i = i'` by fastsimp +    show ?thesis +      using recv `i = i'` by fastforce   qed auto next   case (compr t r s i "done" l ty pt todo skipped m i' done' todo' skipped')  @@ -382,8 +382,8 @@       interpret thread:         reachable_thread P t r s i "done" "Note l ty pt # todo" skipped'         using compr  `i = i'` by unfold_locales auto-      thus ?thesis using compr  `i = i'` `step = Note l ty pt` by (fastsimp dest: thread.skipped_in_done )-    qed fastsimp+      show ?thesis using compr  `i = i'` `step = Note l ty pt` by (fastforce dest: thread.skipped_in_done )+    qed fastforce   qed auto next   case(skip t r s i "done" l ty pt todo skipped i' done' todo' skipped')@@ -396,8 +396,8 @@       interpret thread:         reachable_thread P t r s i "done" "Note l ty pt # todo" skipped         using skip  `i = i'` by unfold_locales auto-      thus ?thesis using skip  `i = i'` `step = Note l ty pt` by fastsimp-    qed fastsimp+      show ?thesis using skip  `i = i'` `step = Note l ty pt` by fastforce+    qed fastforce  qed auto qed auto @@ -406,7 +406,7 @@ using thread_exists proof(induct arbitrary: i "done" todo skipped rule rule: reachable_induct)   case init-    thus "?case" by fastsimp+    thus "?case" by fastforce qed ((unfold map_upd_Some_unfold)?, auto)+  lemma in_steps_send:@@ -414,7 +414,7 @@ using thread_exists proof(induct arbitrary: i "done" todo skipped rule rule: reachable_induct)   case init-    thus "?case" by fastsimp+    thus "?case" by fastforce qed ((unfold map_upd_Some_unfold)?, auto)+  lemmas send_steps_in_done [elim!] = iffD1[OF in_steps_send, rule_format]@@ -444,13 +444,13 @@   "step \<in> set todo \<Longrightarrow> step \<notin> skipped" using distinct using role_in_P-by(fastsimp dest: skipped_in_done)+by(fastforce dest: skipped_in_done)  lemma skipped_notin_todoD:   "step \<in> skipped \<Longrightarrow> step \<notin> set todo" using distinct using role_in_P-by(fastsimp dest: skipped_in_done)+by(fastforce dest: skipped_in_done)  lemma notin_steps_notin_trace:   "(i, step) \<notin> steps t \<Longrightarrow> (Step (i, step)) \<notin> set t"@@ -463,13 +463,13 @@     "step \<in> set done" proof(cases step)   case (Send l pt)-    thus ?thesis using inSteps by (fastsimp dest: in_steps_send[THEN iffD2])+    thus ?thesis using inSteps by (fastforce dest: in_steps_send[THEN iffD2]) next   case (Recv l pt)-    thus ?thesis using inSteps by (fastsimp dest: in_steps_recv[THEN iffD2])+    thus ?thesis using inSteps by (fastforce dest: in_steps_recv[THEN iffD2]) next   case (Note l ty pt)-    thus ?thesis using inSteps by (fastsimp simp add: in_steps_conv_done_skipped)+    thus ?thesis using inSteps by (fastforce simp add: in_steps_conv_done_skipped) qed  @@ -483,7 +483,7 @@  lemma[dest]:   "\<lbrakk> step \<in> set todo; step \<in> set done \<rbrakk> \<Longrightarrow> False"-by(fastsimp dest: todo_notin_doneD)+by(fastforce dest: todo_notin_doneD)  lemma[dest]:   "\<lbrakk> step \<in> set todo; step \<in> skipped \<rbrakk> \<Longrightarrow> False"@@ -509,7 +509,7 @@ proof(induct arbitrary: i "done" todo skipped rule: reachable_induct)   case (init r s i "done" todo)    thus ?case-    by fastsimp+    by fastforce next   case (send t r s i "done" l msg todo skipped m i' done' todo' skipped')   thus ?case using send @@ -518,9 +518,9 @@       interpret this_thread:           reachable_thread P t r s i' "done" "Send l msg # todo'" skipped'           using send `i = i'` by unfold_locales auto-       thus ?thesis using send `i = i'`-          by fastsimp-  qed fastsimp+       show?thesis using send `i = i'`+          by fastforce+  qed fastforce next   case (recv t r s i "done" l msg todo skipped m i' done' todo' skipped')   from recv show ?case @@ -529,9 +529,9 @@       interpret this_thread:           reachable_thread P t r s i' "done" "Recv l msg # todo'" skipped'           using recv `i = i'` by unfold_locales auto-       thus ?thesis using recv `i = i'`-          by fastsimp-  qed fastsimp+       show ?thesis using recv `i = i'`+          by fastforce+  qed fastforce next   case (compr t r s i "done" l ty msg todo skipped m i' done' todo' skipped')   from compr show ?case @@ -540,9 +540,9 @@       interpret this_thread:           reachable_thread P t r s i' "done" "Note l ty msg # todo'" skipped'           using compr `i = i'` by unfold_locales auto-       thus ?thesis using compr `i = i'`-          by fastsimp-  qed fastsimp+       show ?thesis using compr `i = i'`+          by fastforce+  qed fastforce next   case (skip t r s i "done" l ty msg todo skipped i' done' todo' skipped')    from skip show ?case @@ -551,9 +551,9 @@     then interpret this_thread:       reachable_thread P t r s i "done" "Note l ty msg # todo" skipped       using skip `i = i'` by unfold_locales auto-    thus ?thesis using skip `i = i'`-      by fastsimp-  qed fastsimp+    show ?thesis using skip `i = i'`+      by fastforce+  qed fastforce qed auto  lemma listOrd_recv_role_imp_listOrd_trace:@@ -695,21 +695,21 @@     reachable_thread P t r s i "done" "Recv l msg # todo" skipped     by unfold_locales auto   show ?case using  `distinct' t` this_thread.distinct-    by(fastsimp dest: this_thread.in_steps_in_done)+    by(fastforce dest: this_thread.in_steps_in_done) next   case (send t r s i "done" l msg todo skipped m)   then interpret this_thread:      reachable_thread P t r s i "done" "Send l msg # todo" skipped     by unfold_locales auto   show ?case using `distinct' t` and this_thread.distinct-    by(fastsimp dest: this_thread.in_steps_in_done)+    by(fastforce dest: this_thread.in_steps_in_done) next   case (compr t r s i "done" l ty msg todo skipped m)   then interpret this_thread:       reachable_thread P t r s i "done" "Note l ty msg # todo" skipped      by unfold_locales auto   show ?case using `distinct' t` and this_thread.distinct-     by(fastsimp dest: this_thread.in_steps_in_done)+     by(fastforce dest: this_thread.in_steps_in_done) next   case (skip t r s i "done" l ty msg todo skipped)   then interpret this_thread: @@ -827,7 +827,7 @@   "\<lbrakk>predOrd t (St a) (LKR d);   \<lbrakk> a \<in> steps t; RLKR d \<in> reveals t     \<rbrakk> \<Longrightarrow> R \<rbrakk> \<Longrightarrow> R"   "\<lbrakk>predOrd t (Ln x) (LKR d);   \<lbrakk> x \<in> knows t; RLKR d \<in> reveals t     \<rbrakk> \<Longrightarrow> R \<rbrakk> \<Longrightarrow> R"   "\<lbrakk>predOrd t (LKR c) (LKR d);  \<lbrakk> RLKR c \<in> reveals t; RLKR d \<in> reveals t \<rbrakk> \<Longrightarrow> R \<rbrakk> \<Longrightarrow> R"-  by(fastsimp intro: event_predOrdI compr_predOrdI)++  by(fastforce intro: event_predOrdI compr_predOrdI)+   lemma predOrd_LKR_agent1:@@ -1047,7 +1047,7 @@ next   case decr thus ?case by(auto dest: pairParts_idemD) next-  case tuple thus ?case by fastsimp+  case tuple thus ?case by fastforce next   case lkr thus ?case by(auto simp: longTermKeys_def) next@@ -1070,37 +1070,37 @@   then interpret s1: reachable_state P t r s     by unfold_locales   from hash show ?case-    by (fastsimp dest: s1.rev_knows_pairParts_closedD)+    by (fastforce dest: s1.rev_knows_pairParts_closedD) next   case (encr t r s msg key)   then interpret s1: reachable_state P t r s     by unfold_locales   from encr show ?case-    by (fastsimp dest: s1.rev_knows_pairParts_closedD)+    by (fastforce dest: s1.rev_knows_pairParts_closedD) next   case (tuple t r s msg1 msg2)   then interpret s1: reachable_state P t r s     by unfold_locales   from tuple show ?case-    by (fastsimp dest: s1.rev_knows_pairParts_closedD)+    by (fastforce dest: s1.rev_knows_pairParts_closedD) next   case (decr t r s msg key)   then interpret s1: reachable_state P t r s     by unfold_locales   from decr show ?case-    by (fastsimp dest: s1.rev_knows_pairParts_closedD)+    by (fastforce dest: s1.rev_knows_pairParts_closedD) next   case (send t r s i "done" l msg todo msg)   then interpret s1: reachable_state P t r s     by unfold_locales   from send show ?case-    by (fastsimp dest: s1.rev_knows_pairParts_closedD)+    by (fastforce dest: s1.rev_knows_pairParts_closedD) next   case (recv t r s i "done" l msg todo)   then interpret s1: reachable_state P t r s     by unfold_locales   from recv show ?case-    by (fastsimp dest: s1.rev_knows_pairParts_closedD)+    by (fastforce dest: s1.rev_knows_pairParts_closedD) next   case (init r s) thus ?case by simp next@@ -1108,25 +1108,25 @@   then interpret s1: reachable_state P t r s     by unfold_locales   from lkr show ?case-   by (fastsimp dest: s1.rev_knows_pairParts_closedD)+   by (fastforce dest: s1.rev_knows_pairParts_closedD) next   case (skip t r s i "done" l ty pt todo)   then interpret s1: reachable_state P t r s      by unfold_locales   from skip show ?case-    by(fastsimp dest: s1.rev_knows_pairParts_closedD)+    by(fastforce dest: s1.rev_knows_pairParts_closedD) next   case (compr t r s i "done" l ty pt todo skipped m)   then interpret s1: reachable_state P t r s     by unfold_locales   from compr show ?case-    by(fastsimp dest: s1.rev_knows_pairParts_closedD)+    by(fastforce dest: s1.rev_knows_pairParts_closedD) qed  lemma Ln_before_inp:   "(i, Recv l pt) \<in> steps t \<Longrightarrow>     \<exists> m. Some m = inst s i pt \<and> Ln m \<prec> St (i, Recv l pt)"-  by (induct arbitrary: i l pt rule: reachable_induct) fastsimp++  by (induct arbitrary: i l pt rule: reachable_induct) fastforce+  lemma Ln_before_inpE:   "\<lbrakk> (i, Recv l pt) \<in> steps t;@@ -1144,11 +1144,11 @@  lemma split_before:   "Ln (Tup m m') \<prec> y \<Longrightarrow> Ln m \<prec> y \<and> Ln m' \<prec> y"-  by (fastsimp intro: pairParts_before)+  by (fastforce intro: pairParts_before)  lemma split_knows:   "Tup m m' \<in> knows t \<Longrightarrow> m \<in> knows t \<and> m' \<in> knows t"-  by (fastsimp intro: knows_pairParts_closedD)+  by (fastforce intro: knows_pairParts_closedD) end  subsection{* Case Distinction on Learning Messages *}@@ -1207,7 +1207,7 @@     hence "?case"     proof(cases "m' = Enc m k")       case True thus ?thesis-	using `?here` Enc by fastsimp+	using `?here` Enc by fastforce     next       case False thus ?thesis 	using `?here` Enc@@ -1217,7 +1217,7 @@   moreover   { assume "?nested"     hence "?case" using Enc-      by (fastsimp dest!: Enc(2))+      by (fastforce dest!: Enc(2))   }   ultimately show ?case by fast qed auto@@ -1257,17 +1257,17 @@     (is "?ik0 \<or> ?hash \<or> ?enc \<or> ?tup \<or> ?chain t r s \<or> ?note t r s \<or> ?keys")     moreover     { assume "?ik0"  hence "?thesis" by blast }    moreover-    { assume "?hash" hence "?thesis" by fastsimp } moreover-    { assume "?enc"  hence "?thesis" by fastsimp } moreover-    { assume "?tup"  hence "?thesis" by fastsimp } moreover+    { assume "?hash" hence "?thesis" by fastforce } moreover+    { assume "?enc"  hence "?thesis" by fastforce } moreover+    { assume "?tup"  hence "?thesis" by fastforce } moreover     { assume "?chain t r s"       hence "?chain (t@t') r s" -	by (fastsimp intro!: decrChain_append)+	by (fastforce intro!: decrChain_append)       hence "?thesis" by blast     } moreover     { assume "?note t r s"       hence "?note (t@t') r s" -	by (fastsimp intro!: decrChain_append)+	by (fastforce intro!: decrChain_append)       hence "?thesis" by blast     } moreover     { assume "?keys" hence "?thesis" by auto }@@ -1284,14 +1284,14 @@     let ?t' = "t @ [Learns {Hash m}]"     note IH = hash(2)     have "m' \<in> knows t \<or> m' = Hash m" (is "?old \<or> ?new")-      using hash by fastsimp+      using hash by fastforce     moreover     { assume "?new" hence ?case -	using `m \<in> knows t` by fastsimp +	using `m \<in> knows t` by fastforce      }     moreover     { assume "?old" -      hence ?case by (fastsimp intro!: IH cases_appendI_trace)+      hence ?case by (fastforce intro!: IH cases_appendI_trace)     }     ultimately show ?case by fast   next@@ -1299,10 +1299,10 @@     let ?t' = "t @ [Learns {Enc m k}]"     note IH = encr(2)     have "m' \<in> knows t \<or> m' = Enc m k" (is "?old \<or> ?new")-      using encr by fastsimp+      using encr by fastforce     moreover     { assume "?new" hence ?case -	using `m \<in> knows t` and `k \<in> knows t` by fastsimp +	using `m \<in> knows t` and `k \<in> knows t` by fastforce      }     moreover     { assume "?old" @@ -1314,10 +1314,10 @@     let ?t' = "t @ [Learns {Tup x y}]"     note IH = tuple(2)     have "m' \<in> knows t \<or> m' = Tup x y" (is "?old \<or> ?new")-      using tuple by fastsimp+      using tuple by fastforce     moreover     { assume "?new" hence ?case -	using `x \<in> knows t` and `y \<in> knows t` by fastsimp +	using `x \<in> knows t` and `y \<in> knows t` by fastforce      }     moreover     { assume "?old" @@ -1331,30 +1331,28 @@       by clarsimp     moreover     { assume "?ik0"   hence "?case" by blast    } moreover-    { assume "?hash"  hence "?case" by fastsimp } moreover-    { assume "?enc"   hence "?case" by fastsimp } moreover-    { assume "?keys"  hence "?case" by fastsimp } moreover-    { assume "?tup"   hence "?case" by fastsimp } moreover+    { assume "?hash"  hence "?case" by fastforce } moreover+    { assume "?enc"   hence "?case" by fastforce } moreover+    { assume "?keys"  hence "?case" by fastforce } moreover+    { assume "?tup"   hence "?case" by fastforce } moreover     { let ?t' = "t@[Step (i, Recv l pt)]"       and ?r' = "r(i \<mapsto> (done @ [Recv l pt], todo, skipped))"       assume "?chain t r s" then       obtain i' done' todo' l' pt' skipped' m-	where thread': "r i' = Some (done', todo', skipped')"-	and send: "Send l' pt' \<in> set done'"+        where thread': "r i' = Some (done', todo', skipped')"+        and send: "Send l' pt' \<in> set done'"         and msg:  "Some m = inst s i' pt'"-	and chain:"decrChain [] t {St (i', Send l' pt')} m m'"-	by auto+        and chain:"decrChain [] t {St (i', Send l' pt')} m m'"+        by auto       then interpret th1: reachable_thread P t r s i' done' todo' skipped'-	using recv by unfold_locales auto-      moreover-      obtain done'' todo'' skipped''-	where "Send l' pt' \<in> set done''"-	and "?r' i' = Some (done'', todo'', skipped'')"-	using `r i = Some (done, Recv l pt # todo, skipped)` thread' send-	by (cases "i = i'") (fastsimp+)-      ultimately-      have "?chain ?t' ?r' s"-	using chain msg+        using recv by unfold_locales auto+        obtain done'' todo'' skipped''+        where "Send l' pt' \<in> set done''"+        and "?r' i' = Some (done'', todo'', skipped'')"+        using `r i = Some (done, Recv l pt # todo, skipped)` thread' send+        by (cases "i = i'") (fastforce+)+      hence "?chain ?t' ?r' s"+        using chain msg         by (fast intro!: decrChain_append)       hence "?case" by auto     } moreover@@ -1362,27 +1360,25 @@       and ?r' = "r(i \<mapsto> (done @ [Recv l pt], todo, skipped))"       assume "?note t r s" then       obtain i' done' todo' skipped' l' ty' pt' m-	where thread': "r i' = Some (done', todo', skipped')"-	and inDone: "Note l' ty' pt' \<in> set done'"+        where thread': "r i' = Some (done', todo', skipped')"+        and inDone: "Note l' ty' pt' \<in> set done'"         and notSkipped: "Note l' ty' pt' \<notin> skipped'"         and msg: "Some m = inst s i' pt'"-	and chain: "decrChain [] t {St (i', Note l' ty' pt')} m m'"+        and chain: "decrChain [] t {St (i', Note l' ty' pt')} m m'"         by auto       then interpret th1: reachable_thread P t r s i' done' todo' skipped'-	using recv by unfold_locales auto-      moreover+        using recv by unfold_locales auto       obtain done'' todo'' skipped''-	where "Note l' ty' pt' \<in> set done''"+        where "Note l' ty' pt' \<in> set done''"         and "Note l' ty' pt' \<notin> skipped'' "-	and "?r' i' = Some (done'', todo'', skipped'')"-	using `r i = Some (done, Recv l pt # todo, skipped)` thread' inDone notSkipped-	by (cases "i = i'") (fastsimp+)-      ultimately-      have "?note ?t' ?r' s" using msg chain notSkipped inDone+        