diff --git a/CHANGES b/CHANGES --- a/CHANGES +++ b/CHANGES @@ -1,3 +1,8 @@ +* 0.10.0.0 + - upgraded dependency on Isabelle to Isabelle2014 + - add support for explicit matching and non-matching steps in protocols + - new protocol example for optimistic fair exchange + * 0.8.0.0 - upgraded dependency on Isabelle to Isabelle-2013-2 diff --git a/README.md b/README.md --- a/README.md +++ b/README.md @@ -1,10 +1,12 @@ -README: The scyther-proof security protocol verification tool -============================================================= +The scyther-proof security protocol verification tool +===================================================== -Authors: Simon Meier -Creation Date: 2011-05-13 -Last Updated: 2014-01-31 by Andreas Lochbihler +![master branch build-status](https://travis-ci.org/meiersi/scyther-proof.svg?branch=master) +- Authors: Simon Meier , Andreas Lochbihler +- Creation Date: 2011-05-13 +- Last Updated: 2015-02-20 by Andreas Lochbihler + 1. Introduction =============== @@ -55,55 +57,16 @@ 2.2 Installing the Isabelle/HOL theories ---------------------------------------- -Download and install full Isabelle2013-2 according to the installation +Download and install full Isabelle2014 according to the installation instructions at - http://isabelle.in.tum.de/website-Isabelle2013-2/ + http://isabelle.in.tum.de/website-Isabelle2014/ 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`. -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 ----------------------- - -Copy the Emacs keywords file provided with the ESPL distribution at - - $SCYTHER_PROOF_HOME/data/isabelle/src/isar-keywords.el - -to your local Isabelle configuration in - - $ISABELLE_HOME_USER/etc - -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_USER/etc/isar-keywords-ESPL.el - -and start Isabelle using the -k switch as follows. - - isabelle emacs -k ESPL - - - 3. Usage ======== @@ -147,20 +110,6 @@ 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 /src - isabelle emacs Tutorial.thy - - or if you've chosen the elegant variant for the keywords file - - isabelle emacs -k ESPL Tutorial.thy - Using the Isabelle/jEdit Prover IDE ----------------------------------- diff --git a/data/examples/classic/ASW_optimistic_contract.spthy b/data/examples/classic/ASW_optimistic_contract.spthy new file mode 100644 --- /dev/null +++ b/data/examples/classic/ASW_optimistic_contract.spthy @@ -0,0 +1,166 @@ +theory ASW_optimistic_contract +begin + +section{* Optimistic fair exchange following Asokan, Shoup, Waidner *} + +text{* + +We model the contract signing example from + + N. Asokan, V. Shoup, and M. Waidner. Asynchronous protocols for optimistic + fair exchange. In Proceedings of the IEEE Symposium on Research in Security + and Privacy, pages 86--99. IEEE Computer Society Press, 1998. + +Since role scripts are linear, we model the non-deterministic choice to +abort as separate roles that share the same prefix with the non-aborting role. +The trusted party is therefore split into Ta and Tr which run only the +abort protocol or only the resolve protocol. + +*} + +protocol Contract +{ + 00abort. Ta -> : {'bind', $T, n}sk($T) + 00resolve. Tr -> : {'bind', $T, n}sk($T) + + 0regular. A <- : {'bind', $T, n}sk($T) + 1regular. A -> : {$A, $B, $T, n, 'text', h(sA)}sk($A) + -> B : {$A, $B, $T, n, 'text', cA}sk($A) + 2regular. <- B : {{$A, $B, $T, n, 'text', cA}sk($A), h(sB)}sk($B) + A <- : {{$A, $B, $T, n, 'text', h(sA)}sk($A), cB}sk($B) + 3regular. A -> B : sA + 4regular. B : cA -> h(sA) + 5regular. A <- B : sB + 6regular. A : cB -> h(sB) + + 0abort. Aa <- : {'bind', $T, n}sk($T) + 1abort. Aa -> : {$A, $B, $T, n, 'text', h(sA)}sk($A) + 2abort. Aa -> : {'aborted', {$A, $B, $T, n, 'text', h(sA)}sk($A)}sk($A) + -> Ta : {'aborted', {A, B, $T, n, 'text', cA}sk(A)}sk(A) + 3abort. <- Ta : {'aborted', {'aborted', {A, B, $T, n, 'text', cA}sk(A)}sk(A)}sk($T) + Aa <- : {'aborted', {'aborted', {$A, $B, $T, n, 'text', h(sA)}sk($A)}sk($A)}sk($T) + + resolve1. -> Tr : {A, B, $T, n, 'text', cA}sk(A), {{A, B, $T, n, 'text', cA}sk(A), cB}sk(B) + resolve2. <- Tr : {{A, B, $T, n, 'text', cA}sk(A), {{A, B, $T, n, 'text', cA}sk(A), cB}sk(B)}sk($T) + + verify. -> V : {A, B, $T, n, 'text', h(sA)}sk(A), sA, + {{A, B, $T, n, 'text', h(sA)}sk(A), h(sB)}sk(B), sB + verifyr. -> Vr : {{A, B, $T, n, 'text', cA}sk(A), {{A, B, $T, n, 'text', cA}sk(A), cB}sk(B)}sk($T) +} + +subsection{* Security Properties *} + +property (of Contract) Contract_typing: + "n@A :: Known(A_0regular) | n@Ta | n@Tr + n@B :: Known(B_1regular) | n@Ta | n@Tr + cA@B :: Known(B_1regular) | h(sA@A) | h(sA@Aa) + cB@A :: Known(A_2regular) | h(sB@B) + sA@B :: Known(B_3regular) + sB@A :: Known(A_5regular) + + n@Aa :: Known(Aa_0abort) | n@Ta | n@Tr + A@Ta :: Known(Ta_2abort) | Agent + B@Ta :: Known(Ta_2abort) | Agent + cA@Ta :: Known(Ta_2abort) | h(sA@A) | h(sA@Aa) + + A@Tr :: Known(Tr_resolve1) | Agent + B@Tr :: Known(Tr_resolve1) | Agent + cA@Tr :: Known(Tr_resolve1) | h(sA@A) | h(sA@Aa) + cB@Tr :: Known(Tr_resolve1) | h(sB@B) + + A@V :: Known(V_verify) | Agent + B@V :: Known(V_verify) | Agent + n@V :: Known(V_verify) | n@Ta | n@Tr + sA@V :: Known(V_verify) | sA@A + sB@V :: Known(V_verify) | sB@B + + A@Vr :: Known(Vr_verifyr) | Agent + B@Vr :: Known(Vr_verifyr) | Agent + n@Vr :: Known(Vr_verifyr) | n@Ta | n@Tr + cA@Vr :: Known(Vr_verifyr) | h(sA@A) | h(sA@Aa) + cB@Vr :: Known(Vr_verifyr) | h(sB@B) + " + +properties (of Contract) + regular_agree_A: iagree(A_6regular[A,B,T,n,sA,sB] -> B_5regular[A,B,T,n,sA,sB], {A,B}) + regular_agree_B: niagree(B_4regular[A,B,T,n,sA] -> A_3regular[A,B,T,n,sA], {A,B}) + +property (of Contract) regular_verified: + premises + "role(0) = V" + "step(0, V_verify)" + "uncompromised(A#0)" + "uncompromised(B#0)" + imply threads 1, 2 such that + "role(1) = A & + step(1, A_3regular) & + + role(2) = B & + step(2, B_5regular) & + + A#0 = A#1 & A#0 = A#2 & + B#0 = B#1 & B#0 = B#2 & + T#0 = T#1 & T#0 = T#2 & + + n#0 = n#1 & n#0 = n#2 & + sA#0 = sA#1 & + sB#0 = sB#2 + " + +property (of Contract) resolve_verified: + premises + "role(0) = Vr" + "step(0, Vr_verifyr)" + "uncompromised(A#0)" + "uncompromised(B#0)" + "uncompromised(T#0)" + imply threads 1, 2 such that + "( role(1) = A & + step(1, A_1regular) & + A#0 = A#1 & + B#0 = B#1 & + T#0 = T#1 & + n#0 = n#1 & + cA#0 = h(sA#1) + | + role(1) = Aa & + step(1, Aa_1abort) & + A#0 = A#1 & + B#0 = B#1 & + T#0 = T#1 & + n#0 = n#1 & + cA#0 = h(sA#1) + ) & + + role(2) = B & + step(2, B_2regular) & + A#0 = A#2 & + B#0 = B#2 & + T#0 = T#2 & + n#0 = n#2 & + cB#0 = h(sB#2) + " + +property (of Contract) regular_verified_not_aborted: + premises + "role(0) = V" + "step(0, V_verify)" + "uncompromised(A#0)" + "uncompromised(T#0)" + // cA#0 should be replaced with a wildcard + "knows({'aborted', {'aborted', {A#0, B#0, T#0, n#0, 'text', cA#0}sk(A#0)}sk(A#0)}sk(T#0))" + imply + "False" + +property (of Contract) resolve_verified_not_aborted: + premises + "role(0) = Vr" + "step(0, Vr_verifyr)" + "uncompromised(A#0)" + "uncompromised(T#0)" + // cA#0 should be replaced with a wildcard + "knows({'aborted', {'aborted', {A#0, B#0, T#0, n#0, 'text', cA#0}sk(A#0)}sk(A#0)}sk(T#0))" + imply + "False" + +end diff --git a/data/examples/classic/BrandsChaum.spthy b/data/examples/classic/BrandsChaum.spthy new file mode 100644 --- /dev/null +++ b/data/examples/classic/BrandsChaum.spthy @@ -0,0 +1,45 @@ +theory BrandsChaum +begin + +section{* Distance bounding following Brands, Chaum *} + +text{* + +We model the distance bounding protocol following Brands and Chaum + + Stefan Brands and David Chaum. Distance-Bounding Protocols. EUROCRYPT '93 + Lecture Notes in Computer Science 765, pp. 344--359, Springer, 1993. + +Since the Dolev-Yao model has no notion of time, we can only show that +the challenge-response steps have to happen in the right order. + +*} + +protocol BrandsChaum +{ + 1. P -> : P, {m}k + -> V : P, c + 2. P <- V : a + 3. P -> : h(a, m) + -> V : b + 4. P -> : m, k, {a, h(a, m)}sk(P) + -> V : m, k, {a, b}sk(P) + 5. V : c -> {m}k + 6. V : b -> h(a, m) +} + +property (of BrandsChaum) prover_recent: + premises + "role(0) = V" + "step(0, V_6)" + "uncompromised(P#0)" + injectively imply a thread 1 such that + "role(1) = P & + P#0 = P#1 & + m#0 = m#1 & + k#0 = k#1 & + a#0 = a#1 & + St(1, P_1) < St(0, V_2) < St(1, P_3) < St(0, V_3) + " + +end diff --git a/data/examples/classic/BrandsChaum_iterated.spthy b/data/examples/classic/BrandsChaum_iterated.spthy new file mode 100644 --- /dev/null +++ b/data/examples/classic/BrandsChaum_iterated.spthy @@ -0,0 +1,44 @@ +theory BrandsChaum_iterated +begin + +text{* + +The same model of the Brands Chaum distance bounding protocol as in BrandsChaum.spthy +except that now two challenges are exchanged. + +*} + +protocol BrandsChaum +{ + 1. P -> : P, {m1, m2}k + -> V : P, c + 21. P <- V : a1 + 31. P -> : h(a1, m1) + -> V : b1 + 22. P <- V : a2 + 32. P -> : h(a2, m2) + -> V : b2 + 4. P -> : m1, m2, m3, k, {a1, h(a1, m1), a2, h(a2, m2)}sk(P) + -> V : m1, m2, m3, k, {a1, b1, a2, b2}sk(P) + 5. V : c -> {m1, m2}k + 61. V : b1 -> h(a1, m1) + 62. V : b2 -> h(a2, m2) +} + +property (of BrandsChaum) prover_recent: + premises + "role(0) = V" + "step(0, V_62)" + "uncompromised(P#0)" + injectively imply a thread 1 such that + "role(1) = P & + P#0 = P#1 & + m1#0 = m1#1 & m2#0 = m2#1 & + k#0 = k#1 & + a1#0 = a1#1 & a2#0 = a2#1 & + St(1, P_1) < + St(0, V_21) < St(1, P_31) < St(0, V_31) < + St(0, V_22) < St(1, P_32) < St(0, V_32) + " + +end diff --git a/data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-2-bdkey_cert_auto.thy b/data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-2-bdkey_cert_auto.thy --- a/data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-2-bdkey_cert_auto.thy +++ b/data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-2-bdkey_cert_auto.thy @@ -731,1075 +731,1217 @@ 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 + case (isoiec_9798_2_1_bdkey_A_text_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_1_bdkey_A_text_1_Text1 + thus ?case 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 + case (isoiec_9798_2_1_bdkey_A_text_1_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_1_bdkey_A_text_1_Text2 + thus ?case 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 + case (isoiec_9798_2_1_bdkey_B_1_A t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_1_bdkey_B_1_A + thus ?case 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 + case (isoiec_9798_2_1_bdkey_B_1_TNA t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_1_bdkey_B_1_TNA + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_1_bdkey_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_1_bdkey_B_1_Text1 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_1_bdkey_B_1_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_1_bdkey_B_1_Text2 + thus ?case 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 + case (isoiec_9798_2_2_bdkey_A_1_B t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_bdkey_A_1_B + thus ?case 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 + case (isoiec_9798_2_2_bdkey_A_1_RB t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_bdkey_A_1_RB + thus ?case 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 + case (isoiec_9798_2_2_bdkey_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_bdkey_A_1_Text1 + thus ?case 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 + case (isoiec_9798_2_2_bdkey_A_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_bdkey_A_text_2_Text2 + thus ?case 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 + case (isoiec_9798_2_2_bdkey_A_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_bdkey_A_text_2_Text3 + thus ?case 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 + case (isoiec_9798_2_2_bdkey_B_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_bdkey_B_2_Text2 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_2_bdkey_B_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_bdkey_B_2_Text3 + thus ?case 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 + case (isoiec_9798_2_3_bdkey_A_text_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_bdkey_A_text_1_Text1 + thus ?case 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 + case (isoiec_9798_2_3_bdkey_A_text_1_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_bdkey_A_text_1_Text2 + thus ?case 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 + case (isoiec_9798_2_3_bdkey_A_2_TNB t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_bdkey_A_2_TNB + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_3_bdkey_A_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_bdkey_A_2_Text3 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_3_bdkey_A_2_Text4 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_bdkey_A_2_Text4 + thus ?case 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 + case (isoiec_9798_2_3_bdkey_B_1_A t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_bdkey_B_1_A + thus ?case 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 + case (isoiec_9798_2_3_bdkey_B_1_TNA t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_bdkey_B_1_TNA + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_3_bdkey_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_bdkey_B_1_Text1 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_3_bdkey_B_1_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_bdkey_B_1_Text2 + thus ?case 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 + case (isoiec_9798_2_3_bdkey_B_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_bdkey_B_text_2_Text3 + thus ?case 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 + case (isoiec_9798_2_3_bdkey_B_text_2_Text4 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_bdkey_B_text_2_Text4 + thus ?case 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 + case (isoiec_9798_2_4_bdkey_A_1_B t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_bdkey_A_1_B + thus ?case 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 + case (isoiec_9798_2_4_bdkey_A_1_RB t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_bdkey_A_1_RB + thus ?case 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 + case (isoiec_9798_2_4_bdkey_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_bdkey_A_1_Text1 + thus ?case 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 + case (isoiec_9798_2_4_bdkey_A_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_bdkey_A_text_2_Text2 + thus ?case 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 + case (isoiec_9798_2_4_bdkey_A_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_bdkey_A_text_2_Text3 + thus ?case 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 + case (isoiec_9798_2_4_bdkey_A_3_Text4 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_bdkey_A_3_Text4 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_4_bdkey_A_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_bdkey_A_3_Text5 + thus ?case 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 + case (isoiec_9798_2_4_bdkey_B_2_RA t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_bdkey_B_2_RA + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_4_bdkey_B_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_bdkey_B_2_Text2 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_4_bdkey_B_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_bdkey_B_2_Text3 + thus ?case 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 + case (isoiec_9798_2_4_bdkey_B_text_3_Text4 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_bdkey_B_text_3_Text4 + thus ?case 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 + case (isoiec_9798_2_4_bdkey_B_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_bdkey_B_text_3_Text5 + thus ?case 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 + case (isoiec_9798_2_5_bdkey_A_2_Kab t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_A_2_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_bdkey_A_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_A_2_Text3 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_bdkey_A_2_Text4 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_A_2_Text4 + thus ?case 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 + case (isoiec_9798_2_5_bdkey_A_2_TokenPA_for_B t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_A_2_TokenPA_for_B + thus ?case 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 + case (isoiec_9798_2_5_bdkey_A_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_A_text_3_Text5 + thus ?case 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 + case (isoiec_9798_2_5_bdkey_A_text_3_Text6 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_A_text_3_Text6 + thus ?case 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 + case (isoiec_9798_2_5_bdkey_A_4_TNb t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_A_4_TNb + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_bdkey_A_4_Text7 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_A_4_Text7 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_bdkey_A_4_Text8 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_A_4_Text8 + thus ?case 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 + case (isoiec_9798_2_5_bdkey_B_3_A t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_B_3_A + thus ?case 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 + case (isoiec_9798_2_5_bdkey_B_3_Kab t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_B_3_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_bdkey_B_3_P t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_B_3_P + thus ?case 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 + case (isoiec_9798_2_5_bdkey_B_3_TNa t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_B_3_TNa + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_bdkey_B_3_TNp t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_B_3_TNp + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_bdkey_B_3_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_B_3_Text2 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_bdkey_B_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_B_3_Text5 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_bdkey_B_3_Text6 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_B_3_Text6 + thus ?case 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 + case (isoiec_9798_2_5_bdkey_B_text_4_Text7 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_B_text_4_Text7 + thus ?case 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 + case (isoiec_9798_2_5_bdkey_B_text_4_Text8 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_B_text_4_Text8 + thus ?case 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 + case (isoiec_9798_2_5_bdkey_P_1_A t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_P_1_A + thus ?case 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 + case (isoiec_9798_2_5_bdkey_P_1_B t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_P_1_B + thus ?case 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 + case (isoiec_9798_2_5_bdkey_P_1_TVPa t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_P_1_TVPa + thus ?case 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 + case (isoiec_9798_2_5_bdkey_P_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_P_1_Text1 + thus ?case 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 + case (isoiec_9798_2_5_bdkey_P_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_P_text_2_Text2 + thus ?case 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 + case (isoiec_9798_2_5_bdkey_P_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_P_text_2_Text3 + thus ?case 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 + case (isoiec_9798_2_5_bdkey_P_text_2_Text4 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_P_text_2_Text4 + thus ?case 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 + case (isoiec_9798_2_6_bdkey_A_1_B t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_A_1_B + thus ?case 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 + case (isoiec_9798_2_6_bdkey_A_1_Rb t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_A_1_Rb + thus ?case 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 + case (isoiec_9798_2_6_bdkey_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_A_1_Text1 + thus ?case 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 + case (isoiec_9798_2_6_bdkey_A_3_Kab t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_A_3_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_bdkey_A_3_Text4 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_A_3_Text4 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_bdkey_A_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_A_3_Text5 + thus ?case 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 + case (isoiec_9798_2_6_bdkey_A_3_TokenPA_for_B t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_A_3_TokenPA_for_B + thus ?case 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 + case (isoiec_9798_2_6_bdkey_A_text_4_Text6 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_A_text_4_Text6 + thus ?case 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 + case (isoiec_9798_2_6_bdkey_A_text_4_Text7 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_A_text_4_Text7 + thus ?case 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 + case (isoiec_9798_2_6_bdkey_A_5_Text8 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_A_5_Text8 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_bdkey_A_5_Text9 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_A_5_Text9 + thus ?case 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 + case (isoiec_9798_2_6_bdkey_B_4_Kab t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_B_4_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_bdkey_B_4_P t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_B_4_P + thus ?case 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 + case (isoiec_9798_2_6_bdkey_B_4_Rpa t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_B_4_Rpa + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_bdkey_B_4_Text3 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_B_4_Text3 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_bdkey_B_4_Text6 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_B_4_Text6 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_bdkey_B_4_Text7 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_B_4_Text7 + thus ?case 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 + case (isoiec_9798_2_6_bdkey_B_text_5_Text8 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_B_text_5_Text8 + thus ?case 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 + case (isoiec_9798_2_6_bdkey_B_text_5_Text9 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_B_text_5_Text9 + thus ?case 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 + case (isoiec_9798_2_6_bdkey_P_2_A t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_P_2_A + thus ?case 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 + case (isoiec_9798_2_6_bdkey_P_2_B t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_P_2_B + thus ?case 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 + case (isoiec_9798_2_6_bdkey_P_2_Ra t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_P_2_Ra + thus ?case 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 + case (isoiec_9798_2_6_bdkey_P_2_Rb t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_P_2_Rb + thus ?case 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 + case (isoiec_9798_2_6_bdkey_P_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_P_2_Text2 + thus ?case 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 + case (isoiec_9798_2_6_bdkey_P_text_3_Text3 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_P_text_3_Text3 + thus ?case 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 + case (isoiec_9798_2_6_bdkey_P_text_3_Text4 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_P_text_3_Text4 + thus ?case 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 + case (isoiec_9798_2_6_bdkey_P_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_P_text_3_Text5 + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_A_2_Kab