and "?r' i' = Some (done'', todo'', skipped'')"+        using `r i = Some (done, Recv l pt # todo, skipped)` thread' inDone notSkipped+        by (cases "i = i'") (fastforce+)+      hence "?note ?t' ?r' s" using msg chain notSkipped inDone         by (fast intro!: decrChain_append)       hence "?case" by auto     }-    ultimately show ?case by fastsimp+    ultimately show ?case by fastforce   next     case (send t r s i "done" l pt todo skipped m)     then interpret th1: @@ -1392,23 +1388,23 @@     let ?t' = "(t @ [Step (i, Send l pt)]) @ [Learns (pairParts m - knows t)]"     have "m' \<in> knows t \<or> m' \<in> pairParts m \<and> m' \<notin> knows t \<and> Some m = inst s i pt"        (is "?old \<or> ?new")-      using send by fastsimp+      using send by fastforce     moreover     { assume "?new"       hence "decrChain [] ?t' {St (i, Send l pt)} m m'"-	by (fastsimp intro!: decrChain_unpair)+	by (fastforce intro!: decrChain_unpair)       moreover       have "?r' i = Some (done @ [Send l pt], todo, skipped)" 	using th1.thread_exists by auto       ultimately       have ?case using `Some m = inst s i pt`-	apply-+        apply-         apply(rule disjI2)         apply(rule disjI2)         apply(rule disjI2)         apply(rule disjI2)         apply(rule disjI1)-        apply(fastsimp)+        apply(fastforce) 	done     }     moreover@@ -1418,10 +1414,10 @@ 	using send by clarsimp       moreover       { assume "?ik0"   hence "?case" by blast    } moreover-      { assume "?hash"  hence "?case" by fastsimp } moreover-      { assume "?enc"   hence "?case" by fastsimp } moreover-      { assume "?keys"  hence "?case" by fastsimp } moreover-      { assume "?tup"   hence "?case" by fastsimp } moreover+      { assume "?hash"  hence "?case" by fastforce } moreover+      { assume "?enc"   hence "?case" by fastforce } moreover+      { assume "?keys"  hence "?case" by fastforce } moreover+      { assume "?tup"   hence "?case" by fastforce } moreover       { assume "?chain t r s" then 	obtain i' done' todo' l' pt' skipped' m 	  where thread': "r i' = Some (done', todo',skipped')"@@ -1433,7 +1429,7 @@ 	  where "Send l' pt' \<in> set done''" 	  and "(r(i \<mapsto> (done @ [Send l pt], todo, skipped))) i' = Some (done'', todo'',skipped'')" 	  using `r i = Some (done, Send l pt # todo, skipped)` thread' send-	  by (cases "i = i'") (fastsimp+)+	  by (cases "i = i'") (fastforce+) 	hence "?chain ?t' ?r' s" 	  using chain msg           by (fast intro!: decrChain_append)@@ -1452,7 +1448,7 @@           and "Note l' ty' pt' \<notin> skipped'' " 	  and "?r' i' = Some (done'', todo'', skipped'')" 	  using `r i = Some (done, Send l pt # todo, skipped)` thread' inDone notSkipped-	  by (cases "i = i'") (fastsimp+)+	  by (cases "i = i'") (fastforce+)         hence "?note ?t' ?r' s" using chain notSkipped inDone msg  	  by(fast intro!: decrChain_append)         hence "?case" by auto@@ -1468,7 +1464,7 @@     note IH = decr(2)     have "m' \<in> knows t \<or> m' \<in> pairParts m \<and> m' \<notin> knows t"        (is "?old \<or> ?new")-      using decr by fastsimp+      using decr by fastforce     moreover     { assume "?new"       hence "m' \<in> pairParts m" and "m' \<notin> knows t" by auto@@ -1499,9 +1495,9 @@ 	moreover 	hence "decrChain [] ?t' {St (i', Send l' pt')} ms m'" 	  using `?new` `Enc m k \<in> knows t` `inv k \<in> knows t`-	  by (fastsimp intro!: decrChain_decrypt)+	  by (fastforce intro!: decrChain_decrypt) 	ultimately-	have "?decchain ?t' m'" by fastsimp+	have "?decchain ?t' m'" by fastforce 	hence "?case" by blast       }       moreover@@ -1516,9 +1512,9 @@ 	moreover 	hence "decrChain [] ?t' {St (i', Note l' ty' pt')} ms m'" 	  using `?new` `Enc m k \<in> knows t` `inv k \<in> knows t`-	  by (fastsimp intro!: decrChain_decrypt)+	  by (fastforce intro!: decrChain_decrypt) 	ultimately-	have "?notechain ?t' m'" by fastsimp+	have "?notechain ?t' m'" by fastforce 	hence "?case" by blast       }       ultimately have ?case by fast@@ -1536,7 +1532,7 @@     note IH = lkr(2)     have "m' \<in> knows t \<or> m' \<in> longTermKeys a \<and> m' \<notin> knows t"        (is "?old \<or> ?new")-    using lkr by fastsimp+    using lkr by fastforce     moreover      {       assume "?old"@@ -1552,16 +1548,16 @@    case (skip t r s i "done" l ty pt todo skipped)    then interpret this_thread:  reachable_thread P t r s i "done" "Note l ty pt # todo" skipped  by unfold_locales    let ?r' = "r(i \<mapsto> (done @ [Note l ty pt], todo, insert (Note l ty pt) skipped))"-   have "m' \<in> knows t" using skip by fastsimp+   have "m' \<in> knows t" using skip by fastforce    hence "?cases m' t r s"       (is "?ik0 \<or> ?hash \<or> ?enc \<or> ?tup \<or> ?chain t r s \<or> ?note t r s \<or> ?keys")      using skip by clarsimp    moreover    { assume "?ik0"   hence "?case" by blast    } moreover-   { assume "?hash"  hence "?case" by fastsimp } moreover-   { assume "?enc"   hence "?case" by fastsimp } moreover-   { assume "?keys"  hence "?case" by fastsimp } moreover-   { assume "?tup"   hence "?case" by fastsimp } moreover+   { assume "?hash"  hence "?case" by fastforce } moreover+   { assume "?enc"   hence "?case" by fastforce } moreover+   { assume "?keys"  hence "?case" by fastforce } moreover+   { assume "?tup"   hence "?case" by fastforce } moreover    { assume "?chain t r s" then      obtain i' done' todo' l' pt' skipped' m        where thread': "r i' = Some (done', todo',skipped')"@@ -1573,7 +1569,7 @@        where "Send l' pt' \<in> set done''"        and "?r' i' = Some (done'', todo'',skipped'')"        using skip(3) thread' send-       by (cases "i = i'") (fastsimp+)+       by (cases "i = i'") (fastforce+)      hence "?chain t ?r'  s"        using chain msg by fast      hence "?case" by auto@@ -1598,9 +1594,9 @@        by fast      hence "?case" by auto    } moreover-   { assume "?keys" hence "?case" by fastsimp }+   { assume "?keys" hence "?case" by fastforce }    ultimately  -   show  "?case" by fastsimp+   show  "?case" by fastforce   next    case(compr t r s i "done" l ty pt todo skipped m m')    then interpret th1: @@ -1610,7 +1606,7 @@     let ?t' = "(t @ [Step (i, Note l ty pt)]) @ [Learns (pairParts m - knows t)]"     have "m' \<in> knows t \<or> m' \<in> pairParts m \<and> m' \<notin> knows t \<and> Some m = inst s i pt"        (is "?old \<or> ?new")-      using compr by fastsimp+      using compr by fastforce     moreover     { assume "?new"   (*@@ -1618,7 +1614,7 @@       by auto *)         hence "decrChain [] ?t' {St (i, Note l ty pt)} m m'" -          by (fastsimp intro!: decrChain_unpair)+          by (fastforce intro!: decrChain_unpair)       moreover         have "?r' i = Some (done @ [Note l ty pt], todo, skipped)"            using th1.thread_exists by auto@@ -1626,7 +1622,7 @@         have "Note l ty pt \<in> set (Note l ty pt # todo)"            using th1.thread_exists by auto         hence "Note l ty pt \<notin> skipped" -          by (fastsimp dest: th1.todo_notin_skippedD)+          by (fastforce dest: th1.todo_notin_skippedD)       ultimately       have ?case using `Some m = inst s i pt` 	apply-@@ -1645,10 +1641,10 @@ 	using compr by clarsimp       moreover       { assume "?ik0"   hence "?case" by blast    } moreover-      { assume "?hash"  hence "?case" by fastsimp } moreover-      { assume "?enc"   hence "?case" by fastsimp } moreover-      { assume "?keys"  hence "?case" by fastsimp } moreover-      { assume "?tup"   hence "?case" by fastsimp } moreover+      { assume "?hash"  hence "?case" by fastforce } moreover+      { assume "?enc"   hence "?case" by fastforce } moreover+      { assume "?keys"  hence "?case" by fastforce } moreover+      { assume "?tup"   hence "?case" by fastforce } moreover       { assume "?chain t r s" then 	obtain i' done' todo' l' pt' skipped' m 	  where thread': "r i' = Some (done', todo',skipped')"@@ -1660,7 +1656,7 @@ 	  where "Send l' pt' \<in> set done''" 	  and "(r(i \<mapsto> (done @ [Note l ty pt], todo, skipped))) i' = Some (done'', todo'',skipped'')" 	  using compr(3) thread' send-	  by (cases "i = i'") (fastsimp+)+	  by (cases "i = i'") (fastforce+) 	hence "?chain ?t' ?r' s" using chain msg           by(fast intro!: decrChain_append) 	hence "?case"  by auto@@ -1678,7 +1674,7 @@           and "Note l' ty' pt' \<notin> skipped'' " 	  and "?r' i' = Some (done'', todo'', skipped'')" 	  using `r i = Some (done, Note l ty pt # todo, skipped)` thread' inDone notSkipped-	  by (cases "i = i'") (fastsimp+)+	  by (cases "i = i'") (fastforce+)         hence "?note ?t' ?r' s"           using chain notSkipped inDone msg           by(fast intro!: decrChain_append)
data/isabelle/src/ESPLogic/HOL_ext.thy view
@@ -17,7 +17,7 @@  lemma dom_upd [simp]:    "dom (\<lambda> a. if a = x then Some y else m a) = insert x (dom m)"-  by(fastsimp simp: dom_if)+  by(fastforce simp: dom_if)  lemma map_leD: "\<lbrakk> m \<subseteq>\<^sub>m m'; m x = Some y \<rbrakk> \<Longrightarrow> m' x = Some y"   by(force simp: map_le_def)@@ -112,7 +112,7 @@ *) fun forall_permute ctxt p ct =   let-    val cert = Thm.cterm_of (ProofContext.theory_of ctxt);+    val cert = Thm.cterm_of (Proof_Context.theory_of ctxt);     fun mk_cv (_, ty) n = cert (Free (n, ty));     val string_of_perm = commas o map string_of_int;     fun err msg = raise CTERM@@ -213,7 +213,7 @@ *) fun track_HOL_term ctxt x_t =   let-    val thy  = ProofContext.theory_of ctxt;+    val thy  = Proof_Context.theory_of ctxt;     val cert = Thm.cterm_of thy;      val x_ty = Term.fastype_of x_t; @@ -226,7 +226,7 @@     val Qx_ct   = cert (HOLogic.mk_Trueprop (Q_t $ x_t));     val eq_x_ct = cert        (Abs ("y", x_ty, -            Const (@{const_name "op ="}, x_ty --> x_ty --> HOLogic.boolT)+            Const (@{const_name "HOL.eq"}, x_ty --> x_ty --> HOLogic.boolT)             $ x_t $ Bound 0));      fun remove_tracking th' =
data/isabelle/src/ESPLogic/Hints.thy view
@@ -13,10 +13,10 @@ theory Hints imports   Main-uses-  espl_utils begin +ML_file "espl_utils.ML"+ section{* A Theory of Hints for Marking Intermediate Results *}  @@ -90,3 +90,4 @@ *}  end+
data/isabelle/src/ESPLogic/InferenceRules.thy view
@@ -94,12 +94,12 @@ proof -   interpret reachable_thread P t r s i "done" "step#todo" skipped     using facts by unfold_locales auto-  hence "step \<in> set (step # todo)" by auto-  hence "step \<notin> set done" using facts by (fastsimp dest!: todo_notin_doneD)+  have "step \<in> set (step # todo)" by auto+  hence "step \<notin> set done" using facts by (fastforce dest!: todo_notin_doneD)   hence "(takeWhile (\<lambda> x. x \<noteq> step) done) = done" by auto   hence "(takeWhile (\<lambda> x. x \<noteq> step) (done @ (step # todo))) = done" by auto   moreover-  have "R = (done @ (step # todo))" using facts by (fastsimp dest: roleMap_SomeD)+  have "R = (done @ (step # todo))" using facts by (fastforce dest: roleMap_SomeD)   ultimately show ?thesis by auto qed @@ -138,10 +138,10 @@   shows     "(st \<in> set done \<and> st \<noteq> (Note l ty pt)) \<or> (st = step)" proof --  have "(st \<in> set R \<and> st \<noteq> (Note l ty pt)) \<or> (st = step)" using filtered by (fastsimp dest: filtered_role_conv)+  have "(st \<in> set R \<and> st \<noteq> (Note l ty pt)) \<or> (st = step)" using filtered by (fastforce dest: filtered_role_conv)   moreover-  have "(takeWhile (\<lambda> x. x \<noteq> step) R) = done" using isThread by (fastsimp dest: take_while_is_done)-  ultimately show ?thesis using isThread and filtered by fastsimp+  have "(takeWhile (\<lambda> x. x \<noteq> step) R) = done" using isThread by (fastforce dest: take_while_is_done)+  ultimately show ?thesis using isThread and filtered by fastforce qed  lemma filtered_in_done:@@ -153,7 +153,7 @@   interpret this_thread:     reachable_thread P t r s i "done" todo skipped     using role_exists by unfold_locales auto-  hence "step \<in> set done"+  have "step \<in> set done"     using step by (auto dest: this_thread.in_steps_in_done)   moreover   then obtain prefix suffix @@ -167,7 +167,7 @@     assume "st \<noteq> step \<and> takeWhile (\<lambda>x. x \<noteq> step) R = prefix"     hence "st \<in> set prefix" using inFiltered        by auto-    hence ?thesis using done_split by fastsimp+    hence ?thesis using done_split by fastforce   }   moreover {     assume "st = step \<and> step \<in> set done"@@ -236,7 +236,7 @@     \<lbrakk> nextRel (filter (\<lambda> x. \<not> (noteStep x)) (takeWhile (\<lambda> x. x \<noteq> step) R) @ [step]) st st'     \<rbrakk> \<Longrightarrow> St (i, st) \<prec> St (i, st')"   shows "prefixClose s t R step i"-using prems by (auto simp: prefixClose_def)+using assms by (auto simp: prefixClose_def)  lemma prefixCloseI:   assumes step: "(i, step) \<in> steps t"@@ -276,13 +276,13 @@       apply -       apply(rule conjI, assumption)       apply(case_tac "st = step")-        apply(fastsimp dest: this_thread.in_steps_conv_done_skipped[THEN iffD1])-      apply(fastsimp dest!: this_thread.note_in_skipped note_filtered_revRole)+        apply(fastforce dest: this_thread.in_steps_conv_done_skipped[THEN iffD1])+      apply(fastforce dest!: this_thread.note_in_skipped note_filtered_revRole)        apply(rule conjI, assumption)       apply(case_tac "st' = step")-        apply(fastsimp dest: this_thread.in_steps_conv_done_skipped[THEN iffD1])-      by(fastsimp dest!: this_thread.note_in_skipped note_filtered_revRole)+        apply(fastforce dest: this_thread.in_steps_conv_done_skipped[THEN iffD1])+      by(fastforce dest!: this_thread.note_in_skipped note_filtered_revRole)     hence steps: "(i, st) \<in> steps t" "(i, st') \<in> steps t"       by(auto dest: this_thread.in_steps_conv_done_skipped[THEN iffD1])     { assume "recvStep st" then@@ -294,12 +294,12 @@      have "listOrd R st st'"        using nextRel and R_split and done_split-      by(fastsimp dest: nextRel_imp_listOrd listOrd_rev[THEN iffD1] listOrd_filter)+      by(fastforce dest: nextRel_imp_listOrd listOrd_rev[THEN iffD1] listOrd_filter)     hence "St (i, st) \<prec> St (i, st')"       using role_exists steps R_split       apply -       apply(drule this_thread.in_steps_conv_done_skipped[THEN iffD1])-      by(fastsimp dest!: this_thread.roleOrd_notSkipped_imp_listOrd_trace dest:listOrd_imp_predOrd)++      by(fastforce dest!: this_thread.roleOrd_notSkipped_imp_listOrd_trace dest:listOrd_imp_predOrd)+     note input and this   }   ultimately show ?thesis@@ -312,7 +312,7 @@   "\<lbrakk> (i, step) \<in> steps t; roleMap r i = Some R \<rbrakk> \<Longrightarrow>    prefixClose s t R step i \<and>     (recvStep step \<longrightarrow> (\<exists> m. Some m = inst s i (stepPat step) \<and> Ln m \<prec> St (i, step)))"-  by (cases step) (fastsimp intro!: prefixCloseI Ln_before_inp)++  by (cases step) (fastforce intro!: prefixCloseI Ln_before_inp)+  text{*    Used for prefix closing assumptions corresponding to a case of@@ -343,14 +343,14 @@       proof         obtain l pt           where recv_eq: "(Recv l pt) = (last (step # done))"-          using recv by (fastsimp dest!: recvStepD)+          using recv by (fastforce dest!: recvStepD)         hence "Recv l pt \<in> set (step # done)" by auto         thus ?thesis           using thread_exists recv_eq-          by(fastsimp dest!: this_thread.in_steps_recv[THEN iffD1])+          by(fastforce dest!: this_thread.in_steps_recv[THEN iffD1])         qed     hence "?inp_last"-      by (cases "last (step # done)") (fastsimp dest!: Ln_before_inp)++      by (cases "last (step # done)") (fastforce dest!: Ln_before_inp)+   }   moreover   { @@ -361,7 +361,7 @@     hence skipped: "st \<notin> skipped \<and> st' \<notin> skipped"       proof(cases "st = step \<and> st' \<in> set done \<and> \<not> noteStep st'")         case True-        thus "?thesis" using listOrd not_skipped by (fastsimp dest: this_thread.note_in_skipped)+        thus "?thesis" using listOrd not_skipped by (fastforce dest: this_thread.note_in_skipped)       next         case False         note falseAsms = this@@ -382,7 +382,7 @@               assumption)         apply(drule_tac ?Q = "listOrd done st st'" and ?P = "st = step \<and> st' \<in> set done" in disjI1)         apply(drule listOrd.simps(2)[THEN iffD2])-        by(fastsimp dest: listOrd_imp_predOrd this_thread.listOrd_done_imp_listOrd_trace)+        by(fastforce dest: listOrd_imp_predOrd this_thread.listOrd_done_imp_listOrd_trace)     next       case False       note assms = this@@ -397,7 +397,7 @@            apply(drule listOrd_filter)            apply(drule_tac ?Q = "listOrd done st st'" and ?P = "st = step \<and> st' \<in> set done" in disjI2)            apply(drule listOrd.simps(2)[THEN iffD2])-           by (fastsimp dest: listOrd_imp_predOrd this_thread.listOrd_done_imp_listOrd_trace)+           by (fastforce dest: listOrd_imp_predOrd this_thread.listOrd_done_imp_listOrd_trace)       qed     qed     hence recv: "recvStep st \<Longrightarrow> @@ -432,22 +432,22 @@   case (send t r s i "done" l pt todo m y)   then interpret this_state: reachable_state P t r s by unfold_locales   show ?case using send-    by(fastsimp dest: this_state.knows_IK0)+    by(fastforce dest: this_state.knows_IK0) next   case (decr t r s m k y)   then interpret this_state: reachable_state P t r s by unfold_locales   show ?case using decr-    by(fastsimp dest: this_state.knows_IK0)+    by(fastforce dest: this_state.knows_IK0) next    case (lkr t r s a)   then interpret this_state: reachable_state P t r s by unfold_locales   show ?case using lkr-    by(fastsimp dest: this_state.knows_IK0)+    by(fastforce dest: this_state.knows_IK0) next    case (compr t r s "done" l ty pt todo skipped m y)   then interpret this_state: reachable_state P t r s by unfold_locales   show ?case using compr-    by(fastsimp dest: this_state.knows_IK0)+    by(fastforce dest: this_state.knows_IK0) qed auto  lemmas nothing_before_IK0_iffs [iff] = in_IK0_simps[THEN nothing_before_IK0]@@ -485,11 +485,11 @@   and     conc_inj: "\<And> i1 i2 j. \<lbrakk> conc i1 j \<and> conc i2 j \<rbrakk> \<Longrightarrow> i1 = i2"   shows "let prems = prem;               concs = conc-         in \<exists>f. inj_on f prems \<and> (\<forall>i. prems i \<longrightarrow> concs i (f i))"+         in \<exists>f. inj_on f (Collect prems) \<and> (\<forall>i. prems i \<longrightarrow> concs i (f i))" proof -   let ?f = "\<lambda> i. SOME j. conc i j"-  have "inj_on ?f prem"-    apply(auto simp: inj_on_def mem_def dest!: niagree)+  have "inj_on ?f (Collect prem)"+    apply(auto simp: inj_on_def dest!: niagree)     apply(rule_tac j="(SOME j. conc x j)" in conc_inj[OF conjI])     apply(rule someI, simp+)+     done
data/isabelle/src/ESPLogic/Protocol.thy view
@@ -21,7 +21,7 @@  subsubsection{* Patterns *} -types id = string+type_synonym id = string  datatype varid = AVar id | MVar id @@ -108,7 +108,7 @@   They are currently defaulted to strings, but could be anything. *} -types lbl = string+type_synonym lbl = string  datatype notetype = RandGen | State | SessKey @@ -161,7 +161,7 @@ qed auto  -types "role" = "rolestep list"+type_synonym "role" = "rolestep list"  fun recv_before :: "id set \<Rightarrow> role \<Rightarrow> bool" where@@ -181,7 +181,7 @@    subsubsection{* Protocols *} -types proto = "role set"+type_synonym proto = "role set"  locale wf_proto =   fixes P :: proto@@ -242,7 +242,7 @@   moreover have "distinct R" and "recv_before {} R" by auto   ultimately obtain lbl' pt' where "Recv lbl' pt' \<in> set ys"                                  and "v \<in> FMV pt'"-             by (fastsimp dest!: recv_before_sent_distinct_Send_FV intro!: FV)+             by (fastforce dest!: recv_before_sent_distinct_Send_FV intro!: FV)   hence "?received lbl' pt'" using split by auto   thus ?thesis by blast qed@@ -262,7 +262,7 @@   moreover have "distinct R" and "recv_before {} R" by auto   ultimately obtain lbl' pt' where "Recv lbl' pt' \<in> set ys"                                  and "v \<in> FMV pt'"-             by (fastsimp dest!: recv_before_note_distinct_Note_FV intro!: FV)+             by (fastforce dest!: recv_before_note_distinct_Note_FV intro!: FV)   hence "?received lbl' pt'" using split by auto   thus ?thesis by blast qed@@ -291,7 +291,7 @@  lemma aVars_singleton[iff]:   "AVar a \<notin> aVars []"-by(fastsimp simp add: aVars_def)+by(fastforce simp add: aVars_def)  lemma aVars_Nil [iff]: "aVars [] = {}"   by (auto simp: aVars_def)@@ -301,7 +301,7 @@  lemma aVars_FAV_conv:   "(AVar a \<in> aVars R) = (\<exists> s \<in> set R. \<exists> pt. (stepPat s = pt \<and> a \<in> FAV pt))"-by (induct R rule: foldr.induct) ( fastsimp simp add: aVars_def)++by (induct R) ( fastforce simp add: aVars_def)+   definition lastComStep :: "role \<rightharpoonup> rolestep"@@ -334,7 +334,7 @@         s   )" proof (cases "[s\<leftarrow>xs . \<not> noteStep s]")-qed (fastsimp simp add: lastComStep_def)++qed (fastforce simp add: lastComStep_def)+  lemma firstComStep_Nil [iff]: "firstComStep [] = None"   by (auto simp: firstComStep_def)@@ -346,7 +346,7 @@       Some x   )" proof (cases "[s\<leftarrow>xs . \<not> noteStep s]")-qed (fastsimp simp add: firstComStep_def)+ +qed (fastforce simp add: firstComStep_def)+
data/isabelle/src/ESPLogic/Syntax.thy view
@@ -62,7 +62,7 @@  translations   "<|x, y, z|>"   == "<|x, <|y, z|> |>"-  "<|x, y|>"      == "PTup x y"+  "<|x, y|>"      == "CONST PTup x y"   subsubsection{* Execution Messages *}
data/isabelle/src/ESPLogic/Unify.thy view
@@ -19,7 +19,9 @@      espl_methods.ML. With a uses clause it would be      loaded twice, which may result in strange effects.   *)-  Automation  +  Automation+keywords+  "note_prefix_closed" "note_unified" "note_cyclic" :: prf_decl begin  section{* Explicit unification of sets of equality theorems *}@@ -137,14 +139,14 @@    in (prod_ord bool_ord                  (prod_ord bool_ord -                  (prod_ord bool_ord TermOrd.term_ord)))+                  (prod_ord bool_ord Term_Ord.term_ord)))      (proj lhs, proj rhs)    end  fun old_unify_term_ord (arg as (lhs,rhs)) =    if (is_variable_store_lookup lhs) then      if (is_variable_store_lookup rhs) then-      TermOrd.term_ord arg+      Term_Ord.term_ord arg     else       LESS   else@@ -153,38 +155,21 @@     else       if (is_roleMap lhs) then         if (is_roleMap rhs) then-          TermOrd.term_ord arg+          Term_Ord.term_ord arg         else           LESS       else         if (is_roleMap rhs) then           GREATER         else-          TermOrd.term_ord arg;+          Term_Ord.term_ord arg;            *} -(*-context reachable_state begin- ML{* -fun both t = (unify_term_ord t, old_unify_term_ord t);--both (@{term "s (MV a b)"}, @{term "LN x i"});-both (@{term "s (MV a b)"}, @{term "s (MV c d)"});-both (swap (@{term "s (MV a b)"}, @{term "s (AV c d)"}));-both (@{term "roleMap r i"}, @{term "Some R"});-both (swap (@{term "roleMap r i"}, @{term "Some R"}));-  --*}-*)--ML{*- structure UnifyDest = Named_Thms-  (val name ="unify_dest"+  (val name = @{binding "unify_dest"}    val description = "Destruction rules to be used in note_unified")  *}@@ -218,7 +203,7 @@ fun unify do_occurs_check ctxt ths =   let     (* TODO: Remove hack by using Named_Thms data functor. *)-    val thm_by_name = ProofContext.get_thm ctxt;+    val thm_by_name = Proof_Context.get_thm ctxt;     val ss = simpset_of ctxt        delsimps map thm_by_name ["tid_eq_commute", "reorient_store_eq_store"]; @@ -252,12 +237,12 @@             (case remove_Trueprop (Thm.concl_of th) of                (@{const True})           => solve1 (done, todo)              | (@{const False})          => [th]-             | (@{const "op &"} $ _ $ _) =>+             | (@{const "HOL.conj"} $ _ $ _) =>                  solve1 ( done                          , (th RS @{thm conjunct1}) ::                           (th RS @{thm conjunct2}) :: todo                         )-             | (Const (@{const_name "op ="},_) $ _ $ _) => +             | (Const (@{const_name "HOL.eq"},_) $ _ $ _) =>                   (case reorient_HOL_eq unify_term_ord th of                     NONE     => solve1 (done, todo)                   | SOME th' =>@@ -306,7 +291,7 @@      fun modify_bound_thms ctxt b =       let-        val ths  = ProofContext.get_thms ctxt (ProofContext.full_name ctxt b);+        val ths  = Proof_Context.get_thms ctxt (Proof_Context.full_name ctxt b);       in         ((b,[]), [(f ctxt ths,[])])       end;@@ -315,338 +300,41 @@       state       |> map_context_result            (fn ctxt => ctxt |>-            (ProofContext.note_thmss "" +            (Proof_Context.note_thmss ""                (map (modify_bound_thms ctxt) bindings))           )       |> (fn (named_thss, state') =>            state'-           |> Proof.put_facts (SOME (maps snd named_thss))+           |> Proof.set_facts (maps snd named_thss)          )   in-    modify_and_renote o Proof.note_thmss args+    modify_and_renote o Proof.note_thmss_cmd args   end- *}  ML{* local-  structure K = OuterKeyword;-  structure T = Toplevel;-   fun define_cmd name info f =-    OuterSyntax.command name info (K.tag_proof K.prf_decl)-    (SpecParse.name_facts >> (T.print oo (T.proof o (note_modified_thmss f))));+    Outer_Syntax.command name info+    (Parse_Spec.name_facts >> (Toplevel.print oo (Toplevel.proof o (note_modified_thmss f)))); in   val _ = -    define_cmd "note_prefix_closed" +    define_cmd @{command_spec "note_prefix_closed"}        "prefix close facts and store them under the given name"       ESPL_Methods.prefix_close_thms;    val _ = -    define_cmd "note_unified" +    define_cmd @{command_spec "note_unified"}       "unify equality facts and store them under the given name"       (unify true);    (* TODO: Implement this command - currently it is just notes. *)   val _ = -    define_cmd "note_cyclic" +    define_cmd @{command_spec "note_cyclic"}       "try to derive a cyclicity violation from the given facts and store them under the given name"       (K I);  end *}---(*--lemma (in reachable_state) test : "X"-proof --  fix tid\<^isub>1 tid\<^isub>2 tid\<^isub>3-  assume "s (MV ''ni'' tid\<^isub>1) = LN ''ni'' tid\<^isub>3"-  and"s (MV ''ni'' tid\<^isub>1) = LN ''ni'' tid\<^isub>2"-ML_prf{*-  unify true @{context} @{thms this}-  handle THM (_,_,ths) => ths--*}-  note_unified facts = this--lemma--*)--(*--ML{* @{const predOrd} *}-ML{* @{term "predOrd t (Ln \<lbrace>LN ''ni'' i, x\<rbrace>) (Ln y)"} *}-ML{*--case @{term "predOrd t (Ln \<lbrace>LN ''ni'' i, x\<rbrace>) (Ln y)"} of-    (@{const predOrd} $ _ $ (@{const Ln} $ (Const (@{const_name Tup},_) $ _ $ _)) $ _) =>-       Const ("YES 1", TFree ("blah",["blih"]))-  | (Const (@{const_name predOrd}, _) $ _ $ _ $ _ ) =>-       Const ("YES 2", TFree ("blah",["blih"]))-  | (x $ _ $ _ $ _ ) =>-       x-  | _ => Const ("no", TFree ("blah",["blih"]))--*}--lemma test: -  assumes facts:-    "Enc x y = Enc t v"-    "x = v"-  shows "False"-proof --  note_unified this = facts-  thm this-oops---text{* Testing the role definition command *}-role nslXInit-where "nslXInit \<equiv> -  [ Send ''0'' (PEnc \<langle>sC ''0'', sAV ''I'', sN ''ni''\<rangle> (sPK ''R''))-  , Recv ''1'' (PEnc \<langle>sC ''1'', sAV ''R'', sN ''ni'', sMV ''nr''\<rangle> (sPK ''I''))-  , Send ''2'' (PEnc \<langle>sC ''2'', sMV ''nr''\<rangle> (sPK ''R''))-  ]"--text{* An additional role for testing purposes. *}-role nslXResp-where "nslXResp \<equiv>-  [ Recv ''0'' (PEnc \<langle>sC ''0'', sLAV ''I'', sLMV ''ni''\<rangle> (sPK ''R''))-  , Send ''1'' (PEnc \<langle>sC ''1'', sLAV ''R'', sLMV ''ni'', sLN ''nr''\<rangle> (sPK ''I''))-  , Recv ''2'' (PEnc \<langle>sC ''2'', sLN ''nr''\<rangle> (sPK ''R''))-  ]"--protocol nslX-where "nslX = {nslXInit, nslXResp}"--locale atomic_nslX_state = typed_state nslX _ _ _ "weakly_atomic"--lemma (in atomic_nslX_state) SK_from_IK0:-  assumes facts:-    "SK a \<in> knows t"-  shows "a \<in> Compromised"-using facts-proof(sources "SK a")-qed clarsimp--lemma (in atomic_nslX_state) I_sec_ni:-  assumes facts:-    "roleMap r i = Some nslXInit"-    "Ln (Tup (LN ''ni'' i) x) \<prec> Ln y"-    "s(AV ''I'' i) \<notin> Compromised"-    "s(AV ''R'' i) \<notin> Compromised"   -  shows "False"-using facts-proof(sources! "LN ''ni'' i")-  case nslXInit_0_ni-  note_unified facts = facts this-thm split_before[OF `Ln \<lbrace>LN ''ni'' i, x\<rbrace> \<prec> Ln y`]-ML_prf{*-@{term "Ln \<lbrace>LN ''ni'' i, x\<rbrace> \<prec> Ln y"}-*}-  thus ?thesis-  proof(sources! "SK (s (AV ''R'' i))")-    case ik0-    note_unified facts = facts this-    thus ?thesis by clarsimp-  qed-next-  case (nslXInit_2_nr i1)-  note_unified facts = facts this-  thus ?thesis-  proof(sources! "inst s i1 nslXInit_1_pt")-    case fake-    note_unified facts = facts this-    thus ?thesis by order-  next-    case (nslXResp_1_enc r1)-    note_unified facts = facts this-    thus ?thesis .-  qed-next-  case (nslXResp_1_ni r1)-  note_unified facts = facts this-  thus ?thesis-  proof(sources "inst s r1 nslXResp_0_pt")-    case fake-    note_unified facts = facts this-    thus ?thesis by order-  next-    case (nslXInit_0_enc i2)-    note_unified facts = facts this-    thus ?thesis-    proof(sources! "SK (s (AV ''I'' i))")-      case ik0-      note_unified facts = facts this-      thus ?thesis by clarsimp-    qed-  qed-qed------(* OLD TEST INFRASTRUCTURE---ML{*--val th1 = Thm.assume @{cterm "Trueprop (s (AV ''a'' i) = x)"};-val th2 = Thm.assume @{cterm "Trueprop (PK (s (AV ''a'' i)) = inv (y))"};-val th3 = Thm.assume @{cterm "Trueprop (Enc (LN ''a'' i) (PK (s (AV ''a'' j))) = -                                        Enc (LN ''a'' j) (PK (s (AV ''b'' i))))"};-val th4 = Thm.assume @{cterm "Trueprop ((b::nat) < c)"};-val th5 = Thm.assume @{cterm "Trueprop ((x::execmsg) = Enc (Tup y (PK x)) z)"};---*}---ML{*--unify true @{context} [th1,th2,th3,th5,th1,th2,th3,th5,th1,th2,th3,th5,th1,th2,th3,th5]--*}--subsection{* Redefining the notes command *}--text{*-  note[prefix_closed] this = facts-  note[unified] this = facts--^ preferred version--  note this[unified] = facts--*}--ML{*--Proof.note_thmss-*}--ML{* --ProofContext.note_thmss-*}--note_prefix_closed-note_unified-note_cyclic--ML{*--local -  structure P = OuterParse;-  structure S = SpecParse;--  fun bling ctxt =-    let val _ = Output.warning "test";-    in ctxt end;--  fun modifier (name, f) = P.$$$ name >> K f;-  val modifiers = [("test", (K bling)),("unified",unify true)];-in-  val thms_mod = Scan.first (map modifier modifiers @ [Scan.succeed (K I)]);-  val mod_name_facts = thms_mod -- S.name_facts-end-*}- ---lemma test: "blah"-proof --  note_prefix_closed unified = sym allI-    and blah = ballI-  thm this-  thm blah-  thm unified-  ------*)--role C-where "C =-  [ Send ''1'' ( PEnc ( sN ''k'' ) ( sPK ''S'' ) )-  , Recv ''2'' ( PHash ( sN ''k'' ) )             -  ]"                                              --role S-where "S =-  [ Recv ''1'' ( PEnc ( sMV ''k'' ) ( sPK ''S'' ) )-  , Send ''2'' ( PHash ( sMV ''k'' ) )             -  ]"                                               --protocol CR-where "CR = { C, S }"--locale atomic_CR_state = atomic_state CR-locale CR_state = reachable_state CR--lemma (in atomic_CR_state) C_secret_k:-  assumes facts:-    "roleMap r i\<^isub>0 = Some C"-    "s(AV ''S'' i\<^isub>0) \<notin> Compromised"-    "LN ''k'' i\<^isub>0 \<in> knows t"-  shows "False"-using facts proof(sources! " LN ''k'' i\<^isub>0 ")-  case C_1_k note_unified facts = this facts-  thus ?thesis proof(sources! " SK ( s(AV ''S'' i\<^isub>0) ) ")-  qed (insert facts, ((clarsimp, order?))+)?-qed--lemma (in CR_state) weak_atomicity:-  "complete (t,r,s) atomicAnn"-proof (cases rule: complete_atomicAnnI[completeness_cases_rule])-  case (S_1_k t r s i\<^isub>0) note facts = this-  then interpret state: atomic_state CR t r s-    by unfold_locales assumption+-  show ?case using facts-  proof(sources! "-      Enc ( s(MV ''k'' i\<^isub>0) ) ( PK ( s(AV ''S'' i\<^isub>0) ) ) ")-  qed (insert facts, ((fastsimp simp: atomicAnn_def dest: state.extract_knows_hyps))+)?-qed--lemma (in atomic_CR_state) C_ni_synch:-  assumes facts:-    "roleMap r i\<^isub>1 = Some C"-    "s(AV ''S'' i\<^isub>1) \<notin> Compromised"-    "(i\<^isub>1, C_2) \<in> steps t"-  shows-    "\<exists>i\<^isub>2.-       roleMap r i\<^isub>2 = Some S &-       s(AV ''S'' i\<^isub>2) = s(AV ''S'' i\<^isub>1) &-       s(MV ''k'' i\<^isub>2) = LN ''k'' i\<^isub>1 &-       St(i\<^isub>1, C_1) \<prec> St(i\<^isub>1, C_2) &-       St(i\<^isub>1, C_1) \<prec> St(i\<^isub>2, S_1) &-       St(i\<^isub>2, S_2) \<prec> St(i\<^isub>1, C_2) &-       St(i\<^isub>2, S_1) \<prec> St(i\<^isub>2, S_2)"-proof --  note_prefix_closed facts = facts-  thus ?thesis proof(sources! " Hash ( LN ''k'' i\<^isub>1 ) ")-    case fake note_unified facts = this facts-    thus ?thesis by (fastsimp dest: C_secret_k intro: event_predOrdI)-  next-    case (S_2_hash i\<^isub>2) note_unified facts = this facts-    thus ?thesis proof(sources! "-                     Enc ( LN ''k'' i\<^isub>1 ) ( PK ( s(AV ''S'' i\<^isub>2) ) ) ")-      case fake note_unified facts = this facts-      thus ?thesis by (fastsimp dest: C_secret_k intro: event_predOrdI)-    next-      case C_1_enc note_unified facts = this facts-      thus ?thesis by force-    qed-  qed-qed--*)  end
data/isabelle/src/ESPLogic/WeakTyping.thy view
@@ -35,17 +35,17 @@   to their type. *} -types msgtype = "tid \<Rightarrow> state \<Rightarrow> execmsg set"+type_synonym msgtype = "tid \<Rightarrow> state \<Rightarrow> execmsg set" -types typing = "(role \<times> id) \<Rightarrow> msgtype"+type_synonym typing = "(role \<times> id) \<Rightarrow> msgtype"  definition approx :: "typing \<Rightarrow> state set"-where "approx typing q \<equiv> case q of (t,r,s) \<Rightarrow>+where "approx typing \<equiv> {q. case q of (t,r,s) \<Rightarrow>   \<forall> (i,step) \<in> steps t.      \<forall> R. roleMap r i = Some R \<longrightarrow>       (\<forall> n. MVar n \<in> FV (stepPat step) \<longrightarrow>          s (MVar n, i) \<in> typing (R, n) i (t,r,s)-      )"+      )}"  locale typed_state = reachable_state+   fixes typing :: "typing"@@ -65,7 +65,7 @@       \<forall> R. roleMap r i = Some R \<longrightarrow>         (\<forall> n. MVar n \<in> FV (stepPat step) \<longrightarrow>            s (MVar n, i) \<in> typing (R, n) i (t,r,s)))"-by (auto simp: approx_def mem_def)+by (auto simp: approx_def)  lemma in_approxI:   assumes all_vars:@@ -299,7 +299,7 @@         then obtain l' msg'            where "(i, Recv l' msg') \<in> steps t"                  "MVar n \<in> FV msg'"-          by (fastsimp dest!: th1.send_step_FV[OF th1.thread_exists])+          by (fastforce dest!: th1.send_step_FV[OF th1.thread_exists])         hence typed: "s (MV n i) \<in> typing (?role, n) i (t, r, s)"           by (auto dest: IH[OF th1.thread_exists])         have "done'@todo' = ?role"@@ -388,9 +388,9 @@               apply -               apply(drule listOrd_append[THEN iffD1])               apply(case_tac "listOrd done (Recv l'' pt'') (Note l' ty' pt')")-                apply(fastsimp dest: in_set_listOrd1)+                apply(fastforce dest: in_set_listOrd1)               apply(case_tac "listOrd (Recv l pt # todo) (Recv l'' pt'') (Note l' ty' pt')")-                apply(fastsimp dest: in_set_listOrd2 th1.done_notin_todoD)+                apply(fastforce dest: in_set_listOrd2 th1.done_notin_todoD)               apply(case_tac "Recv l'' pt'' \<in> set done \<and> Note l' ty' pt' \<in> set (Recv l pt # todo)")               by(auto dest: th1.done_notin_todoD)             hence "(i, Recv l'' pt'') \<in> steps t" by auto@@ -424,7 +424,7 @@               done          qed       }-      ultimately show ?case by fastsimp+      ultimately show ?case by fastforce     next       case (compr t r s i "done" l ty pt todo skipped m i' done' todo' step n skipped')       then interpret th1: @@ -450,7 +450,7 @@         then obtain l' msg'            where "(i, Recv l' msg') \<in> steps t"                  "MVar n \<in> FV msg'"-          by (fastsimp dest!: th1.note_step_FV[OF th1.thread_exists])+          by (fastforce dest!: th1.note_step_FV[OF th1.thread_exists])         hence typed: "s (MV n i) \<in> typing (?role, n) i (t, r, s)"           by (auto dest: IH[OF th1.thread_exists])         have "done'@todo' = ?role"@@ -974,7 +974,7 @@     then interpret th1: typed_thread P t r s i "done" todo skipped "typing"       using approximates by unfold_locales     from inDone and notinSkipped have note_step: "(i, Note l ty pt) \<in> steps t" -      by (fastsimp dest!: th1.in_steps_eq_in_done)+      by (fastforce dest!: th1.in_steps_eq_in_done)     moreover     have "prefixClose s t (done@todo) (Note l ty pt) i" using note_step       by(auto intro!: prefixCloseI th1.roleMap)@@ -994,7 +994,7 @@     hence ?thesis by blast    }   ultimately-  show ?thesis by fastsimp+  show ?thesis by fastforce qed  @@ -1025,9 +1025,9 @@     apply(erule disjE)     apply(clarsimp)     apply(rule disjI2)-    apply(fastsimp intro: less_le_trans)+    apply(fastforce intro: less_le_trans)     done-qed fastsimp++qed fastforce+  lemma (in reachable_state) decrChain_KnownT:   assumes decrChain: "decrChain path t from m m'"@@ -1039,7 +1039,7 @@     where "im \<in> pairParts m" and "\<forall>f \<in> from. f \<prec> Ln im"     using decrChain by (fast dest!: decrChain_imp_predOrd)   with KnownT show ?thesis-    by (fastsimp intro: pairParts_before)+    by (fastforce intro: pairParts_before) qed  lemma (in reachable_state) decrChain_KnownTE:
data/isabelle/src/ESPLogic/espl_definitions.ML view
@@ -21,7 +21,7 @@   (* Additional Utilities *)   val unnamed_caseN: string -  datatype steptyp = Recv | Send+  datatype steptyp = Recv | Send | Note of term   val mk_rolestep: steptyp * term * term -> term   val dest_rolestep: term -> steptyp * term * term   val dest_role: term -> (steptyp * term * term) list@@ -120,26 +120,26 @@     TODO: Check if there is a more stable machinery for that purpose. *)-fun get_unfold_thms ctxt (Const (c,_)) = ProofContext.get_thms ctxt (c ^ ".unfold")-  | get_unfold_thms ctxt (Free  (c,_)) = ProofContext.get_thms ctxt (c ^ ".unfold")+fun get_unfold_thms ctxt (Const (c,_)) = Proof_Context.get_thms ctxt (c ^ ".unfold")+  | get_unfold_thms ctxt (Free  (c,_)) = Proof_Context.get_thms ctxt (c ^ ".unfold")   | get_unfold_thms _ t = raise TERM ("get_unfold_thms", [t])  (* Lookup the term of the message of a role step *) fun get_rolestep_msg ctxt step_name = -  ProofContext.get_thm ctxt (Thm.def_name (step_name ^ "_pt"))+  Proof_Context.get_thm ctxt (Thm.def_name (step_name ^ "_pt"))   |> Thm.prop_of   |> dest_HOL_def   |> snd  (* Extract identifiers of message variables in a pattern *) fun pat_msgvars (Const (@{const_name "PEnc"},_) $ m $ k)  = -      OrdList.union fast_string_ord (pat_msgvars m) (pat_msgvars k)+      Ord_List.union fast_string_ord (pat_msgvars m) (pat_msgvars k)   | pat_msgvars (Const (@{const_name "PTup"},_) $ x $ y)  = -      OrdList.union fast_string_ord (pat_msgvars x) (pat_msgvars y)+      Ord_List.union fast_string_ord (pat_msgvars x) (pat_msgvars y)   | pat_msgvars (Const (@{const_name "PHash"},_) $ x)     =        pat_msgvars x   | pat_msgvars (Const (@{const_name "PSymK"},_) $ a $ b) = -      OrdList.union fast_string_ord (pat_msgvars a) (pat_msgvars b)+      Ord_List.union fast_string_ord (pat_msgvars a) (pat_msgvars b)   | pat_msgvars (Const (@{const_name "PAsymPK"},_) $ a)   =       pat_msgvars a   | pat_msgvars (Const (@{const_name "PAsymSK"},_) $ a)   =@@ -288,7 +288,7 @@       pat_def |> Thm.prop_of |> dest_HOL_def |> #2 |> pat_msgvars;      val msgvars = Library.foldl -      (fn (vs,def) => OrdList.union fast_string_ord vs (pat_def_msgvars def)) +      (fn (vs,def) => Ord_List.union fast_string_ord vs (pat_def_msgvars def))        ([],pat_defs);    in@@ -346,16 +346,12 @@   end  (* registering the role definition command as an outer keyword *)-local structure P = OuterParse and K = OuterKeyword in--  val roledef_parser = -    P.binding --| P.where_ -- (SpecParse.opt_thm_name ":" -- P.prop);--  val _ =-    OuterSyntax.local_theory "role" "security protocol role definition" -      K.thy_decl (roledef_parser >> (fn spec => define_role_cmd spec #> snd));-end;+val roledef_parser = +  Parse.binding --| Parse.where_ -- (Parse_Spec.opt_thm_name ":" -- Parse.prop); +val _ =+  Outer_Syntax.local_theory @{command_spec "role"} "security protocol role definition" +    (roledef_parser >> (fn spec => define_role_cmd spec #> snd));  (****************************************************************************** **  Protocol Definitions@@ -402,14 +398,14 @@   let     val ((proto_const, (_, proto_def)), spec_ctxt) = params_ctxt        |> Specification.definition_cmd -        (SOME (raw_bind, SOME "Protocol.proto", NoSyn), raw_spec);+        (SOME (raw_bind, SOME "Protocol.proto", NoSyn), raw_spec) true;      val proto_name          = Binding.name_of raw_bind;     fun mk_rel_binding name =        (Binding.qualify true proto_name (Binding.name name), srcs);   in     setup_proto mk_rel_binding (proto_const, proto_def) spec_ctxt-    |> apsnd (Local_Theory.theory (fn thy =>+    |> apsnd (Local_Theory.raw_theory (fn thy =>         let           val locale_b = Binding.name (proto_name ^ "_state");           val _ = Output.writeln ("\nlocale\n  " ^ (Binding.name_of locale_b));@@ -424,15 +420,14 @@   end;  (* registering the protocol definition command *)-local structure P = OuterParse and K = OuterKeyword in-  val protodef_parser = -    P.binding --| P.where_ -- (SpecParse.opt_thm_name ":" -- P.prop);-  val _ =-    OuterSyntax.local_theory "protocol" "security protocol definition" -      K.thy_decl (protodef_parser >> (fn spec => define_proto_cmd spec #> #2));-end;+val protodef_parser = +  Parse.binding --| Parse.where_ -- (Parse_Spec.opt_thm_name ":" -- Parse.prop); +val _ =+  Outer_Syntax.local_theory @{command_spec "protocol"} "security protocol definition" +    (protodef_parser >> (fn spec => define_proto_cmd spec #> #2)); + (****************************************************************************** **  Sources Case Name Computation ******************************************************************************)@@ -550,7 +545,7 @@ (* Insert the case names into a theorem *) fun insert_case_names ctxt th =   let-    val thy           = ProofContext.theory_of ctxt;+    val thy           = Proof_Context.theory_of ctxt;     val cases         = source_case_names th;     val case_hint     = Hints.mk_hint_thm thy "case_name" o HOLogic.mk_string o nth cases;     fun ins_tac (_,i) = Method.insert_tac [case_hint (i-1)] i;@@ -638,13 +633,13 @@         ]   in     (FIRST' (map mk_elim_tac ty_elim_ths)) THEN'-    (TRY o Clasimp.clarsimp_tac (clasimpset_of ctxt))+    (TRY o Clasimp.clarsimp_tac ctxt)   end;   fun expand_knows_cases_tac ctxt ty_elim_ths =   REPEAT_DETERM1 (-    FIRST [ safe_tac (claset_of ctxt)+    FIRST [ safe_tac ctxt           , CHANGED_PROP (TRYALL (full_simp_tac (simpset_of ctxt)))           , CHANGED_PROP (TRYALL (type_elim_tac ctxt ty_elim_ths))           ] @@ -690,7 +685,7 @@     val knows_ct =        HOLogic.mk_mem (msg_t, @{term "knows t"})       |> HOLogic.mk_Trueprop-      |> Thm.cterm_of (ProofContext.theory_of lthy);+      |> Thm.cterm_of (Proof_Context.theory_of lthy);      val knows_th = Thm.assume knows_ct;   in @@ -698,7 +693,7 @@     |> HOL_Ext.make_HOL_elim     |> refine_knows_cases lthy (SOME msg_t)     |> Thm.implies_intr knows_ct-    |> singleton (ProofContext.export lthy ctxt) +    |> singleton (Proof_Context.export lthy ctxt)      |> Drule.zero_var_indexes   end; @@ -706,7 +701,7 @@ (*** Precomputing and storing chain rule expansion in the actual theory ***)  structure KnowsCasesCache = Named_Thms-  (val name ="knows_cases_cache"+  (val name = @{binding "knows_cases_cache"}    val description = "Cache of protocol and message specific specializations of the knows_cases theorem")  (* shorthand for attributes modifying the knowledge cases *)@@ -758,10 +753,9 @@   let     val (typ_const,typ_def) = ann_def; -    val cs = Classical.claset_of ctxt;-    val ss = Simplifier.simpset_of ctxt -               addsimps [typ_def];-    val ss_full = ss addsimps  @{thms mk_typing_def};+    val autom_tac = auto_tac (map_simpset (fn ss => ss addsimps [typ_def]) ctxt)+    val ss_full = Simplifier.simpset_of ctxt +               addsimps [typ_def] addsimps @{thms mk_typing_def};          val vars = typ_def |> Thm.prop_of        |> ESPL_Utils.dest_HOL_def |> snd |> dest_mk_typing |> map fst;@@ -770,9 +764,9 @@      val mono_typ_th = (@{const monoTyp} $ typ_const)       |> HOLogic.mk_Trueprop-      |> Thm.cterm_of (ProofContext.theory_of ctxt)+      |> Thm.cterm_of (Proof_Context.theory_of ctxt)       |> (fn ct => Goal.prove_internal [] ct-           (K (auto_tac (cs, ss)))+           (K autom_tac)          );   in    ctxt@@ -792,9 +786,9 @@       (Binding.qualify true (Binding.name_of b) (Binding.name name), srcs);      val ((typ_const, (_, typ_def)), spec_ctxt) = params_ctxt -      |> Specification.definition_cmd +      |> Specification.definition_cmd           (SOME (b, SOME "WeakTyping.typing", NoSyn)-          , ((att,srcs), raw_def));+          , ((att,srcs), raw_def)) true;   in     setup_typing mk_rel_binding (typ_const, typ_def) spec_ctxt   end;@@ -811,7 +805,7 @@ fun type_invariant_cmd (spec as ((typing_b,proto_name),_)) lthy =   lthy   |> #2 o define_typing_cmd spec-  |> Local_Theory.theory (fn thy =>+  |> Local_Theory.raw_theory (fn thy =>       let         val typ_name = Binding.name_of typing_b;         val typ_t    = Syntax.read_term_global thy typ_name;@@ -821,7 +815,7 @@          val (_,lthy) =            add_type_invariant_locale (locale_b, (typ_t, proto_t)) thy;-        val case_th  = ProofContext.get_thm lthy "knows_cases";+        val case_th  = Proof_Context.get_thm lthy "knows_cases";       in         lthy         |> #2 o precompute_source_elim_rules case_th@@ -830,14 +824,14 @@    );  (* register the type invariant definition command *)-local structure P = OuterParse and K = OuterKeyword in+local structure P = Parse and K = Keyword in   val for_proto = P.$$$ "for" |-- P.term;    val type_invariant_parser = -    P.binding -- for_proto --| P.where_ -- (SpecParse.opt_thm_name ":" -- P.prop);+    P.binding -- for_proto --| P.where_ -- (Parse_Spec.opt_thm_name ":" -- P.prop);   val _ =-    OuterSyntax.local_theory "type_invariant" "type invariant definition" -      K.thy_decl (type_invariant_parser >> type_invariant_cmd);+    Outer_Syntax.local_theory @{command_spec "type_invariant"} "type invariant definition" +      (type_invariant_parser >> type_invariant_cmd); end;  end;
data/isabelle/src/ESPLogic/espl_methods.ML view
@@ -20,8 +20,8 @@      : Proof.context -> bool -> term ->        thm option -> thm list -> int -> thm -> (cases * thm) Seq.seq   val sourcesP-     : Context.generic * OuterLex.token list ->-       ((bool * term) * thm option) * (Context.generic * OuterLex.token list)+     : Context.generic * Token.T list ->+       ((bool * term) * thm option) * (Context.generic * Token.T list)    (* "prefix_close" proof state transformation *)   val prefix_close_thms: Proof.context -> thm list -> thm list@@ -69,7 +69,7 @@            else              TRY o Method.insert_tac facts' THEN'              TRY o (-                Clasimp.clarsimp_tac (clasimpset_of ctxt) THEN'+                Clasimp.clarsimp_tac ctxt THEN'                 TRY o Orders.order_tac ctxt []              )           )@@ -86,9 +86,9 @@ (* The tactic underlying the "sources" proof method *) fun sources_tac ctxt minimal msg_t opt_raw_rule facts =   let-    val thy = ProofContext.theory_of ctxt;+    val thy = Proof_Context.theory_of ctxt;     val cert = Thm.cterm_of thy;-    val css as (_, ss) = Clasimp.clasimpset_of ctxt;+    val ss = simpset_of ctxt;      val raw_rules = case opt_raw_rule of         SOME th => [th]@@ -113,7 +113,7 @@         (fn facts' =>          ALLGOALS (Method.insert_tac (facts' @ facts)) THEN         (ALLGOALS (assume_tac ORELSE' eresolve_tac predOrd_elim_ths)-         ORELSE auto_tac (css addIs2 predOrd_elim_ths))+         ORELSE auto_tac (ctxt addIs predOrd_elim_ths))         )       |> simplify ss @@ -123,7 +123,7 @@       | SOME th => finalize_knows_cases ctxt minimal facts th   in     fn i => fn st =>-      CASES (Rule_Cases.make_common false (thy, Thm.prop_of rule) (fst cases)+      CASES (Rule_Cases.make_common (thy, Thm.prop_of rule) (fst cases)             )             (Tactic.rtac rule i) st   end;@@ -139,10 +139,9 @@    explicitly. *) local-  structure P = OuterParse;   val ruleN = "rule";   val rule = Scan.lift (Args.$$$ ruleN -- Args.colon) |-- Attrib.thm;-  val opt_bang = Scan.lift (Scan.optional (P.$$$ "!" >> K true) false);+  val opt_bang = Scan.lift (Scan.optional (Parse.$$$ "!" >> K true) false); in   val sourcesP = opt_bang -- Args.term -- Scan.option rule; end;@@ -182,7 +181,7 @@ *) fun prefix_close_thms ctxt facts =    let-    val prefixClose_th = ProofContext.get_thm ctxt "ext_prefixClose";+    val prefixClose_th = Proof_Context.get_thm ctxt "ext_prefixClose";     fun close step roleMap = [step, roleMap] MRS prefixClose_th;     val expand = Simplifier.simplify (Simplifier.simpset_of ctxt);     val distinct_prop = distinct (Thm.eq_thm);@@ -207,7 +206,7 @@   let val ctxt  = Proof.context_of state;       val facts = Proof.the_facts state;       val facts' = facts @ prefix_close_thms ctxt facts-  in Proof.put_facts (SOME facts') state end+  in Proof.set_facts facts' state end  (* A proof state transformation implementing prefix closing of    the currently used facts.@@ -219,12 +218,11 @@       |> (fn {context = ctxt, facts=using, goal=_} =>             prefix_close_thms ctxt using) -  in Proof.using_i [[(using,[])]] state end;+  in Proof.using [[(using,[])]] state end;  (* registering the prefix_close command *) val _ =-  OuterSyntax.command "prefix_close" "prefix close facts being used"-    (OuterKeyword.tag_proof OuterKeyword.prf_decl)+  Outer_Syntax.command @{command_spec "prefix_close"} "prefix close facts being used"     (Scan.succeed (Toplevel.print o (Toplevel.proof prefix_close_cmd)));  @@ -277,7 +275,7 @@    in      th-    |> SINGLE (REPEAT (safe_tac cs THEN (TRYALL (full_simp_tac ss))))    +    |> SINGLE (REPEAT (safe_tac (Context.proof_of ctxt) THEN (TRYALL (full_simp_tac ss))))         |> the     |> add_case_info   end
data/isabelle/src/ESPLogic/espl_utils.ML view
@@ -103,19 +103,19 @@    premises  *) val local_standard' =-  forall_intr_frees+  Thm.forall_intr_frees   #> `Thm.maxidx_of   #-> (fn maxidx =>     Thm.forall_elim_vars (maxidx + 1)     #> Thm.strip_shyps     #> zero_var_indexes-    #> Thm.varifyT);+    #> Thm.varifyT_global);  (* Generate the theorem proving the expansion of a term wrto to the given    simpset and convert it into a rule. *) fun expand_term ss t = t-  |> Thm.cterm_of (ProofContext.theory_of (MetaSimplifier.the_context ss))+  |> Thm.cterm_of (Proof_Context.theory_of (Raw_Simplifier.the_context ss))   |> Simplifier.rewrite ss   |> (fn conv => conv RS @{thm meta_eq_to_obj_eq})    |> local_standard'@@ -125,7 +125,7 @@  (* create a simpset consisting only of the given theorems in the given context *) fun thms_to_simpset ctxt ths = -  Simplifier.context ctxt (MetaSimplifier.empty_ss addsimps ths);+  Simplifier.context ctxt (Raw_Simplifier.empty_ss addsimps ths);  (* Expand a list of terms and note the resulting theorems. *) fun notes_expansion ss to_expand = @@ -151,7 +151,7 @@    inst is a positional instantiation. *) fun add_simple_locale b loc_name inst thy =-  Expression.add_locale b (Binding.empty)+  Expression.add_locale I b (Binding.empty)   ( [ ( Locale.intern thy loc_name       , ( ("",false)         , Expression.Positional inst
data/isabelle/src/compromising_adversaries/CR_paper_acm.thy view
@@ -71,7 +71,7 @@     show ?case using facts     proof(sources! "         Enc ( s(MV ''k'' tid0) ) ( PK ( s(AV ''S'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits) | (fastsimp intro: event_predOrdI split: if_splits))+)?+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits) | (fastforce intro: event_predOrdI split: if_splits))+)?   qed   thus "auto_msc_typing_state t r s" by unfold_locales auto qed@@ -213,12 +213,12 @@     proof(sources "Enc (LN ''k'' test) (PK (s (AV ''S'' tid')))")       case C_2_enc       thus ?thesis -        by (fastsimp dest: compr_predOrdI)+        by (fastforce dest: compr_predOrdI)     qed   next     case C_5_k     thus ?thesis-      by (fastsimp dest: compr_predOrdI)+      by (fastforce dest: compr_predOrdI)   qed qed @@ -232,7 +232,7 @@   shows     False using facts-by(fastsimp dest: C_k_origin allowed_reveals)+by(fastforce dest: C_k_origin allowed_reveals)  lemma (in CR_state_ADVint) C_k_secrecy_others:   assumes facts:@@ -313,7 +313,7 @@   proof(sources "Hash ( LN ''k'' test )")     case fake     thus ?thesis -      by(fastsimp dest: C_k_secrecy_protected intro: event_predOrdI)+      by(fastforce dest: C_k_secrecy_protected intro: event_predOrdI)   next     case (S_3_hash tid2)     thus ?thesis@@ -323,23 +323,23 @@     next       case fake       thus ?thesis-        by (fastsimp dest: C_k_secrecy_protected intro: event_predOrdI)+        by (fastforce dest: C_k_secrecy_protected intro: event_predOrdI)     qed   next     case C_3_hash     thus ?thesis-      by(fastsimp dest: compr_predOrdI allowed_reveals)+      by(fastforce dest: compr_predOrdI allowed_reveals)   next     case (S_2_hash tid2)     thus ?thesis     proof(sources "Enc (LN ''k'' test) (PK (s (AV ''S'' tid2)))")       case fake       thus ?thesis-        by (fastsimp dest: C_k_secrecy_protected intro: event_predOrdI)+        by (fastforce dest: C_k_secrecy_protected intro: event_predOrdI)     next       case C_2_enc       thus ?thesis-        by(fastsimp dest: compr_predOrdI allowed_reveals)+        by(fastforce dest: compr_predOrdI allowed_reveals)     qed   qed qed@@ -363,7 +363,7 @@   proof(sources "Hash ( LN ''k'' test )")     case fake     thus ?thesis -      by(fastsimp dest: C_k_secrecy_others intro: event_predOrdI)+      by(fastforce dest: C_k_secrecy_others intro: event_predOrdI)   next     case (S_3_hash tid2)     thus ?thesis@@ -373,23 +373,23 @@     next       case fake       thus ?thesis-        by (fastsimp dest: C_k_secrecy_others intro: event_predOrdI)+        by (fastforce dest: C_k_secrecy_others intro: event_predOrdI)     qed   next     case C_3_hash     thus ?thesis-      by(fastsimp dest: compr_predOrdI allowed_reveals)+      by(fastforce dest: compr_predOrdI allowed_reveals)   next     case (S_2_hash tid2)     thus ?thesis     proof(sources "Enc (LN ''k'' test) (PK (s (AV ''S'' tid2)))")       case fake       thus ?thesis-        by (fastsimp dest: C_k_secrecy_others intro: event_predOrdI)+        by (fastforce dest: C_k_secrecy_others intro: event_predOrdI)     next       case C_2_enc       thus ?thesis-        by(fastsimp dest: compr_predOrdI allowed_reveals)+        by(fastforce dest: compr_predOrdI allowed_reveals)     qed   qed qed@@ -412,7 +412,7 @@   proof(sources "Hash ( LN ''k'' test )")     case fake     thus ?thesis -      by(fastsimp dest: C_k_secrecy_sessKey intro: event_predOrdI)+      by(fastforce dest: C_k_secrecy_sessKey intro: event_predOrdI)   next     case (S_3_hash tid2)     thus ?thesis@@ -422,23 +422,23 @@     next       case fake       thus ?thesis-        by (fastsimp dest: C_k_secrecy_sessKey intro: event_predOrdI)+        by (fastforce dest: C_k_secrecy_sessKey intro: event_predOrdI)     qed   next     case C_3_hash     thus ?thesis-      by(fastsimp dest: compr_predOrdI allowed_reveals)+      by(fastforce dest: compr_predOrdI allowed_reveals)   next     case (S_2_hash tid2)     thus ?thesis     proof(sources "Enc (LN ''k'' test) (PK (s (AV ''S'' tid2)))")       case fake       thus ?thesis-        by (fastsimp dest: C_k_secrecy_sessKey intro: event_predOrdI)+        by (fastforce dest: C_k_secrecy_sessKey intro: event_predOrdI)     next       case C_2_enc       thus ?thesis-        by(fastsimp dest: compr_predOrdI allowed_reveals)+        by(fastforce dest: compr_predOrdI allowed_reveals)     qed   qed qed@@ -461,7 +461,7 @@   proof(sources "Hash ( LN ''k'' test )")     case fake     thus ?thesis -      by(fastsimp dest: C_k_secrecy_state intro: event_predOrdI)+      by(fastforce dest: C_k_secrecy_state intro: event_predOrdI)   next     case (S_3_hash tid2)     thus ?thesis@@ -471,23 +471,23 @@     next       case fake       thus ?thesis-        by (fastsimp dest: C_k_secrecy_state intro: event_predOrdI)+        by (fastforce dest: C_k_secrecy_state intro: event_predOrdI)     qed   next     case C_3_hash     thus ?thesis-      by(fastsimp dest: compr_predOrdI allowed_reveals)+      by(fastforce dest: compr_predOrdI allowed_reveals)   next     case (S_2_hash tid2)     thus ?thesis     proof(sources "Enc (LN ''k'' test) (PK (s (AV ''S'' tid2)))")       case fake       thus ?thesis-        by (fastsimp dest: C_k_secrecy_state intro: event_predOrdI)+        by (fastforce dest: C_k_secrecy_state intro: event_predOrdI)     next       case C_2_enc       thus ?thesis-        by(fastsimp dest: compr_predOrdI allowed_reveals)+        by(fastforce dest: compr_predOrdI allowed_reveals)     qed   qed qed@@ -510,7 +510,7 @@   proof(sources "Hash ( LN ''k'' test )")     case fake     thus ?thesis -      by(fastsimp dest: C_k_secrecy_actor intro: event_predOrdI)+      by(fastforce dest: C_k_secrecy_actor intro: event_predOrdI)   next     case (S_3_hash tid2)     thus ?thesis@@ -520,23 +520,23 @@     next       case fake       thus ?thesis-        by (fastsimp dest: C_k_secrecy_actor intro: event_predOrdI)+        by (fastforce dest: C_k_secrecy_actor intro: event_predOrdI)     qed   next     case C_3_hash     thus ?thesis-      by(fastsimp dest: compr_predOrdI allowed_reveals)+      by(fastforce dest: compr_predOrdI allowed_reveals)   next     case (S_2_hash tid2)     thus ?thesis     proof(sources "Enc (LN ''k'' test) (PK (s (AV ''S'' tid2)))")       case fake       thus ?thesis-        by (fastsimp dest: C_k_secrecy_actor intro: event_predOrdI)+        by (fastforce dest: C_k_secrecy_actor intro: event_predOrdI)     next       case C_2_enc       thus ?thesis-        by(fastsimp dest: compr_predOrdI allowed_reveals)+        by(fastforce dest: compr_predOrdI allowed_reveals)     qed   qed qed@@ -561,7 +561,7 @@   proof(sources "Hash ( LN ''k'' test )")     case fake     thus ?thesis -      by(fastsimp dest: C_k_secrecy_all intro: event_predOrdI)+      by(fastforce dest: C_k_secrecy_all intro: event_predOrdI)   next     case (S_3_hash tid2)     thus ?thesis@@ -571,23 +571,23 @@     next       case fake       thus ?thesis-        by (fastsimp dest: C_k_secrecy_all intro: event_predOrdI)+        by (fastforce dest: C_k_secrecy_all intro: event_predOrdI)     qed   next     case C_3_hash     thus ?thesis-      by(fastsimp dest: compr_predOrdI allowed_reveals)+      by(fastforce dest: compr_predOrdI allowed_reveals)   next     case (S_2_hash tid2)     thus ?thesis     proof(sources "Enc (LN ''k'' test) (PK (s (AV ''S'' tid2)))")       case fake       thus ?thesis-        by (fastsimp dest: C_k_secrecy_all intro: event_predOrdI)+        by (fastforce dest: C_k_secrecy_all intro: event_predOrdI)     next       case C_2_enc       thus ?thesis-        by(fastsimp dest: compr_predOrdI allowed_reveals)+        by(fastforce dest: compr_predOrdI allowed_reveals)     qed   qed qed
data/isabelle/src/compromising_adversaries/NS_Public_acm.thy view
@@ -75,7 +75,7 @@                s(AV ''R'' tid0)             |}             ( PK ( s(AV ''I'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits) | (fastsimp intro: event_predOrdI split: if_splits))+)?+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits) | (fastforce intro: event_predOrdI split: if_splits))+)?   next     case (R_1_ni t r s tid0)     note facts = this@@ -85,7 +85,7 @@     proof(sources! "         Enc {| LC ''1'', s(MV ''ni'' tid0), s(AV ''I'' tid0) |}             ( PK ( s(AV ''R'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits) | (fastsimp intro: event_predOrdI split: if_splits))+)?+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits) | (fastforce intro: event_predOrdI split: if_splits))+)?   qed   thus "auto_msc_typing_state t r s" by unfold_locales auto qed@@ -199,7 +199,7 @@       "Enc {| LC ''2'', LN ''ni'' test, s(MV ''nr'' test), s(AV ''R'' test)|} ( PK ( s(AV ''I'' test) ) ) ")     case fake     thus ?thesis-      by(fastsimp dest: I_ni_origin intro: event_predOrdI)+      by(fastforce dest: I_ni_origin intro: event_predOrdI)   next     case (R_2_enc tid1')     thus ?thesis@@ -223,18 +223,18 @@   proof(sources "Enc {| LC ''3'', LN ''nr'' test |} ( PK ( s(AV ''R'' test) ) ) ")     case fake     thus ?thesis -      by (fastsimp dest: R_nr_origin intro: event_predOrdI)+      by (fastforce dest: R_nr_origin intro: event_predOrdI)   next     case (I_3_enc tid1)      thus ?thesis     proof(sources "Enc {| LC ''2'', LN ''ni'' tid1, LN ''nr'' test, s(AV ''R'' test)|}( PK ( s(AV ''I'' tid1) ) ) ")       case fake        thus ?thesis-        by(fastsimp dest: R_nr_origin intro: event_predOrdI) +        by(fastforce dest: R_nr_origin intro: event_predOrdI)      next       case R_2_enc       thus ?thesis -        by (fastsimp dest: I_ni_origin intro: event_predOrdI) +        by (fastforce dest: I_ni_origin intro: event_predOrdI)      qed   qed qed@@ -256,7 +256,7 @@   proof(sources "Hash \<lbrace>LN ''ni'' test, s (MV ''nr'' test)\<rbrace>")     case fake     thus ?thesis-      by(fastsimp dest: I_ni_origin intro: event_predOrdI)+      by(fastforce dest: I_ni_origin intro: event_predOrdI)   next     case I_4_hash     thus ?thesis@@ -268,7 +268,7 @@        (PK (s (AV ''I'' test)))")       case fake       thus ?thesis-        by(fastsimp dest: I_ni_origin intro: event_predOrdI)+        by(fastforce dest: I_ni_origin intro: event_predOrdI)     next       case R_2_enc       thus ?thesis@@ -294,7 +294,7 @@   proof(sources "Hash \<lbrace>s (MV ''ni'' test), LN ''nr'' test\<rbrace>")     case fake     thus ?thesis-      by(fastsimp dest: R_nr_origin intro: event_predOrdI)+      by(fastforce dest: R_nr_origin intro: event_predOrdI)   next     case R_4_hash     thus ?thesis@@ -306,7 +306,7 @@        (PK (s (AV ''I'' tid1)))")       case fake       thus ?thesis-        by(fastsimp dest: R_nr_origin intro: event_predOrdI)+        by(fastforce dest: R_nr_origin intro: event_predOrdI)     next       case R_2_enc       thus ?thesis@@ -324,7 +324,7 @@     "LN ''ni'' test \<in> knows t"   shows "False" using facts-by(insert I_ni_origin, fastsimp dest!: allowed_reveals)+by(insert I_ni_origin, fastforce dest!: allowed_reveals)  lemma (in ns_public_state_ADVall) R_nr_secrecy:   assumes facts:@@ -332,7 +332,7 @@     "LN ''nr'' test \<in> knows t"   shows "False" using facts-by(insert R_nr_origin, fastsimp dest!: allowed_reveals)+by(insert R_nr_origin, fastforce dest!: allowed_reveals)  lemma (in ns_public_state_ADVall) I_nr_secrecy:   assumes facts:@@ -341,7 +341,7 @@     "s(MV ''nr'' test) \<in>  knows t"   shows "False" using facts-by(insert I_nr_origin, fastsimp dest!: allowed_reveals)+by(insert I_nr_origin, fastforce dest!: allowed_reveals)   lemma (in ns_public_state_ADVall) R_ni_secrecy:@@ -351,7 +351,7 @@     "s(MV ''ni'' test) \<in> knows t"   shows "False" using facts-by(insert R_ni_origin, fastsimp dest!: allowed_reveals)+by(insert R_ni_origin, fastforce dest!: allowed_reveals)  lemma (in ns_public_state_ADVall) I_sessKey_secrecy:   assumes facts:@@ -410,7 +410,7 @@     next       case I_1_enc       thus ?thesis-        by(fastsimp)+        by(fastforce)     qed   qed qed
data/isabelle/src/compromising_adversaries/PFS_acm.thy view
@@ -82,8 +82,8 @@       thus ?thesis proof(sources! "                        Enc \<lbrace> LC ''2'', s(AV ''A'' tid0), s(MV ''k'' tid0) \<rbrace>                            ( SK ( s(AV ''B'' tid0) ) ) ")-      qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits) | (fastsimp intro: event_predOrdI split: if_splits))+)?-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?+      qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits) | (fastforce intro: event_predOrdI split: if_splits))+)?+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?   next     case (B_1_pkNa t r s tid0) note facts = this     then interpret state: auto_msc_typing_state t r s@@ -92,7 +92,7 @@     proof(sources! "         Enc \<lbrace> LC ''1'', s(AV ''B'' tid0), s(MV ''pkNa'' tid0) \<rbrace>             ( SK ( s(AV ''A'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits) | (fastsimp intro: event_predOrdI split: if_splits))+)?+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits) | (fastforce intro: event_predOrdI split: if_splits))+)?   qed   thus "auto_msc_typing_state t r s" by unfold_locales auto qed@@ -156,7 +156,7 @@                        ( SK ( s(AV ''A'' test) ) ) ")       case fake       thus ?thesis -      by (sources "SK (s (AV ''A'' test))") (fastsimp intro: predOrd_distinct'_trans)+      by (sources "SK (s (AV ''A'' test))") (fastforce intro: predOrd_distinct'_trans)     next       case (A_1_enc tid1)       thus ?thesis @@ -177,7 +177,7 @@        (SK (s (AV ''A'' tid1)))")           case fake           thus ?thesis-            by (sources "SK (s (AV ''A'' test))") (fastsimp intro: predOrd_distinct'_trans)+            by (sources "SK (s (AV ''A'' test))") (fastforce intro: predOrd_distinct'_trans)         next           case (A_1_enc tid1')           thus ?thesis@@ -218,7 +218,7 @@                        ( SK ( s(AV ''B'' test) ) ) ")       case fake       thus ?thesis-      by (sources "SK (s (AV ''B'' test))") (fastsimp intro: predOrd_distinct'_trans)+      by (sources "SK (s (AV ''B'' test))") (fastforce intro: predOrd_distinct'_trans)     next       case (B_2_enc_1 tid1)       thus ?thesis@@ -226,7 +226,7 @@        (SK (s (AV ''A'' test)))")         case fake         thus ?thesis-          by (sources "SK (s (AV ''A'' tid1))")(fastsimp intro: predOrd_distinct'_trans)    next+          by (sources "SK (s (AV ''A'' tid1))")(fastforce intro: predOrd_distinct'_trans)    next         case (A_1_enc tid1')         thus ?thesis            by (sources "SK (LN ''na'' tid1')")@@ -345,7 +345,7 @@       proof(sources "Enc \<lbrace>LC ''2'', s (AV ''A'' test), s (MV ''k'' test)\<rbrace> (SK (s (AV ''B'' test)))")         case fake         thus ?thesis-          by (fastsimp dest: A_sec_k event_predOrdI)+          by (fastforce dest: A_sec_k event_predOrdI)       next         case (B_2_enc_1 tid1)         thus ?thesis@@ -357,7 +357,7 @@             thus ?thesis               apply -               apply(frule lkr_in_reveals_predOrd1)-              by (fastsimp dest: allowed_reveals)+              by (fastforce dest: allowed_reveals)           qed         next           case (A_1_enc test)@@ -376,7 +376,7 @@             thus ?thesis               apply -               apply(frule lkr_in_reveals_predOrd1)-              by (fastsimp dest: allowed_reveals)+              by (fastforce dest: allowed_reveals)           qed         next           case A_1_enc@@ -426,7 +426,7 @@             thus ?thesis               apply -               apply(frule lkr_in_reveals_predOrd1)-              by (fastsimp dest: allowed_reveals)              +              by (fastforce dest: allowed_reveals)                         qed         next           case B_2_enc_1@@ -439,7 +439,7 @@               thus ?thesis                 apply -                 apply(frule lkr_in_reveals_predOrd1)-                by (fastsimp dest: allowed_reveals)+                by (fastforce dest: allowed_reveals)             qed           next             case (A_1_enc tid2)@@ -458,7 +458,7 @@               thus ?thesis                 apply -                 apply(frule lkr_in_reveals_predOrd1)-                by (fastsimp dest: allowed_reveals)+                by (fastforce dest: allowed_reveals)             qed         next           case A_1_enc
data/isabelle/src/compromising_adversaries/TLS_acm.thy view
@@ -142,31 +142,31 @@     then interpret state: auto_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (C_4_ps t r s tid0) note facts = this     then interpret state: auto_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (S_1_nc t r s tid0) note facts = this     then interpret state: auto_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (S_1_pc t r s tid0) note facts = this     then interpret state: auto_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (S_1_sid t r s tid0) note facts = this     then interpret state: auto_msc_typing_state t r s       by unfold_locales auto     show ?case using facts-    by (fastsimp intro: event_predOrdI split: if_splits)+    by (fastforce intro: event_predOrdI split: if_splits)   next     case (S_5_pms t r s tid0) note facts = this     then interpret state: auto_msc_typing_state t r s@@ -175,7 +175,7 @@     proof(sources! "         Enc {| LC ''TT0'', s(MV ''pms'' tid0) |}             ( PK ( s(AV ''S'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits) | (fastsimp intro: event_predOrdI split: if_splits))+)?+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits) | (fastforce intro: event_predOrdI split: if_splits))+)?   qed   thus "auto_msc_typing_state t r s" by unfold_locales auto qed@@ -1339,7 +1339,7 @@ proof -   from facts   have "roleMap r tid1 = Some S"-    by (fastsimp dest: mk_partneringRole simp add: TLS_partners_conv)+    by (fastforce dest: mk_partneringRole simp add: TLS_partners_conv)   note_prefix_closed facts = facts this   thus ?thesis   proof -@@ -1348,14 +1348,14 @@         {(sLAV ''C'', sLAV ''C'', S_1), (sLAV ''S'', sLAV ''S'', S_1),          (sLMV ''ns'', sLN ''ns'', S_3), (sLN ''pms'', sLMV ''pms'', S_5)}         (t, r, s)"-      by (fastsimp simp add: TLS_partners_conv dest: mk_partneringRole)+      by (fastforce simp add: TLS_partners_conv dest: mk_partneringRole)     moreover     from facts      have "(i, test) \<in> mk_partnering TLS_acm.C S         {(sLAV ''C'', sLAV ''C'', S_1), (sLAV ''S'', sLAV ''S'', S_1),          (sLMV ''ns'', sLN ''ns'', S_3), (sLN ''pms'', sLMV ''pms'', S_5)}         (t, r, s)"-      by (fastsimp simp add: TLS_partners_conv dest: mk_partneringRole)+      by (fastforce simp add: TLS_partners_conv dest: mk_partneringRole)     ultimately     show ?thesis       using facts@@ -1485,12 +1485,12 @@     note_unified facts = facts this      hence "(test,tid1) \<in> TLS_partners (t,r,s)"-      by fastsimp+      by fastforce     note_unified facts = facts this     moreover      {       assume "RLKR (s (AV ''S'' tid1)) \<in> reveals t"-      hence "?thesis" using facts by fastsimp+      hence "?thesis" using facts by fastforce     }     moreover{       assume "(tid1, Note ''5'' State C_5_pt) \<in> steps t"@@ -1509,20 +1509,20 @@       note_unified facts = facts this       obtain tid1a where         partCompr: "(tid1, tid1a) \<in> TLS_partners (t, r, s) \<and> (tid1a, Note ''6'' State S_6_pt) \<in> steps t"-        using facts by fastsimp+        using facts by fastforce       hence  "test = tid1a" using facts         apply -         apply(rule TLS_partners_revealsExist,assumption,assumption,rule event_predOrdI, assumption)          -        by fastsimp++        by fastforce+       hence "?thesis"         using facts partCompr-        by fastsimp+        by fastforce     }     ultimately     show ?thesis using facts       apply -       apply(frule event_predOrdI, frule C_pms_origin_reuse, assumption)-      by fastsimp+      by fastforce   qed qed end
data/isabelle/src/compromising_adversaries/wPFS_acm.thy view
@@ -93,8 +93,8 @@                        Enc \<lbrace> LC ''2'', LN ''sid'' tid0, s(AV ''A'' tid0), s(MV ''k'' tid0)                            \<rbrace>                            ( SK ( s(AV ''B'' tid0) ) ) ")-      qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits) | (fastsimp intro: event_predOrdI split: if_splits))+)?-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits))+)?+      qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits) | (fastforce intro: event_predOrdI split: if_splits))+)?+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)?   next     case (B_1_pkNa t r s tid0) note facts = this     then interpret state: auto_msc_typing_state t r s@@ -105,7 +105,7 @@               s(MV ''pkNa'' tid0)             \<rbrace>             ( SK ( s(AV ''A'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits) | (fastsimp intro: event_predOrdI split: if_splits))+)?+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits) | (fastforce intro: event_predOrdI split: if_splits))+)?   next     case (B_1_sid t r s tid0) note facts = this     then interpret state: auto_msc_typing_state t r s@@ -116,7 +116,7 @@               s(MV ''pkNa'' tid0)             \<rbrace>             ( SK ( s(AV ''A'' tid0) ) ) ")-    qed (insert facts, ((fastsimp intro: event_predOrdI split: if_splits) | (fastsimp intro: event_predOrdI split: if_splits))+)?+    qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits) | (fastforce intro: event_predOrdI split: if_splits))+)?   qed   thus "auto_msc_typing_state t r s" by unfold_locales auto qed@@ -181,18 +181,18 @@        (SK (s (AV ''A'' test)))")       case fake       thus ?thesis-        by (sources "SK (s (AV ''A'' test))") (fastsimp intro: predOrd_distinct'_trans)+        by (sources "SK (s (AV ''A'' test))") (fastforce intro: predOrd_distinct'_trans)     next       case (A_1_enc tid1)       thus ?thesis        proof(sources " SK ( LN ''na'' tid1 ) ")         case A_N1_SK         thus ?thesis -          by (fastsimp intro: compr_predOrdI)+          by (fastforce intro: compr_predOrdI)       next         case A_N0_SK         thus ?thesis-          by (fastsimp intro: compr_predOrdI)+          by (fastforce intro: compr_predOrdI)       qed     qed   next@@ -268,14 +268,14 @@     proof(sources "Enc \<lbrace>LC ''2'', LN ''sid'' test, s (AV ''A'' test), s (MV ''k'' test)\<rbrace> (SK (s (AV ''B'' test)))")       case fake       thus ?thesis-        by (sources "SK (s (AV ''B'' test))") (fastsimp intro: predOrd_distinct'_trans)+        by (sources "SK (s (AV ''B'' test))") (fastforce intro: predOrd_distinct'_trans)     next       case (B_2_enc_1 tid1)       thus ?thesis       proof(sources "Enc \<lbrace>LC ''1'', LN ''sid'' test, s (AV ''B'' test), s (MV ''pkNa'' tid1)\<rbrace> (SK (s (AV ''A'' test)))")         case fake         thus ?thesis-          by (sources "SK (s (AV ''A'' test))") (fastsimp intro: predOrd_distinct'_trans)+          by (sources "SK (s (AV ''A'' test))") (fastforce intro: predOrd_distinct'_trans)       qed     qed   next@@ -420,7 +420,7 @@       proof(sources "Enc \<lbrace>LC ''2'', LN ''sid'' test, s (AV ''A'' test), s (MV ''k'' test)\<rbrace> (SK (s (AV ''B'' test)))")         case fake         thus ?thesis-          by (fastsimp dest: A_sec_k event_predOrdI)+          by (fastforce dest: A_sec_k event_predOrdI)       next         case (B_2_enc_1 tid1)         thus ?thesis@@ -432,7 +432,7 @@             thus ?thesis               apply -               apply(frule lkr_in_reveals_predOrd1)-              by (fastsimp dest: allowed_reveals)+              by (fastforce dest: allowed_reveals)           qed         qed       qed@@ -447,7 +447,7 @@             thus ?thesis               apply -               apply(frule lkr_in_reveals_predOrd1)-              by (fastsimp dest: allowed_reveals)+              by (fastforce dest: allowed_reveals)           qed         next           case A_1_enc@@ -480,7 +480,7 @@       thus ?thesis         apply -         apply(frule lkr_in_reveals_predOrd1)-        by (fastsimp dest: allowed_reveals)+        by (fastforce dest: allowed_reveals)     qed   next     case (A_1_enc tid1)
data/isabelle/src/isar-keywords.el view
@@ -1,6 +1,6 @@ ;; ;; Keyword classification tables for Isabelle/Isar.-;; Generated from Pure + Pure-ProofGeneral + HOL + HOLCF + IOA + HOL-Boogie + HOL-Nominal + HOL-SMT + HOL-Statespace.+;; Generated from HOLCF + HOL-BNF + HOL-Boogie + HOL-Library + HOL-Nominal + HOL-Statespace + HOL-SPARK + HOL-TPTP + HOL-Import. ;; *** DO NOT EDIT *** DO NOT EDIT *** DO NOT EDIT *** ;; @@ -8,12 +8,9 @@   '("\\."     "\\.\\."     "Isabelle\\.command"-    "Isar\\.begin_document"-    "Isar\\.define_command"-    "Isar\\.edit_document"-    "Isar\\.end_document"     "ML"     "ML_command"+    "ML_file"     "ML_prf"     "ML_val"     "ProofGeneral\\.inform_file_processed"@@ -30,21 +27,17 @@     "arities"     "assume"     "atom_decl"-    "atp_info"-    "atp_kill"-    "atp_messages"-    "atp_minimize"     "attribute_setup"-    "automaton"     "ax_specification"-    "axclass"     "axiomatization"     "axioms"     "back"+    "bnf_def"     "boogie_end"     "boogie_open"     "boogie_status"     "boogie_vc"+    "bundle"     "by"     "cannot_undo"     "case"@@ -54,6 +47,7 @@     "class_deps"     "classes"     "classrel"+    "codata"     "code_abort"     "code_class"     "code_const"@@ -61,28 +55,26 @@     "code_deps"     "code_include"     "code_instance"-    "code_library"-    "code_module"     "code_modulename"     "code_monad"     "code_pred"+    "code_reflect"     "code_reserved"     "code_thms"     "code_type"     "coinductive"     "coinductive_set"     "commit"-    "constdefs"     "consts"-    "consts_code"     "context"     "corollary"     "cpodef"+    "data"     "datatype"     "declaration"     "declare"     "def"-    "defaultsort"+    "default_sort"     "defer"     "defer_recdef"     "definition"@@ -91,35 +83,45 @@     "display_drafts"     "domain"     "domain_isomorphism"+    "domaindef"     "done"     "enable_pr"     "end"+    "enriched_type"     "equivariance"     "exit"     "export_code"     "extract"     "extract_type"-    "finalconsts"     "finally"     "find_consts"     "find_theorems"+    "find_unused_assms"     "fix"-    "fixpat"     "fixrec"     "from"     "full_prf"     "fun"     "function"-    "global"     "guess"     "have"     "header"     "help"     "hence"-    "hide"+    "hide_class"+    "hide_const"+    "hide_fact"+    "hide_type"+    "import_const_map"+    "import_file"+    "import_tptp"+    "import_type_map"+    "include"+    "including"     "inductive"     "inductive_cases"     "inductive_set"+    "inductive_simps"     "init_toplevel"     "instance"     "instantiation"@@ -131,39 +133,42 @@     "lemma"     "lemmas"     "let"+    "lift_definition"     "linear_undo"-    "local"     "local_setup"     "locale"+    "locale_deps"     "method_setup"     "moreover"-    "new_domain"     "next"     "nitpick"     "nitpick_params"     "no_notation"     "no_syntax"     "no_translations"+    "no_type_notation"     "nominal_datatype"     "nominal_inductive"     "nominal_inductive2"     "nominal_primrec"-    "nonterminals"-    "normal_form"+    "nonterminal"     "notation"     "note"+    "note_cyclic"     "note_prefix_closed"     "note_unified"-    "note_cyclic"+    "notepad"     "obtain"     "oops"     "oracle"     "overloading"     "parse_ast_translation"     "parse_translation"+    "partial_function"     "pcpodef"     "pr"     "prefer"+    "prefix_close"     "presume"     "pretty_setmargin"     "prf"@@ -171,25 +176,35 @@     "print_abbrevs"     "print_antiquotations"     "print_ast_translation"-    "print_atps"     "print_attributes"     "print_binds"+    "print_bnfs"+    "print_bundles"     "print_cases"     "print_claset"     "print_classes"     "print_codeproc"     "print_codesetup"+    "print_coercion_maps"+    "print_coercions"     "print_commands"     "print_configs"     "print_context"+    "print_dependencies"     "print_drafts"     "print_facts"     "print_induct_rules"+    "print_inductives"     "print_interps"     "print_locale"     "print_locales"     "print_methods"     "print_orders"+    "print_quotconsts"+    "print_quotients"+    "print_quotientsQ3"+    "print_quotmaps"+    "print_quotmapsQ3"     "print_rules"     "print_simpset"     "print_statement"@@ -204,8 +219,11 @@     "pwd"     "qed"     "quickcheck"+    "quickcheck_generator"     "quickcheck_params"     "quit"+    "quotient_definition"+    "quotient_type"     "realizability"     "realizers"     "recdef"@@ -216,15 +234,28 @@     "remove_thy"     "rep_datatype"     "role"-    "repdef"+    "schematic_corollary"+    "schematic_lemma"+    "schematic_theorem"     "sect"     "section"     "setup"+    "setup_lifting"     "show"     "simproc_setup"     "sledgehammer"+    "sledgehammer_params"     "smt_status"+    "solve_direct"     "sorry"+    "spark_end"+    "spark_open"+    "spark_open_siv"+    "spark_open_vcg"+    "spark_proof_functions"+    "spark_status"+    "spark_types"+    "spark_vc"     "specification"     "statespace"     "subclass"@@ -234,6 +265,7 @@     "subsubsect"     "subsubsection"     "syntax"+    "syntax_declaration"     "term"     "termination"     "text"@@ -246,17 +278,18 @@     "thm_deps"     "thus"     "thy_deps"-    "touch_thy"     "translations"+    "try"+    "try0"     "txt"     "txt_raw"     "typ"+    "type_invariant"+    "type_notation"+    "type_synonym"     "typed_print_translation"     "typedecl"     "typedef"-    "types"-    "types_code"-    "type_invariant"     "ultimately"     "undo"     "undos_proof"@@ -265,77 +298,66 @@     "use"     "use_thy"     "using"-    "prefix_close"     "value"     "values"     "welcome"     "with"+    "wrap_data"+    "write"     "{"     "}"))  (defconst isar-keywords-minor-  '("actions"-    "advanced"+  '("advanced"     "and"     "assumes"     "attach"     "avoids"     "begin"     "binder"-    "compose"+    "checking"     "congs"     "constrains"-    "contains"+    "datatypes"+    "defaults"     "defines"     "file"     "fixes"     "for"-    "hide_action"+    "functions"     "hints"     "identifier"     "if"     "imports"     "in"+    "includes"     "infix"     "infixl"     "infixr"-    "initially"-    "inputs"-    "internals"     "is"+    "keywords"     "lazy"     "module_name"     "monos"     "morphisms"+    "no_dests"     "notes"     "obtains"     "open"     "output"-    "outputs"     "overloaded"     "permissive"     "pervasive"-    "post"-    "pre"-    "rename"-    "restrict"+    "rep_compat"     "shows"-    "signature"-    "states"     "structure"-    "to"-    "transitions"-    "transrel"     "unchecked"+    "unsafe"     "uses"     "where"))  (defconst isar-keywords-control   '("Isabelle\\.command"-    "Isar\\.begin_document"-    "Isar\\.define_command"-    "Isar\\.edit_document"-    "Isar\\.end_document"     "ProofGeneral\\.inform_file_processed"     "ProofGeneral\\.inform_file_retracted"     "ProofGeneral\\.kill_proof"@@ -343,64 +365,73 @@     "ProofGeneral\\.restart"     "ProofGeneral\\.undo"     "cannot_undo"+    "cd"+    "commit"+    "disable_pr"+    "enable_pr"     "exit"     "init_toplevel"     "kill"+    "kill_thy"     "linear_undo"     "quit"+    "remove_thy"     "undo"-    "undos_proof"))+    "undos_proof"+    "use_thy"))  (defconst isar-keywords-diag   '("ML_command"     "ML_val"     "ProofGeneral\\.pr"-    "atp_info"-    "atp_kill"-    "atp_messages"-    "atp_minimize"     "boogie_status"-    "cd"     "class_deps"     "code_deps"     "code_thms"-    "commit"-    "disable_pr"     "display_drafts"-    "enable_pr"     "export_code"     "find_consts"     "find_theorems"+    "find_unused_assms"     "full_prf"     "header"     "help"-    "kill_thy"+    "locale_deps"     "nitpick"-    "normal_form"     "pr"     "pretty_setmargin"     "prf"     "print_abbrevs"     "print_antiquotations"-    "print_atps"     "print_attributes"     "print_binds"+    "print_bnfs"+    "print_bundles"     "print_cases"     "print_claset"     "print_classes"     "print_codeproc"     "print_codesetup"+    "print_coercion_maps"+    "print_coercions"     "print_commands"     "print_configs"     "print_context"+    "print_dependencies"     "print_drafts"     "print_facts"     "print_induct_rules"+    "print_inductives"     "print_interps"     "print_locale"     "print_locales"     "print_methods"     "print_orders"+    "print_quotconsts"+    "print_quotients"+    "print_quotientsQ3"+    "print_quotmaps"+    "print_quotmapsQ3"     "print_rules"     "print_simpset"     "print_statement"@@ -412,17 +443,18 @@     "pwd"     "quickcheck"     "refute"-    "remove_thy"     "sledgehammer"     "smt_status"+    "solve_direct"+    "spark_status"     "term"     "thm"     "thm_deps"     "thy_deps"-    "touch_thy"+    "try"+    "try0"     "typ"     "unused_thms"-    "use_thy"     "value"     "values"     "welcome"))@@ -444,128 +476,153 @@  (defconst isar-keywords-theory-decl   '("ML"+    "ML_file"     "abbreviation"     "arities"     "atom_decl"     "attribute_setup"-    "automaton"-    "axclass"     "axiomatization"     "axioms"     "boogie_end"     "boogie_open"+    "bundle"     "class"     "classes"     "classrel"+    "codata"     "code_abort"     "code_class"     "code_const"     "code_datatype"     "code_include"     "code_instance"-    "code_library"-    "code_module"     "code_modulename"     "code_monad"+    "code_reflect"     "code_reserved"     "code_type"     "coinductive"     "coinductive_set"-    "constdefs"     "consts"-    "consts_code"     "context"+    "data"     "datatype"     "declaration"     "declare"-    "defaultsort"+    "default_sort"     "defer_recdef"     "definition"     "defs"     "domain"     "domain_isomorphism"+    "domaindef"     "equivariance"     "extract"     "extract_type"-    "finalconsts"-    "fixpat"     "fixrec"     "fun"-    "global"-    "hide"+    "hide_class"+    "hide_const"+    "hide_fact"+    "hide_type"+    "import_const_map"+    "import_file"+    "import_tptp"+    "import_type_map"     "inductive"     "inductive_set"     "instantiation"     "judgment"     "lemmas"-    "local"     "local_setup"     "locale"     "method_setup"-    "new_domain"     "nitpick_params"     "no_notation"     "no_syntax"     "no_translations"+    "no_type_notation"     "nominal_datatype"-    "nonterminals"+    "nonterminal"     "notation"+    "notepad"     "oracle"     "overloading"     "parse_ast_translation"     "parse_translation"+    "partial_function"     "primrec"     "print_ast_translation"     "print_translation"     "protocol"+    "quickcheck_generator"     "quickcheck_params"     "realizability"     "realizers"     "recdef"     "record"     "refute_params"-    "repdef"     "role"     "setup"+    "setup_lifting"     "simproc_setup"+    "sledgehammer_params"+    "spark_end"+    "spark_open"+    "spark_open_siv"+    "spark_open_vcg"+    "spark_proof_functions"+    "spark_types"     "statespace"     "syntax"+    "syntax_declaration"     "text"     "text_raw"     "theorems"     "translations"+    "type_invariant"+    "type_notation"+    "type_synonym"     "typed_print_translation"     "typedecl"-    "types"-    "types_code"-    "type_invariant"     "use"))  (defconst isar-keywords-theory-script-  '("inductive_cases"))+  '("inductive_cases"+    "inductive_simps"))  (defconst isar-keywords-theory-goal   '("ax_specification"+    "bnf_def"     "boogie_vc"     "code_pred"     "corollary"     "cpodef"+    "enriched_type"     "function"     "instance"     "interpretation"     "lemma"+    "lift_definition"     "nominal_inductive"     "nominal_inductive2"     "nominal_primrec"     "pcpodef"+    "quotient_definition"+    "quotient_type"     "recdef_tc"     "rep_datatype"+    "schematic_corollary"+    "schematic_lemma"+    "schematic_theorem"+    "spark_vc"     "specification"     "subclass"     "sublocale"     "termination"     "theorem"-    "typedef"))+    "typedef"+    "wrap_data"))  (defconst isar-keywords-qed   '("\\."@@ -610,17 +667,19 @@ (defconst isar-keywords-proof-decl   '("ML_prf"     "also"+    "include"+    "including"     "let"     "moreover"     "note"+    "note_cyclic"     "note_prefix_closed"     "note_unified"-    "note_cyclic"     "txt"     "txt_raw"     "unfolding"     "using"-    "prefix_close"))+    "write"))  (defconst isar-keywords-proof-asm   '("assume"
interactive-only-src/Paths_scyther_proof.hs view
@@ -12,7 +12,7 @@   version :: Version-version = Version {versionBranch = [0,5,0,0], versionTags = []}+version = Version {versionBranch = [0,6,0,0], versionTags = []} bindir, libdir, datadir, libexecdir :: FilePath  bindir     = "."
scyther-proof.cabal view
@@ -1,25 +1,27 @@ build-type:         Simple name:               scyther-proof-version:            0.5.0.0+version:            0.6.0.0 license:            GPL license-file:       LICENSE category:           Security, Theorem Provers-author:             Simon Meier <simon.meier@inf.ethz.ch>-maintainer:         Simon Meier <simon.meier@inf.ethz.ch>-copyright:          Simon Meier, ETH Zurich, 2009-2011-synopsis:           Automatic generation of Isabelle/HOL correctness proofs for security protocols.-description:-                    scyther-proof is a security protocol verification tool+author:             Simon Meier <iridcode@gmail.com>, +                    Andreas Lochbihler <andreas.lochbihler@inf.ethz.ch>+maintainer:         Simon Meier <iridcode@gmail.com>+copyright:          Simon Meier, Andreas Lochbihler, ETH Zurich, 2009-2013++synopsis:           Automatic generation of Isabelle/HOL correctness proofs +                    for security protocols.++description:        scyther-proof is a security protocol verification tool                     based on an algorithm similar to the Scyther tool developed                     by Cas Cremers                     (<http://people.inf.ethz.ch/cremersc/scyther/index.html>).                     The theory underlying scyther-proof is described in the-                    paper \"Strong Invariants for the Efficient Construction of-                    Machine-Checked Protocol Security Proofs\" by Meier,-                    Cremers, and Basin available from-                    <http://people.inf.ethz.ch/meiersi/publications/index.html>--homepage:           http://www.infsec.ethz.ch/people/meiersi/+                    2013 Journal of Computer Security paper +                    \"Efficient Construction of +                    Machine-Checked Protocol Security Proofs\" +                    by Meier, Cremers, and Basin available from+                    <https://github.com/meiersi/scyther-proof/tree/master/publications>. stability:          Beta cabal-version:      >= 1.8 data-dir:           data@@ -81,10 +83,9 @@    isabelle/AUTHORS   isabelle/document/root.tex-  isabelle/IsaMakefile   isabelle/Makefile   isabelle/README-  isabelle/ROOT.ML+  isabelle/ROOT   isabelle/src/isar-keywords.el   isabelle/src/*.thy   isabelle/src/ESPLogic/*.thy
src/Main.hs view
@@ -24,7 +24,6 @@ import System.Directory import System.Isabelle import System.Info-import System.Timeout import System.Timing import System.Environment import System.Process@@ -63,7 +62,7 @@   [ programName   , " "   , showVersion version-  , ", (C) Simon Meier, ETH Zurich, 2009-2012"+  , ", (C) Simon Meier, Andreas Lochbihler, ETH Zurich, 2009-2013"   ]  -- | Version string with HTML markup.@@ -73,8 +72,9 @@     , " "     , showVersion version     , ", &copy; "-    , link "http://people.inf.ethz.ch/meiersi" "Simon Meier"-    , ", ETH Zurich, 2009-2012"+    , link "https://github.com/meiersi/scyther-proof" "Simon Meier"+    , link "http://github.com/meiersi" "Andreas Lochbihler"+    , ", ETH Zurich, 2009-2013"     ]   where     link href name =@@ -86,8 +86,10 @@  -- | ESPL Theory directory. esplTheoryDir :: IO String-esplTheoryDir = getDataFileName "isabelle"-+esplTheoryDir = do+  currDir <- getCurrentDirectory+  esplDir <- getDataFileName "isabelle"+  return (if isAbsolute esplDir then esplDir else currDir </> esplDir)  ------------------------------------------------------------------------------ -- Argument parsing helpers@@ -149,8 +151,8 @@           , "  The '--html' flag requires the 'dot' tool from GraphViz available at:"           , "    " ++ "http://www.graphviz.org/"           , "  "-          , "  The '--isabelle' flag requires the 'Isabelle-2009-1' release of Isabelle/HOL:"-          , "    " ++ "http://isabelle.in.tum.de/website-Isabelle2009-1/download_x86-linux.html"+          , "  The '--isabelle' flag requires the 'Isabelle-2013' release of Isabelle/HOL:"+          , "    " ++ "http://isabelle.in.tum.de/website-Isabelle2013/index.html"           , ""           , "  Check the '" ++ readmePath ++ "' file for instructions on how to load the generated theory files in Isabelle's interactive mode."           ]@@ -196,15 +198,9 @@                   "Number of parellel threads to be used for proof checking. \                   \(The default is to use as many threads as there are cores.)" -              , flagNone ["rebuild-logic"] (addEmpty "rebuildLogic")-                  "Rebuild the ESPL logic image (required after updating its source)"-               , flagNone ["no-generation"] (addEmpty "noGeneration")                   "Do not generate the theory files, but check the results using Isabelle." -              , flagOpt "0" ["timeout"]   (upd "timeout") "SECONDS"-                  "Timeout in seconds for proof generation and checking."-               , flagOpt "" ["hide-prefix"]   (upd "hidePrefix") "VALUE"                   "Hide non-referenced properties with this prefix (default=auto)." @@ -297,12 +293,11 @@                 -> MVar (T.Table String) -- ^ Empty MVar for building the report.                 -> IO () translateWorker as templateFile reportVar-  | null inFiles && not rebuildLogic = errHelpExit "no input iles given"-  | otherwise                        = do+  | null inFiles = errHelpExit "no input files given"+  | otherwise    = do       -- check required tools       when (not dryRun && html)     (ensureGraphVizDot dotTool)-      when (rebuildLogic || (not dryRun && isabelle))-          (ensureIsabelleESPL rebuildLogic isabelleTool)+      when (not dryRun && isabelle) (ensureIsabelleESPL isabelleTool)        -- translate all input files and ensure report is written with a special       -- interrupted marker when an exception like Ctrl-C happened@@ -315,7 +310,6 @@   where     -- Tool paths and flags     ------------------------    rebuildLogic = argExists "rebuildLogic" as     isabelleTool = fromMaybe "isabelle" $ findArg "isabelle" as     dotTool      = fromMaybe "dot"      $ findArg "html" as @@ -370,28 +364,6 @@       | argExists "composeParallel" as = composeParallel       | otherwise                      = id -    -- timeout handling-    --------------------    maxTime :: Maybe Int-    maxTime = findCheckedArg (0 <) "timeout" as--    execWithTimeout :: IO a -> IO a-    execWithTimeout io = case maxTime of-        Nothing -> io-        Just t  -> do-            res <- timeout (t * 1000000) io-            case res of-              Nothing -> do-                updateReport (T.appendCell $ "timeout: "++show maxTime++"s")-                throw CustomTimeout-              Just x -> return x--    ignoringTimeout :: IO () -> IO ()-    ignoringTimeout io = E.catch io handler-      where-      handler :: CustomTimeout -> IO ()-      handler _ = return ()-     -- progress output for batch mode     ---------------------------------     putInfo   msg = unless dryRun (putStr   msg >> hFlush stdout)@@ -467,6 +439,7 @@       cmdLine <- getCommandLine       time    <- getCurrentTime       cpu     <- getCpuModel+      esplSrc <- esplTheoryDir       theoryToHtml $ GenerationInput {           giHeader      = "Generated by " ++ htmlVersionStr         , giTime        = time@@ -483,7 +456,7 @@         , giDotTool     = dotTool         , giIsabelle    =             if isabelle-              then Just $ checkTheoryFile isabelleTool isabelleThreads 0 "ESPL"+              then Just $ checkTheoryFile isabelleTool isabelleThreads esplSrc               else Nothing         } @@ -615,7 +588,7 @@     writeThyFile outPath thy = do       if not noGeneration         then do-          tGen <- execWithTimeout . timed_ . writeFile outPath .+          tGen <- timed_ . writeFile outPath .                   thyToString $ adaptTheoryName outPath thy           let prfSize = theoryProofSize thy           reportNumber "Generation Time" tGen@@ -628,9 +601,8 @@           sequence_ . replicate 3 $ reportString "-" "--n"       if isabelle         then do-          -- let isabelleTimeout = maxTime * 10^6 -- in microseconds-          let isabelleTimeout = 0 -- because timeout construction for Isabelle is buggy currently-          ((_, result), tCheck) <- timed $ checkTheoryFile isabelleTool isabelleThreads isabelleTimeout "ESPL" outPath+          esplSrc <- esplTheoryDir+          (result, tCheck) <- timed $ checkTheoryFile isabelleTool isabelleThreads esplSrc outPath           reportNumber "Checking Time" tCheck           case result of             Nothing -> do@@ -638,7 +610,7 @@               reportString "Isabelle Status" "checked"               reportString "Isabelle Message" ""             Just msg -> do-              mapM_ (putInfo . ('\t':)) ["CHECK FAILED", show tCheck, show msg]+              mapM_ (putInfo . ('\t':)) ["CHECK FAILED", show tCheck, '\n' : msg]               reportString "Isabelle Status" "check failed"               reportString "Isabelle Message" (show msg)         else@@ -664,7 +636,7 @@       outPath = mkOutPath inFile      translateOneFile :: FilePath -> IO ()-    translateOneFile inFile = ignoringTimeout (readThy inFile >>= processThy inFile)+    translateOneFile inFile = readThy inFile >>= processThy inFile   ------------------------------------------------------------------------------@@ -774,27 +746,24 @@  -- | Ensure a suitable version of the Isabelle/HOL 'isabelle' tool is installed -- and the 'ESPL' head is compiled.-ensureIsabelleESPL :: Bool     -- ^ True if logic must rebuilt anyways.-                   -> FilePath -- ^ Path to the 'isabelle' tool.+ensureIsabelleESPL :: FilePath -- ^ Path to the 'isabelle' tool.                    -> IO ()-ensureIsabelleESPL rebuild isabelle = do+ensureIsabelleESPL isabelle = do     putStrLn $ "checking suitability of Isabelle tool: '" ++ isabelle ++ "'"     _ <- testProcess checkVersion " version: " isabelle ["version"] ""     success <- testProcess checkLogics " installed logics: " isabelle ["findlogics"] ""-    if success && not rebuild-      then putStrLn " (use the flag --rebuild-logic if your image of ESPL is outdated)"-      else buildESPL+    unless success buildESPL     putStrLn ""   where     checkVersion out _-      | "Isabelle2009-1" `isInfixOf` out = Right $ init out ++ ". OK."+      | "Isabelle2013" `isInfixOf` out = Right $ init out ++ ". OK."       | otherwise                        = Left  $ unlines $           [ "WARNING:"           , ""-          , " " ++ programName ++ " requires Isabelle2009-1."+          , " " ++ programName ++ " requires Isabelle2013."           , " Proof checking is likely not to work."-          , " Please download Isabelle2009-1 from:"-          , "   http://isabelle.in.tum.de/website-Isabelle2009-1/download_x86-linux.html"+          , " Please download Isabelle2013 from:"+          , "   http://isabelle.in.tum.de/website-Isabelle2013/index.html"           ]      checkLogics out _@@ -807,9 +776,9 @@       putStrLn "Attempting to build ESPL logic (this may take several minutes):"       theoryDir <- esplTheoryDir       let isamake args =-            runProcess isabelle ("make" :args) (Just theoryDir) Nothing Nothing Nothing Nothing+            runProcess isabelle ("build" : "-d" : theoryDir : args) (Just theoryDir) Nothing Nothing Nothing Nothing               >>= waitForProcess-      exitCode <- isamake ["clean"] >> isamake []+      exitCode <- isamake ["-b", "ESPL"]       case exitCode of         ExitSuccess -> putStrLn "Sucess! :-)\n---"         ExitFailure code -> putStrLn $ unlines
src/Scyther/Theory/Html.hs view
@@ -74,10 +74,9 @@   , giDotTool     :: String    -- ^ 'dot' tool to use.   , giCmdLine     :: String    -- ^ The command line that was used in this call to                                --   scyther-proof.-  , giIsabelle    :: Maybe (FilePath -> IO (IO String, Maybe String))+  , giIsabelle    :: Maybe (FilePath -> IO (Maybe String))                                -- ^ A checking function calling isabelle with-                               -- the right parameters and returning an IO function-                               -- for retrieving the logfile contents and an error+                               -- the right parameters which return an error                                -- message in case the check didn't succeed.   } @@ -85,7 +84,6 @@ data PathInfo = PathInfo {     inputFileCopy   :: FilePath  -- ^ Path of input file copy.   , proofScriptFile :: FilePath  -- ^ Path of generated Isabelle proof script.-  , logFileCopy     :: FilePath  -- ^ Path of the copy of the logFile   , outDir          :: FilePath  -- ^ Output directory.   , imageDir        :: FilePath  -- ^ Relative directory for graphs.   , filesDir        :: FilePath  -- ^ Relative directory for input and output files.@@ -99,7 +97,6 @@       { inputFileCopy   = filesDir info </> takeFileName (giInputFile input)       , proofScriptFile = filesDir info </>            addExtension (takeBaseName (giInputFile input) ++ "_cert_auto") "thy"-      , logFileCopy     = filesDir info </> "logfile"       , outDir          = giOutDir input       , imageDir        = "img"       , filesDir        = "files"@@ -119,8 +116,8 @@ -- theories for exporting as JSON. jsGenerationInfo :: GenerationInput                  -> NominalDiffTime  -- ^ Proof script generation time.-                 -> Maybe (Bool, NominalDiffTime, FilePath) -                                     -- ^ Proof checking time and relative logfile path.+                 -> Maybe (Bool, NominalDiffTime) +                                     -- ^ Proof checking time.                  -> JSObject JSValue jsGenerationInfo input genTime optCheckInfo = toJSObject $     [ ("header",      showJSON . toJSString $ giHeader input)@@ -138,10 +135,8 @@      checkInfo Nothing                              =          [ ("certificateStatus", showJSON . toJSString $ genTimeString) ]-    checkInfo (Just (success, checkTime, logFile)) =-        [ ( "certificateStatus", showJSON . toJSString $ genTimeString ++ status)-        , ( "logFile", showJSON (toJSString "logfile", toJSString logFile))-        ]+    checkInfo (Just (success, checkTime)) =+        [ ( "certificateStatus", showJSON . toJSString $ genTimeString ++ status) ]       where         status | success   = ", successfully checked in " ++ show checkTime                | otherwise = ", CHECK FAILED after " ++ show checkTime@@ -164,13 +159,11 @@     Nothing           -> return Nothing     Just machineCheck -> do       putStr " checking proof script: " >> hFlush stdout-      ((logFileContents, optErrMsg), checkTime) <- timed $ +      (optErrMsg, checkTime) <- timed $          machineCheck (mkAbsolute paths $ proofScriptFile paths)       putStrLn $ show checkTime       -- write log file copy-      contents <- logFileContents-      writeAbsolute (logFileCopy paths) contents-      return $ Just (isNothing optErrMsg, checkTime, logFileCopy paths)+      return $ Just (isNothing optErrMsg, checkTime)   -- json output   let thyJSON = mkThyJSON (jsGenerationInfo input genTime optCheckInfo)   writeAbsolute "theory.js"
src/Scyther/Theory/Pretty.hs view
@@ -343,8 +343,8 @@ -- Isabelle tactic. isaTactic :: TrivReason -> String isaTactic TrivContradictoryPremises   = "((clarsimp, order?) | order)"-isaTactic (TrivLongTermKeySecrecy _)  = "(fastsimp dest!: ltk_secrecy)"-isaTactic TrivPremisesImplyConclusion = "(fastsimp intro: event_predOrdI split: if_splits)"+isaTactic (TrivLongTermKeySecrecy _)  = "(fastforce dest!: ltk_secrecy)"+isaTactic TrivPremisesImplyConclusion = "(fastforce intro: event_predOrdI split: if_splits)"  -- | Isabelle proof of long-term key secrecy. isaLongTermKeySecrecyProof :: Protocol -> Doc@@ -460,7 +460,7 @@     prettyForwardContradiction thRef =-    kwBy <-> text "(fastsimp dest:" <-> thRef <-> text "intro: event_predOrdI)"+    kwBy <-> text "(fastforce dest:" <-> thRef <-> text "intro: event_predOrdI)"   prettyForwardResolution thRef thSe mapping     | isJust . destTypingFormula . seConcl $ thSe = emptyDoc     | otherwise = do@@ -491,7 +491,7 @@       | any (`isPrefixOf` name) ["ik0", "fake"] || null newVars = text name       | otherwise = parens $ text name <-> hsep (map ppNewVar newVars)   prettyChainRuleQED _ trivCases-    | null tactics = kwQED <-> text "(insert facts, fastsimp+)?" -- be conservative+    | null tactics = kwQED <-> text "(insert facts, fastforce+)?" -- be conservative     | otherwise    =         kwQED <-> text "(insert facts, (" <> hsep (intersperse (text "|") tactics) <> text ")+)?"     where@@ -535,7 +535,7 @@     ) $-$     (text "thus ?thesis proof(cases rule: Kbd_cases)") -  prettySplitEqQed = text "qed (fastsimp+)?"+  prettySplitEqQed = text "qed (fastforce+)?"    -- theory output   prettyComment comment = text "(*" <-> text comment <-> text "*)"@@ -601,7 +601,7 @@     pure body $-$     text "" $-$ text "end"     where-    imports = ["../ESPLogic"]+    imports = ["ESPLogic"]   -- | Pretty-print an injectivity sequent. Works only for two-party@@ -614,7 +614,7 @@            , nest 2 (sep [text "prems =", nest 2 $ ppPrems <> semi])            , nest 2 (sep [text "concs =", nest 2 $ ppConcs])            , text "in" <->-               isaExists conf <> text "f. inj_on f prems" <-> isaAnd conf <->+               isaExists conf <> text "f. inj_on f (Collect prems)" <-> isaAnd conf <->                parens ( isaForall conf <> text "i. prems i" <->                         isaImplies conf <-> text "concs i (f i)" )            ]
src/System/Isabelle.hs view
@@ -2,57 +2,20 @@ -- -- Requirements: -----   1. A working installation of Isabelle2009-1 (http://isabelle.in.tum.de/)+--   1. A working installation of Isabelle2013 (http://isabelle.in.tum.de/) --   2. The \'isabelle\' command must be on the PATH. -- module System.Isabelle (   checkTheoryFile ) where -import Data.Maybe import Data.List  import System.FilePath import System.Directory import System.Process import System.IO--import Control.Concurrent-import Control.Monad-import Control.Exception----------------------------------------------------------------------------------- Utilities: TODO MOVE INTO GENERAL FILE----------------------------------------------------------------------------------- | Create and use a temporary file ensuring that it is closed if the--- computation fails.------ See 'openTempFile' for more information on the parameters.-withTempFile :: FilePath -> String -> ((FilePath, Handle) -> IO a) -> IO (a, FilePath)-withTempFile dir nameTemplate io = -  bracket (openTempFile dir nameTemplate) (hClose . snd) -          (\args@(file,_) -> do{ x <- io args; return (x, file) })---- | Like 'withTempFile' buth without returning the results of the inner--- computation.-withTempFile_ :: FilePath -> String -> ((FilePath, Handle) -> IO a) -> IO FilePath-withTempFile_ dir nameTemplate io = snd `liftM` withTempFile dir nameTemplate io---- | Waits the given amount of microseconds before trying to terminate the--- process using 'terminateProcess'.-waitForProcessTimeout :: Int -> ProcessHandle -> IO Bool-waitForProcessTimeout maxTime hProc-  | maxTime <= 0 = do _<- waitForProcess hProc; return False-  | otherwise    = do-      timeout <- newMVar False-      _ <- forkIO $ do-        threadDelay maxTime-        modifyMVar_ timeout (return . const True)-        terminateProcess hProc-      _ <- waitForProcess hProc-      readMVar timeout-    +import System.Exit  ------------------------------------------------------------------------------ -- Isabelle commands@@ -61,51 +24,31 @@ -- | Use Isabelle to check the correctness of a theory file. checkTheoryFile :: FilePath            -- ^ Path to 'isabelle' binary.                 -> Maybe Int           -- ^ Number of parallel thread to use while checking.-                -> Int                 -- ^ Maximal available time in micro-seconds-                -> String              -- ^ Logic Image to use+                -> FilePath            -- ^ Path to ESPL sources                 -> FilePath            -- ^ Path to file to be checked-                -> IO (IO String, Maybe String)+                -> IO (Maybe String)                    -- ^ If the check went through, log-file content only, otherwise                    -- also an error message.-checkTheoryFile isabelleTool threads maxTime logic thyFile = do+checkTheoryFile isabelleTool threads esplSrc thyFile = do   let thyName     = takeBaseName thyFile-      rootName    = "ROOT-" ++ thyName ++ ".ML"+      rootName    = "ROOT"       sessionName = "scyther-proof-" ++ thyName-  -- create ROOT.ML file-  tmpDir <- getTemporaryDirectory-  rootFile <- withTempFile_ tmpDir rootName -    (\(_, hRootFile) -> -      hPutStrLn hRootFile $ "use_thy \"" ++ dropExtension thyFile ++ "\""-    )+  +  -- setup temporary directory+  tmpDir <- createTempDirectory+  copyFile thyFile (tmpDir </> addExtension thyName "thy")+  writeFile (tmpDir </> rootName) ("session \"" ++ sessionName ++ "\" = ESPL + theories \"" ++ thyName ++ "\"")   -- call "isabelle usedir"-  finally -    (do let cmd = isabelleTool ++ -                     " usedir -f " ++ rootFile ++ -                     " -s " ++ sessionName ++ -                     " -M " ++ maybe "0" show threads ++-                        " " ++ logic ++ " ."-        (_,   _,    hErr, hProc) <- runInteractiveCommand cmd-        isaOutVar <- newEmptyMVar-        _ <-forkIO $ redirect hErr isaOutVar-        timeout <- waitForProcessTimeout maxTime hProc-        isaOut <- takeMVar isaOutVar-        if timeout-          then do return (return $ isaOut ++ "Interrupted due to timeout!"-                         , Just $ "timeout: " ++ -                              show ((fromIntegral maxTime / 10E6)::Double) ++ "s")-          else do return $ parseIsaOutput sessionName isaOut-    )-    (do removeFile rootFile)+  (code, out, _err) <- readProcessWithExitCode isabelleTool+     ["build", "-d", esplSrc, "-D", tmpDir, "-j", maybe "0" show threads]+     ""+  if code == ExitSuccess+    then do+      removeDirectoryRecursive tmpDir+      return Nothing+    else+      return (Just (errMsg out))           where-  -- | Redirect the contents of a the given handle into the message variable.-  redirect hIn mvar = hGetContents hIn >>= putMVar mvar--  -- | extract the log file name from the isabelle output-  logFileName str = fromMaybe "no log file" $ do-    let logIndicator = "(see also "-    line <- find (logIndicator `isPrefixOf`) (lines str) -    init `liftM` stripPrefix logIndicator line-     -- | Extract the error message from the isabelle output   errMsg str = case break ("***" `isPrefixOf`) (lines str) of     (_,[]) -> str@@ -113,9 +56,12 @@       (_,[]) -> unlines (first : ls)       (ls',(fin:_)) -> unlines (first : ls'++[fin]) -  -- | Parse the Isabelle output.-  parseIsaOutput sessionName str-    | ("Finished "++logic++"-"++sessionName) `isInfixOf` str = (return str, Nothing)-    | otherwise = (readFile (logFileName str), Just (errMsg str))--        +  createTempDirectory :: IO FilePath+  createTempDirectory = do+      tmpBase <- getTemporaryDirectory+      -- hack to create a unique temporary directory+      (tmpDir, handle) <- openTempFile tmpBase "scyther-proof_tmp"+      hClose handle+      removeFile tmpDir+      createDirectory tmpDir+      return tmpDir