t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_A_2_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_special_TTP_bdkey_A_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_A_2_Text3 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_special_TTP_bdkey_A_2_Text4 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_A_2_Text4 + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_A_2_TokenPA_for_B t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_A_2_TokenPA_for_B + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_A_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_A_text_3_Text5 + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_A_text_3_Text6 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_A_text_3_Text6 + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_A_4_TNb t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_A_4_TNb + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_special_TTP_bdkey_A_4_Text7 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_A_4_Text7 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_special_TTP_bdkey_A_4_Text8 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_A_4_Text8 + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_B_3_A t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_B_3_A + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_B_3_Kab t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_B_3_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_special_TTP_bdkey_B_3_P t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_B_3_P + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_B_3_TNa t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_B_3_TNa + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_special_TTP_bdkey_B_3_TNp t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_B_3_TNp + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_special_TTP_bdkey_B_3_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_B_3_Text2 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_special_TTP_bdkey_B_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_B_3_Text5 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_special_TTP_bdkey_B_3_Text6 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_B_3_Text6 + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_B_text_4_Text7 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_B_text_4_Text7 + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_B_text_4_Text8 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_B_text_4_Text8 + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_P_1_A t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_P_1_A + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_P_1_B t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_P_1_B + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_P_1_TVPa t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_P_1_TVPa + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_P_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_P_1_Text1 + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_P_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_P_text_2_Text2 + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_P_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_P_text_2_Text3 + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_P_text_2_Text4 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_P_text_2_Text4 + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_A_1_B t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_A_1_B + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_A_1_Rb t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_A_1_Rb + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_A_1_Text1 + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_A_3_Kab t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_A_3_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_special_TTP_bdkey_A_3_Text4 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_A_3_Text4 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_special_TTP_bdkey_A_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_A_3_Text5 + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_A_3_TokenPA_for_B t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_A_3_TokenPA_for_B + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_A_text_4_Text6 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_A_text_4_Text6 + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_A_text_4_Text7 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_A_text_4_Text7 + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_A_5_Text8 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_A_5_Text8 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_special_TTP_bdkey_A_5_Text9 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_A_5_Text9 + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Kab t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_B_4_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_special_TTP_bdkey_B_4_P t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_B_4_P + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Rpa t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_B_4_Rpa + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Text3 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_B_4_Text3 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Text6 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_B_4_Text6 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Text7 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_B_4_Text7 + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_B_text_5_Text8 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_B_text_5_Text8 + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_B_text_5_Text9 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_B_text_5_Text9 + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_P_2_A t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_P_2_A + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_P_2_B t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_P_2_B + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_P_2_Ra t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_P_2_Ra + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_P_2_Rb t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_P_2_Rb + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_P_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_P_2_Text2 + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_P_text_3_Text3 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_P_text_3_Text3 + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_P_text_3_Text4 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_P_text_3_Text4 + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_P_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_P_text_3_Text5 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) qed thus "isoiec_9798_2_bdkey_composed_typing_state t r s" by unfold_locales auto @@ -1880,11 +2022,11 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_2_bdkey_B_injective_agreement: @@ -1919,11 +2061,11 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -1960,11 +2102,11 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_3_bdkey_B_non_injective_agreement: @@ -1990,11 +2132,11 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_4_bdkey_A_injective_agreement: @@ -2029,7 +2171,7 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -2043,11 +2185,11 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid1) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) next case swapped note_unified facts = this facts thus ?thesis proof(sources! " @@ -2056,13 +2198,13 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''A'' tid1) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed (fastforce+)? - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2108,11 +2250,11 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2136,11 +2278,11 @@ 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) + thus ?thesis by (auto 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+)? + thus ?thesis by (auto dest!: ltk_secrecy) +qed (safe?, simp_all?, insert facts, (fastforce+)?) lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_bdkey_A_secret_Kab: assumes facts: @@ -2160,11 +2302,11 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_bdkey_B_secret_Kab: @@ -2185,11 +2327,11 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_bdkey_A_injective_agreement_B: @@ -2228,7 +2370,7 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_2_5_bdkey_P_2_enc tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -2268,11 +2410,11 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2311,7 +2453,7 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_2_5_bdkey_P_2_enc_1 tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -2333,9 +2475,9 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_bdkey_A_injective_agreement_P: @@ -2372,11 +2514,11 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2415,11 +2557,11 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_bdkey_P_secret_Kab: @@ -2432,11 +2574,11 @@ 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) + thus ?thesis by (auto 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+)? + thus ?thesis by (auto dest!: ltk_secrecy) +qed (safe?, simp_all?, insert facts, (fastforce+)?) lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_bdkey_A_secret_Kab: assumes facts: @@ -2456,11 +2598,11 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_bdkey_B_secret_Kab: @@ -2481,11 +2623,11 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_bdkey_A_injective_agreement_B: @@ -2524,7 +2666,7 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_2_6_bdkey_P_3_enc tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -2555,10 +2697,10 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2608,7 +2750,7 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_2_6_bdkey_P_3_enc_1 tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -2630,9 +2772,9 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2680,11 +2822,11 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2732,11 +2874,11 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2761,11 +2903,11 @@ 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) + thus ?thesis by (auto 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+)? + thus ?thesis by (auto dest!: ltk_secrecy) +qed (safe?, simp_all?, insert facts, (fastforce+)?) lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_special_TTP_bdkey_A_secret_Kab: assumes facts: @@ -2784,7 +2926,7 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -2797,7 +2939,7 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_special_TTP_bdkey_B_secret_Kab: @@ -2817,7 +2959,7 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -2830,7 +2972,7 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_special_TTP_bdkey_A_injective_agreement_B: @@ -2868,7 +3010,7 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -2916,12 +3058,12 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed (fastforce+)? - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2985,14 +3127,14 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed (fastforce+)? - qed (insert facts, fastforce+)? - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_special_TTP_bdkey_A_injective_agreement_P: @@ -3028,7 +3170,7 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -3041,7 +3183,7 @@ case swapped note_unified facts = this facts thus ?thesis by (fastforce intro: event_predOrdI split: if_splits) qed (fastforce+)? - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -3079,7 +3221,7 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -3106,13 +3248,13 @@ 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+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed @@ -3127,11 +3269,11 @@ 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) + thus ?thesis by (auto 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+)? + thus ?thesis by (auto dest!: ltk_secrecy) +qed (safe?, simp_all?, insert facts, (fastforce+)?) lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_special_TTP_bdkey_A_secret_Kab: assumes facts: @@ -3150,7 +3292,7 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -3163,7 +3305,7 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_special_TTP_bdkey_B_secret_Kab: @@ -3183,7 +3325,7 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -3196,7 +3338,7 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_special_TTP_bdkey_A_injective_agreement_B: @@ -3234,7 +3376,7 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -3281,12 +3423,12 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed (fastforce+)? - qed (insert facts, fastforce+)? - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed (fastforce+)? - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -3335,7 +3477,7 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -3374,10 +3516,10 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed (fastforce+)? - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -3424,7 +3566,7 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -3437,7 +3579,7 @@ case swapped note_unified facts = this facts thus ?thesis by (fastforce intro: event_predOrdI split: if_splits) qed (fastforce+)? - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -3484,7 +3626,7 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -3497,7 +3639,7 @@ case swapped note_unified facts = this facts thus ?thesis by (fastforce intro: event_predOrdI split: if_splits) qed (fastforce+)? - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this diff --git a/data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-2-udkey_cert_auto.thy b/data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-2-udkey_cert_auto.thy --- a/data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-2-udkey_cert_auto.thy +++ b/data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-2-udkey_cert_auto.thy @@ -441,667 +441,756 @@ 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 + case (isoiec_9798_2_1_udkey_A_text_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_1_udkey_A_text_1_Text1 + thus ?case 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 + case (isoiec_9798_2_1_udkey_A_text_1_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_1_udkey_A_text_1_Text2 + thus ?case 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 + case (isoiec_9798_2_1_udkey_B_1_A t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_1_udkey_B_1_A + thus ?case 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 + case (isoiec_9798_2_1_udkey_B_1_TNA t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_1_udkey_B_1_TNA + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_1_udkey_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_1_udkey_B_1_Text1 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_1_udkey_B_1_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_1_udkey_B_1_Text2 + thus ?case 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 + case (isoiec_9798_2_2_udkey_A_1_B t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_udkey_A_1_B + thus ?case 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 + case (isoiec_9798_2_2_udkey_A_1_RB t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_udkey_A_1_RB + thus ?case 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 + case (isoiec_9798_2_2_udkey_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_udkey_A_1_Text1 + thus ?case 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 + case (isoiec_9798_2_2_udkey_A_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_udkey_A_text_2_Text2 + thus ?case 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 + case (isoiec_9798_2_2_udkey_A_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_udkey_A_text_2_Text3 + thus ?case 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 + case (isoiec_9798_2_2_udkey_B_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_udkey_B_2_Text2 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_2_udkey_B_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_udkey_B_2_Text3 + thus ?case 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 + case (isoiec_9798_2_3_udkey_A_text_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_udkey_A_text_1_Text1 + thus ?case 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 + case (isoiec_9798_2_3_udkey_A_text_1_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_udkey_A_text_1_Text2 + thus ?case 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 + case (isoiec_9798_2_3_udkey_A_2_TNB t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_udkey_A_2_TNB + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_3_udkey_A_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_udkey_A_2_Text3 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_3_udkey_A_2_Text4 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_udkey_A_2_Text4 + thus ?case 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 + case (isoiec_9798_2_3_udkey_B_1_A t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_udkey_B_1_A + thus ?case 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 + case (isoiec_9798_2_3_udkey_B_1_TNA t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_udkey_B_1_TNA + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_3_udkey_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_udkey_B_1_Text1 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_3_udkey_B_1_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_udkey_B_1_Text2 + thus ?case 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 + case (isoiec_9798_2_3_udkey_B_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_udkey_B_text_2_Text3 + thus ?case 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 + case (isoiec_9798_2_3_udkey_B_text_2_Text4 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_udkey_B_text_2_Text4 + thus ?case 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 + case (isoiec_9798_2_4_udkey_A_1_B t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_udkey_A_1_B + thus ?case 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 + case (isoiec_9798_2_4_udkey_A_1_RB t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_udkey_A_1_RB + thus ?case 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 + case (isoiec_9798_2_4_udkey_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_udkey_A_1_Text1 + thus ?case 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 + case (isoiec_9798_2_4_udkey_A_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_udkey_A_text_2_Text2 + thus ?case 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 + case (isoiec_9798_2_4_udkey_A_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_udkey_A_text_2_Text3 + thus ?case 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 + case (isoiec_9798_2_4_udkey_A_3_Text4 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_udkey_A_3_Text4 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_4_udkey_A_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_udkey_A_3_Text5 + thus ?case 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 + case (isoiec_9798_2_4_udkey_B_2_RA t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_udkey_B_2_RA + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_4_udkey_B_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_udkey_B_2_Text2 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_4_udkey_B_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_udkey_B_2_Text3 + thus ?case 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 + case (isoiec_9798_2_4_udkey_B_text_3_Text4 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_udkey_B_text_3_Text4 + thus ?case 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 + case (isoiec_9798_2_4_udkey_B_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_udkey_B_text_3_Text5 + thus ?case 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 + case (isoiec_9798_2_5_udkey_A_2_Kab t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_A_2_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_udkey_A_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_A_2_Text3 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_udkey_A_2_Text4 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_A_2_Text4 + thus ?case 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 + case (isoiec_9798_2_5_udkey_A_2_TokenPA_for_B t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_A_2_TokenPA_for_B + thus ?case 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 + case (isoiec_9798_2_5_udkey_A_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_A_text_3_Text5 + thus ?case 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 + case (isoiec_9798_2_5_udkey_A_text_3_Text6 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_A_text_3_Text6 + thus ?case 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 + case (isoiec_9798_2_5_udkey_A_4_TNb t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_A_4_TNb + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_udkey_A_4_Text7 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_A_4_Text7 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_udkey_A_4_Text8 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_A_4_Text8 + thus ?case 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 + case (isoiec_9798_2_5_udkey_B_3_A t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_B_3_A + thus ?case 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 + case (isoiec_9798_2_5_udkey_B_3_Kab t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_B_3_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_udkey_B_3_P t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_B_3_P + thus ?case 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 + case (isoiec_9798_2_5_udkey_B_3_TNa t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_B_3_TNa + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_udkey_B_3_TNp t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_B_3_TNp + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_udkey_B_3_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_B_3_Text2 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_udkey_B_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_B_3_Text5 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_udkey_B_3_Text6 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_B_3_Text6 + thus ?case 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 + case (isoiec_9798_2_5_udkey_B_text_4_Text7 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_B_text_4_Text7 + thus ?case 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 + case (isoiec_9798_2_5_udkey_B_text_4_Text8 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_B_text_4_Text8 + thus ?case 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 + case (isoiec_9798_2_5_udkey_P_1_A t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_P_1_A + thus ?case 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 + case (isoiec_9798_2_5_udkey_P_1_B t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_P_1_B + thus ?case 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 + case (isoiec_9798_2_5_udkey_P_1_TVPa t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_P_1_TVPa + thus ?case 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 + case (isoiec_9798_2_5_udkey_P_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_P_1_Text1 + thus ?case 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 + case (isoiec_9798_2_5_udkey_P_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_P_text_2_Text2 + thus ?case 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 + case (isoiec_9798_2_5_udkey_P_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_P_text_2_Text3 + thus ?case 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 + case (isoiec_9798_2_5_udkey_P_text_2_Text4 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_P_text_2_Text4 + thus ?case 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 + case (isoiec_9798_2_6_udkey_A_1_B t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_A_1_B + thus ?case 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 + case (isoiec_9798_2_6_udkey_A_1_Rb t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_A_1_Rb + thus ?case 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 + case (isoiec_9798_2_6_udkey_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_A_1_Text1 + thus ?case 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 + case (isoiec_9798_2_6_udkey_A_3_Kab t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_A_3_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_udkey_A_3_Text4 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_A_3_Text4 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_udkey_A_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_A_3_Text5 + thus ?case 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 + case (isoiec_9798_2_6_udkey_A_3_TokenPA_for_B t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_A_3_TokenPA_for_B + thus ?case 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 + case (isoiec_9798_2_6_udkey_A_text_4_Text6 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_A_text_4_Text6 + thus ?case 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 + case (isoiec_9798_2_6_udkey_A_text_4_Text7 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_A_text_4_Text7 + thus ?case 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 + case (isoiec_9798_2_6_udkey_A_5_Text8 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_A_5_Text8 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_udkey_A_5_Text9 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_A_5_Text9 + thus ?case 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 + case (isoiec_9798_2_6_udkey_B_4_Kab t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_B_4_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_udkey_B_4_P t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_B_4_P + thus ?case 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 + case (isoiec_9798_2_6_udkey_B_4_Rpa t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_B_4_Rpa + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_udkey_B_4_Text3 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_B_4_Text3 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_udkey_B_4_Text6 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_B_4_Text6 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_udkey_B_4_Text7 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_B_4_Text7 + thus ?case 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 + case (isoiec_9798_2_6_udkey_B_text_5_Text8 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_B_text_5_Text8 + thus ?case 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 + case (isoiec_9798_2_6_udkey_B_text_5_Text9 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_B_text_5_Text9 + thus ?case 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 + case (isoiec_9798_2_6_udkey_P_2_A t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_P_2_A + thus ?case 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 + case (isoiec_9798_2_6_udkey_P_2_B t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_P_2_B + thus ?case 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 + case (isoiec_9798_2_6_udkey_P_2_Ra t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_P_2_Ra + thus ?case 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 + case (isoiec_9798_2_6_udkey_P_2_Rb t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_P_2_Rb + thus ?case 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 + case (isoiec_9798_2_6_udkey_P_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_P_2_Text2 + thus ?case 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 + case (isoiec_9798_2_6_udkey_P_text_3_Text3 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_P_text_3_Text3 + thus ?case 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 + case (isoiec_9798_2_6_udkey_P_text_3_Text4 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_P_text_3_Text4 + thus ?case 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 + case (isoiec_9798_2_6_udkey_P_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_P_text_3_Text5 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) qed thus "isoiec_9798_2_bdkey_composed_typing_state t r s" by unfold_locales auto @@ -1182,11 +1271,11 @@ |} ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_2_udkey_B_injective_agreement: @@ -1220,11 +1309,11 @@ |} ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -1261,11 +1350,11 @@ |} ( K ( s(AV ''B'' tid0) ) ( s(AV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_3_udkey_B_non_injective_agreement: @@ -1291,11 +1380,11 @@ |} ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_4_udkey_A_injective_agreement: @@ -1330,7 +1419,7 @@ |} ( K ( s(MV ''B'' tid0) ) ( s(AV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_2_4_udkey_B_3_enc tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -1339,12 +1428,12 @@ |} ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid1) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -1390,11 +1479,11 @@ |} ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -1418,11 +1507,11 @@ 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) + thus ?thesis by (auto 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+)? + thus ?thesis by (auto dest!: ltk_secrecy) +qed (safe?, simp_all?, insert facts, (fastforce+)?) lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_udkey_A_secret_Kab: assumes facts: @@ -1441,11 +1530,11 @@ |} ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_udkey_B_secret_Kab: @@ -1465,11 +1554,11 @@ |} ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_udkey_A_injective_agreement_B: @@ -1507,7 +1596,7 @@ |} ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_2_5_udkey_P_2_enc tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -1547,11 +1636,11 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -1589,7 +1678,7 @@ |} ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_2_5_udkey_P_2_enc_1 tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -1611,9 +1700,9 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_5_udkey_A_injective_agreement_P: @@ -1649,11 +1738,11 @@ |} ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -1691,11 +1780,11 @@ |} ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_udkey_P_secret_Kab: @@ -1708,11 +1797,11 @@ 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) + thus ?thesis by (auto 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+)? + thus ?thesis by (auto dest!: ltk_secrecy) +qed (safe?, simp_all?, insert facts, (fastforce+)?) lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_udkey_A_secret_Kab: assumes facts: @@ -1731,11 +1820,11 @@ |} ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_udkey_B_secret_Kab: @@ -1755,11 +1844,11 @@ |} ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_bdkey_state) isoiec_9798_2_6_udkey_A_injective_agreement_B: @@ -1797,7 +1886,7 @@ |} ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_2_6_udkey_P_3_enc tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -1828,10 +1917,10 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -1880,7 +1969,7 @@ |} ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_2_6_udkey_P_3_enc_1 tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -1902,9 +1991,9 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -1951,11 +2040,11 @@ |} ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2002,11 +2091,11 @@ |} ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this diff --git a/data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-3_cert_auto.thy b/data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-3_cert_auto.thy --- a/data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-3_cert_auto.thy +++ b/data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-3_cert_auto.thy @@ -686,352 +686,410 @@ 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 + case (isoiec_9798_3_1_A_text_1_Text1 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_1_A_text_1_Text1 + thus ?case 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 + case (isoiec_9798_3_1_A_text_1_Text2 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_1_A_text_1_Text2 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_1_B_1_A t r s tid0) note facts = this + case (isoiec_9798_3_1_B_1_A t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_1_B_1_A + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_1_B_1_TNA t r s tid0) note facts = this + case (isoiec_9798_3_1_B_1_TNA t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_1_B_1_TNA + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_1_B_1_Text1 t r s tid0) note facts = this + case (isoiec_9798_3_1_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_1_B_1_Text1 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_1_B_1_Text2 t r s tid0) note facts = this + case (isoiec_9798_3_1_B_1_Text2 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_1_B_1_Text2 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_2_A_1_B t r s tid0) note facts = this + case (isoiec_9798_3_2_A_1_B t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_2_A_1_B + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_2_A_1_Rb t r s tid0) note facts = this + case (isoiec_9798_3_2_A_1_Rb t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_2_A_1_Rb + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_2_A_1_Text1 t r s tid0) note facts = this + case (isoiec_9798_3_2_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_2_A_1_Text1 + thus ?case 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 + case (isoiec_9798_3_2_A_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_2_A_text_2_Text2 + thus ?case 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 + case (isoiec_9798_3_2_A_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_2_A_text_2_Text3 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_2_B_2_Ra t r s tid0) note facts = this + case (isoiec_9798_3_2_B_2_Ra t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_2_B_2_Ra + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_2_B_2_Text2 t r s tid0) note facts = this + case (isoiec_9798_3_2_B_2_Text2 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_2_B_2_Text2 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_2_B_2_Text3 t r s tid0) note facts = this + case (isoiec_9798_3_2_B_2_Text3 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_2_B_2_Text3 + thus ?case 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 + case (isoiec_9798_3_3_A_text_1_Text1 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_3_A_text_1_Text1 + thus ?case 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 + case (isoiec_9798_3_3_A_text_1_Text2 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_3_A_text_1_Text2 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_3_A_2_TNB t r s tid0) note facts = this + case (isoiec_9798_3_3_A_2_TNB t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_3_A_2_TNB + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_3_A_2_Text3 t r s tid0) note facts = this + case (isoiec_9798_3_3_A_2_Text3 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_3_A_2_Text3 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_3_A_2_Text4 t r s tid0) note facts = this + case (isoiec_9798_3_3_A_2_Text4 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_3_A_2_Text4 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_3_B_1_A t r s tid0) note facts = this + case (isoiec_9798_3_3_B_1_A t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_3_B_1_A + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_3_B_1_TNA t r s tid0) note facts = this + case (isoiec_9798_3_3_B_1_TNA t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_3_B_1_TNA + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_3_B_1_Text1 t r s tid0) note facts = this + case (isoiec_9798_3_3_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_3_B_1_Text1 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_3_B_1_Text2 t r s tid0) note facts = this + case (isoiec_9798_3_3_B_1_Text2 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_3_B_1_Text2 + thus ?case 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 + case (isoiec_9798_3_3_B_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_3_B_text_2_Text3 + thus ?case 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 + case (isoiec_9798_3_3_B_text_2_Text4 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_3_B_text_2_Text4 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_4_A_1_B t r s tid0) note facts = this + case (isoiec_9798_3_4_A_1_B t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_4_A_1_B + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_4_A_1_RB t r s tid0) note facts = this + case (isoiec_9798_3_4_A_1_RB t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_4_A_1_RB + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_4_A_1_Text1 t r s tid0) note facts = this + case (isoiec_9798_3_4_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_4_A_1_Text1 + thus ?case 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 + case (isoiec_9798_3_4_A_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_4_A_text_2_Text2 + thus ?case 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 + case (isoiec_9798_3_4_A_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_4_A_text_2_Text3 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_4_A_3_Text4 t r s tid0) note facts = this + case (isoiec_9798_3_4_A_3_Text4 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_4_A_3_Text4 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_4_A_3_Text5 t r s tid0) note facts = this + case (isoiec_9798_3_4_A_3_Text5 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_4_A_3_Text5 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_4_B_2_RA t r s tid0) note facts = this + case (isoiec_9798_3_4_B_2_RA t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_4_B_2_RA + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_4_B_2_Text2 t r s tid0) note facts = this + case (isoiec_9798_3_4_B_2_Text2 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_4_B_2_Text2 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_4_B_2_Text3 t r s tid0) note facts = this + case (isoiec_9798_3_4_B_2_Text3 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_4_B_2_Text3 + thus ?case 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 + case (isoiec_9798_3_4_B_text_3_Text4 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_4_B_text_3_Text4 + thus ?case 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 + case (isoiec_9798_3_4_B_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_4_B_text_3_Text5 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_5_A_2_RB t r s tid0) note facts = this + case (isoiec_9798_3_5_A_2_RB t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_A_2_RB + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_5_A_2_Text2 t r s tid0) note facts = this + case (isoiec_9798_3_5_A_2_Text2 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_A_2_Text2 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_5_A_3_Text5 t r s tid0) note facts = this + case (isoiec_9798_3_5_A_3_Text5 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_A_3_Text5 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_5_A_3_Text6 t r s tid0) note facts = this + case (isoiec_9798_3_5_A_3_Text6 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_A_3_Text6 + thus ?case 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 + case (isoiec_9798_3_5_A_text_4_Text3 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_A_text_4_Text3 + thus ?case 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 + case (isoiec_9798_3_5_A_text_4_Text4 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_A_text_4_Text4 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_5_B_1_A t r s tid0) note facts = this + case (isoiec_9798_3_5_B_1_A t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_B_1_A + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_5_B_1_RA t r s tid0) note facts = this + case (isoiec_9798_3_5_B_1_RA t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_B_1_RA + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_5_B_1_Text1 t r s tid0) note facts = this + case (isoiec_9798_3_5_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_B_1_Text1 + thus ?case 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 + case (isoiec_9798_3_5_B_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_B_text_3_Text5 + thus ?case 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 + case (isoiec_9798_3_5_B_text_3_Text6 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_B_text_3_Text6 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_5_B_4_Text3 t r s tid0) note facts = this + case (isoiec_9798_3_5_B_4_Text3 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_B_4_Text3 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_5_B_4_Text4 t r s tid0) note facts = this + case (isoiec_9798_3_5_B_4_Text4 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_B_4_Text4 + thus ?case 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 + case (isoiec_9798_3_6_1_A_2_Rb t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_A_2_Rb + thus ?case 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 + case (isoiec_9798_3_6_1_A_2_Text3 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_A_2_Text3 + thus ?case 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 + case (isoiec_9798_3_6_1_A_2_TokenBA t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_A_2_TokenBA + thus ?case 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 + case (isoiec_9798_3_6_1_A_4_Text6 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_A_4_Text6 + thus ?case 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 + case (isoiec_9798_3_6_1_A_4_Text7 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_A_4_Text7 + thus ?case 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 + case (isoiec_9798_3_6_1_A_4_TokenTA_for_B t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_A_4_TokenTA_for_B + thus ?case 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 + case (isoiec_9798_3_6_1_A_4_pkB t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_A_4_pkB + thus ?case 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 + case (isoiec_9798_3_6_1_A_check_4_in_Text2 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_A_check_4_in_Text2 + thus ?case proof(sources! " Enc {| LC ''check_4'', {| LC ''isoiec_9798_3_6_opt_1_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0, @@ -1043,168 +1101,195 @@ ( inv(s(MV ''pkB'' tid0)) ) |} ( LN ''check_nonce_4'' tid0 ) ") - qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_3_6_1_A_text_5_Text8 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_A_text_5_Text8 + thus ?case 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 + case (isoiec_9798_3_6_1_A_text_5_Text9 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_A_text_5_Text9 + thus ?case 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 + case (isoiec_9798_3_6_1_B_1_A t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_B_1_A + thus ?case 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 + case (isoiec_9798_3_6_1_B_1_Ra t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_B_1_Ra + thus ?case 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 + case (isoiec_9798_3_6_1_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_B_1_Text1 + thus ?case 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 + case (isoiec_9798_3_6_1_B_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_B_text_2_Text2 + thus ?case 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 + case (isoiec_9798_3_6_1_B_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_B_text_2_Text3 + thus ?case 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 + case (isoiec_9798_3_6_1_B_5_T t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_B_5_T + thus ?case 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 + case (isoiec_9798_3_6_1_B_5_Text5 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_B_5_Text5 + thus ?case 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 + case (isoiec_9798_3_6_1_B_5_Text8 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_B_5_Text8 + thus ?case 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 + case (isoiec_9798_3_6_1_B_5_Text9 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_B_5_Text9 + thus ?case 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 + case (isoiec_9798_3_6_1_B_5_pkA t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_B_5_pkA + thus ?case 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 + case (isoiec_9798_3_6_1_T_3_A t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_T_3_A + thus ?case 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 + case (isoiec_9798_3_6_1_T_3_B t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_T_3_B + thus ?case 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 + case (isoiec_9798_3_6_1_T_3_Rb t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_T_3_Rb + thus ?case 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 + case (isoiec_9798_3_6_1_T_3_Rpa t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_T_3_Rpa + thus ?case 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 + case (isoiec_9798_3_6_1_T_3_Text4 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_T_3_Text4 + thus ?case 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 + case (isoiec_9798_3_6_1_T_text_4_Text5 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_T_text_4_Text5 + thus ?case 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 + case (isoiec_9798_3_6_1_T_text_4_Text6 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_T_text_4_Text6 + thus ?case 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 + case (isoiec_9798_3_6_1_T_text_4_Text7 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_T_text_4_Text7 + thus ?case 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 + case (isoiec_9798_3_6_2_A_2_Rb t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_A_2_Rb + thus ?case 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 + case (isoiec_9798_3_6_2_A_2_Text3 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_A_2_Text3 + thus ?case 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 + case (isoiec_9798_3_6_2_A_2_TokenBA t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_A_2_TokenBA + thus ?case 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 + case (isoiec_9798_3_6_2_A_4_Text7 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_A_4_Text7 + thus ?case 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 + case (isoiec_9798_3_6_2_A_4_TokenTA t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_A_4_TokenTA + thus ?case 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 + case (isoiec_9798_3_6_2_A_4_pkB t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_A_4_pkB + thus ?case 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 + case (isoiec_9798_3_6_2_A_check_4_in_Text2 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_A_check_4_in_Text2 + thus ?case proof(sources! " Enc {| LC ''check_4'', {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0, @@ -1226,12 +1311,13 @@ ( inv(s(MV ''pkB'' tid0)) ) |} ( LN ''check_nonce_4'' tid0 ) ") - qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_3_6_2_A_check_4_in_Text5 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_A_check_4_in_Text5 + thus ?case proof(sources! " Enc {| LC ''check_4'', {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0, @@ -1253,12 +1339,13 @@ ( inv(s(MV ''pkB'' tid0)) ) |} ( LN ''check_nonce_4'' tid0 ) ") - qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_3_6_2_A_check_4_in_pkA t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_A_check_4_in_pkA + thus ?case proof(sources! " Enc {| LC ''check_4'', {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0, @@ -1280,336 +1367,391 @@ ( inv(s(MV ''pkB'' tid0)) ) |} ( LN ''check_nonce_4'' tid0 ) ") - qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_3_6_2_A_text_5_Text8 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_A_text_5_Text8 + thus ?case 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 + case (isoiec_9798_3_6_2_A_text_5_Text9 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_A_text_5_Text9 + thus ?case 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 + case (isoiec_9798_3_6_2_B_1_A t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_B_1_A + thus ?case 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 + case (isoiec_9798_3_6_2_B_1_Ra t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_B_1_Ra + thus ?case 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 + case (isoiec_9798_3_6_2_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_B_1_Text1 + thus ?case 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 + case (isoiec_9798_3_6_2_B_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_B_text_2_Text2 + thus ?case 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 + case (isoiec_9798_3_6_2_B_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_B_text_2_Text3 + thus ?case 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 + case (isoiec_9798_3_6_2_B_5_Rpa t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_B_5_Rpa + thus ?case 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 + case (isoiec_9798_3_6_2_B_5_T t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_B_5_T + thus ?case 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 + case (isoiec_9798_3_6_2_B_5_Text5 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_B_5_Text5 + thus ?case 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 + case (isoiec_9798_3_6_2_B_5_Text8 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_B_5_Text8 + thus ?case 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 + case (isoiec_9798_3_6_2_B_5_Text9 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_B_5_Text9 + thus ?case 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 + case (isoiec_9798_3_6_2_B_5_pkA t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_B_5_pkA + thus ?case 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 + case (isoiec_9798_3_6_2_B_5_pkB t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_B_5_pkB + thus ?case 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 + case (isoiec_9798_3_6_2_T_3_A t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_T_3_A + thus ?case 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 + case (isoiec_9798_3_6_2_T_3_B t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_T_3_B + thus ?case 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 + case (isoiec_9798_3_6_2_T_3_Rb t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_T_3_Rb + thus ?case 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 + case (isoiec_9798_3_6_2_T_3_Rpa t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_T_3_Rpa + thus ?case 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 + case (isoiec_9798_3_6_2_T_3_Text4 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_T_3_Text4 + thus ?case 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 + case (isoiec_9798_3_6_2_T_text_4_Text5 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_T_text_4_Text5 + thus ?case 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 + case (isoiec_9798_3_6_2_T_text_4_Text7 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_T_text_4_Text7 + thus ?case 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 + case (isoiec_9798_3_7_1_A_1_B t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_A_1_B + thus ?case 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 + case (isoiec_9798_3_7_1_A_1_Rb t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_A_1_Rb + thus ?case 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 + case (isoiec_9798_3_7_1_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_A_1_Text1 + thus ?case 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 + case (isoiec_9798_3_7_1_A_3_Text4 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_A_3_Text4 + thus ?case 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 + case (isoiec_9798_3_7_1_A_3_Text5 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_A_3_Text5 + thus ?case 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 + case (isoiec_9798_3_7_1_A_3_TokenTA_for_B t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_A_3_TokenTA_for_B + thus ?case 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 + case (isoiec_9798_3_7_1_A_3_pkB t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_A_3_pkB + thus ?case 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 + case (isoiec_9798_3_7_1_A_text_4_Text6 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_A_text_4_Text6 + thus ?case 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 + case (isoiec_9798_3_7_1_A_text_4_Text7 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_A_text_4_Text7 + thus ?case 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 + case (isoiec_9798_3_7_1_A_5_Text8 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_A_5_Text8 + thus ?case 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 + case (isoiec_9798_3_7_1_A_5_Text9 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_A_5_Text9 + thus ?case 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 + case (isoiec_9798_3_7_1_B_4_Ra t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_B_4_Ra + thus ?case 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 + case (isoiec_9798_3_7_1_B_4_Rpa t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_B_4_Rpa + thus ?case 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 + case (isoiec_9798_3_7_1_B_4_T t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_B_4_T + thus ?case 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 + case (isoiec_9798_3_7_1_B_4_Text3 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_B_4_Text3 + thus ?case 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 + case (isoiec_9798_3_7_1_B_4_Text6 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_B_4_Text6 + thus ?case 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 + case (isoiec_9798_3_7_1_B_4_Text9 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_B_4_Text9 + thus ?case 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 + case (isoiec_9798_3_7_1_B_4_pkA t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_B_4_pkA + thus ?case 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 + case (isoiec_9798_3_7_1_B_text_5_Text8 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_B_text_5_Text8 + thus ?case 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 + case (isoiec_9798_3_7_1_T_2_A t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_T_2_A + thus ?case 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 + case (isoiec_9798_3_7_1_T_2_B t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_T_2_B + thus ?case 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 + case (isoiec_9798_3_7_1_T_2_Rb t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_T_2_Rb + thus ?case 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 + case (isoiec_9798_3_7_1_T_2_Rpa t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_T_2_Rpa + thus ?case 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 + case (isoiec_9798_3_7_1_T_2_Text2 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_T_2_Text2 + thus ?case 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 + case (isoiec_9798_3_7_1_T_text_3_Text3 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_T_text_3_Text3 + thus ?case 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 + case (isoiec_9798_3_7_1_T_text_3_Text4 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_T_text_3_Text4 + thus ?case 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 + case (isoiec_9798_3_7_1_T_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_T_text_3_Text5 + thus ?case 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 + case (isoiec_9798_3_7_2_A_1_B t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_A_1_B + thus ?case 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 + case (isoiec_9798_3_7_2_A_1_Rb t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_A_1_Rb + thus ?case 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 + case (isoiec_9798_3_7_2_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_A_1_Text1 + thus ?case 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 + case (isoiec_9798_3_7_2_A_3_Text5 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_A_3_Text5 + thus ?case 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 + case (isoiec_9798_3_7_2_A_3_TokenTA t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_A_3_TokenTA + thus ?case 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 + case (isoiec_9798_3_7_2_A_3_pkB t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_A_3_pkB + thus ?case 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 + case (isoiec_9798_3_7_2_A_check_3_in_Text3 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_A_check_3_in_Text3 + thus ?case proof(sources! " Enc {| LC ''check_4'', {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0, @@ -1623,12 +1765,13 @@ ( SK ( s(AV ''T'' tid0) ) ) |} ( LN ''check_nonce_4'' tid0 ) ") - qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_3_7_2_A_check_3_in_pkA t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_A_check_3_in_pkA + thus ?case proof(sources! " Enc {| LC ''check_4'', {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0, @@ -1642,126 +1785,146 @@ ( SK ( s(AV ''T'' tid0) ) ) |} ( LN ''check_nonce_4'' tid0 ) ") - qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_3_7_2_A_text_4_Text6 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_A_text_4_Text6 + thus ?case 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 + case (isoiec_9798_3_7_2_A_text_4_Text7 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_A_text_4_Text7 + thus ?case 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 + case (isoiec_9798_3_7_2_A_5_Text8 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_A_5_Text8 + thus ?case 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 + case (isoiec_9798_3_7_2_A_5_Text9 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_A_5_Text9 + thus ?case 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 + case (isoiec_9798_3_7_2_B_4_Ra t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_B_4_Ra + thus ?case 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 + case (isoiec_9798_3_7_2_B_4_Rpa t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_B_4_Rpa + thus ?case 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 + case (isoiec_9798_3_7_2_B_4_T t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_B_4_T + thus ?case 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 + case (isoiec_9798_3_7_2_B_4_Text3 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_B_4_Text3 + thus ?case 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 + case (isoiec_9798_3_7_2_B_4_Text6 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_B_4_Text6 + thus ?case 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 + case (isoiec_9798_3_7_2_B_4_Text9 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_B_4_Text9 + thus ?case 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 + case (isoiec_9798_3_7_2_B_4_pkA t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_B_4_pkA + thus ?case 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 + case (isoiec_9798_3_7_2_B_4_pkB t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_B_4_pkB + thus ?case 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 + case (isoiec_9798_3_7_2_B_text_5_Text8 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_B_text_5_Text8 + thus ?case 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 + case (isoiec_9798_3_7_2_T_2_A t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_T_2_A + thus ?case 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 + case (isoiec_9798_3_7_2_T_2_B t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_T_2_B + thus ?case 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 + case (isoiec_9798_3_7_2_T_2_Rb t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_T_2_Rb + thus ?case 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 + case (isoiec_9798_3_7_2_T_2_Rpa t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_T_2_Rpa + thus ?case 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 + case (isoiec_9798_3_7_2_T_2_Text2 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_T_2_Text2 + thus ?case 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 + case (isoiec_9798_3_7_2_T_text_3_Text3 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_T_text_3_Text3 + thus ?case 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 + case (isoiec_9798_3_7_2_T_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_3_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_T_text_3_Text5 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) qed thus "isoiec_9798_3_composed_typing_state t r s" by unfold_locales auto @@ -1841,11 +2004,11 @@ |} ( SK ( s(MV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_2_B_injective_agreement: @@ -1879,11 +2042,11 @@ |} ( SK ( s(AV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -1919,11 +2082,11 @@ |} ( SK ( s(AV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_3_B_non_injective_agreement: @@ -1948,11 +2111,11 @@ |} ( SK ( s(MV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_3_state) isoiec_9798_3_4_A_injective_agreement: @@ -1987,7 +2150,7 @@ |} ( SK ( s(MV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_3_4_B_3_enc tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -1996,12 +2159,12 @@ |} ( SK ( s(AV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2046,11 +2209,11 @@ |} ( SK ( s(AV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2095,11 +2258,11 @@ |} ( SK ( s(AV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2145,7 +2308,7 @@ |} ( SK ( s(MV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_3_5_A_4_enc tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -2154,12 +2317,12 @@ |} ( SK ( s(AV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2212,7 +2375,7 @@ ( 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+)? + qed (safe?, simp_all?, 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! " @@ -2227,16 +2390,16 @@ |} ( SK ( s(AV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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+)? + thus ?thesis by (auto dest!: ltk_secrecy) + qed (safe?, simp_all?, 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2282,7 +2445,7 @@ |} ( SK ( s(MV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_3_6_1_T_4_enc_1 tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -2292,12 +2455,12 @@ |} ( SK ( s(MV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2342,11 +2505,11 @@ |} ( SK ( s(AV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2391,11 +2554,11 @@ |} ( SK ( s(MV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2458,7 +2621,7 @@ ( 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+)? + qed (safe?, simp_all?, 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! " @@ -2474,16 +2637,16 @@ |} ( SK ( s(AV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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+)? + thus ?thesis by (auto dest!: ltk_secrecy) + qed (safe?, simp_all?, 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2530,7 +2693,7 @@ |} ( SK ( s(MV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_3_6_2_T_4_enc tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -2540,12 +2703,12 @@ |} ( SK ( s(MV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2609,7 +2772,7 @@ ( 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+)? + qed (safe?, simp_all?, 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! " @@ -2619,12 +2782,12 @@ |} ( SK ( s(AV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2672,11 +2835,11 @@ |} ( SK ( s(MV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2722,7 +2885,7 @@ |} ( SK ( s(AV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_3_7_1_T_3_enc tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -2732,12 +2895,12 @@ |} ( SK ( s(MV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2783,7 +2946,7 @@ |} ( SK ( s(MV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_3_7_1_T_3_enc_1 tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -2793,12 +2956,12 @@ |} ( SK ( s(AV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2843,11 +3006,11 @@ |} ( SK ( s(AV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2892,11 +3055,11 @@ |} ( SK ( s(MV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2951,7 +3114,7 @@ ( 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+)? + qed (safe?, simp_all?, 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! " @@ -2961,7 +3124,7 @@ |} ( SK ( s(AV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_3_7_2_T_3_enc tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -2971,13 +3134,13 @@ |} ( SK ( s(MV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -3024,7 +3187,7 @@ |} ( SK ( s(MV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_3_7_2_T_3_enc tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -3034,12 +3197,12 @@ |} ( SK ( s(AV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -3095,7 +3258,7 @@ ( 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+)? + qed (safe?, simp_all?, 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! " @@ -3105,12 +3268,12 @@ |} ( SK ( s(AV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -3158,11 +3321,11 @@ |} ( SK ( s(MV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this diff --git a/data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-4-bdkey_cert_auto.thy b/data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-4-bdkey_cert_auto.thy --- a/data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-4-bdkey_cert_auto.thy +++ b/data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-4-bdkey_cert_auto.thy @@ -210,220 +210,256 @@ have "(t,r,s) : approx isoiec_9798_4_bdkey_composed_typing" proof(cases rule: reachable_in_approxI_ext [OF isoiec_9798_4_bdkey_composed_typing.monoTyp, completeness_cases_rule]) - case (isoiec_9798_4_1_bdkey_A_text_1_Text1 t r s tid0) note facts = this + case (isoiec_9798_4_1_bdkey_A_text_1_Text1 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_1_bdkey_A_text_1_Text1 + thus ?case 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 + case (isoiec_9798_4_1_bdkey_A_text_1_Text2 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_1_bdkey_A_text_1_Text2 + thus ?case 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 + case (isoiec_9798_4_1_bdkey_B_1_A t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_1_bdkey_B_1_A + thus ?case 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 + case (isoiec_9798_4_1_bdkey_B_1_TNA t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_1_bdkey_B_1_TNA + thus ?case 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 + case (isoiec_9798_4_1_bdkey_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_1_bdkey_B_1_Text1 + thus ?case 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 + case (isoiec_9798_4_1_bdkey_B_1_Text2 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_1_bdkey_B_1_Text2 + thus ?case 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 + case (isoiec_9798_4_2_bdkey_A_1_B t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_bdkey_A_1_B + thus ?case 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 + case (isoiec_9798_4_2_bdkey_A_1_Rb t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_bdkey_A_1_Rb + thus ?case 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 + case (isoiec_9798_4_2_bdkey_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_bdkey_A_1_Text1 + thus ?case 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 + case (isoiec_9798_4_2_bdkey_A_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_bdkey_A_text_2_Text2 + thus ?case 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 + case (isoiec_9798_4_2_bdkey_A_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_bdkey_A_text_2_Text3 + thus ?case 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 + case (isoiec_9798_4_2_bdkey_B_2_Text2 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_bdkey_B_2_Text2 + thus ?case 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 + case (isoiec_9798_4_2_bdkey_B_2_Text3 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_bdkey_B_2_Text3 + thus ?case 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 + case (isoiec_9798_4_3_bdkey_A_text_1_Text1 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_A_text_1_Text1 + thus ?case 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 + case (isoiec_9798_4_3_bdkey_A_text_1_Text2 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_A_text_1_Text2 + thus ?case 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 + case (isoiec_9798_4_3_bdkey_A_2_TNb t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_A_2_TNb + thus ?case 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 + case (isoiec_9798_4_3_bdkey_A_2_Text3 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_A_2_Text3 + thus ?case 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 + case (isoiec_9798_4_3_bdkey_A_2_Text4 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_A_2_Text4 + thus ?case 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 + case (isoiec_9798_4_3_bdkey_B_1_A t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_B_1_A + thus ?case 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 + case (isoiec_9798_4_3_bdkey_B_1_TNa t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_B_1_TNa + thus ?case 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 + case (isoiec_9798_4_3_bdkey_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_B_1_Text1 + thus ?case 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 + case (isoiec_9798_4_3_bdkey_B_1_Text2 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_B_1_Text2 + thus ?case 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 + case (isoiec_9798_4_3_bdkey_B_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_B_text_2_Text3 + thus ?case 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 + case (isoiec_9798_4_3_bdkey_B_text_2_Text4 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_B_text_2_Text4 + thus ?case 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 + case (isoiec_9798_4_4_bdkey_A_1_B t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_A_1_B + thus ?case 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 + case (isoiec_9798_4_4_bdkey_A_1_Rb t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_A_1_Rb + thus ?case 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 + case (isoiec_9798_4_4_bdkey_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_A_1_Text1 + thus ?case 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 + case (isoiec_9798_4_4_bdkey_A_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_A_text_2_Text2 + thus ?case 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 + case (isoiec_9798_4_4_bdkey_A_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_A_text_2_Text3 + thus ?case 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 + case (isoiec_9798_4_4_bdkey_A_3_Text4 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_A_3_Text4 + thus ?case 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 + case (isoiec_9798_4_4_bdkey_A_3_Text5 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_A_3_Text5 + thus ?case 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 + case (isoiec_9798_4_4_bdkey_B_2_Ra t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_B_2_Ra + thus ?case 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 + case (isoiec_9798_4_4_bdkey_B_2_Text2 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_B_2_Text2 + thus ?case 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 + case (isoiec_9798_4_4_bdkey_B_2_Text3 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_B_2_Text3 + thus ?case 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 + case (isoiec_9798_4_4_bdkey_B_text_3_Text4 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_B_text_3_Text4 + thus ?case 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 + case (isoiec_9798_4_4_bdkey_B_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_4_bdkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_B_text_3_Text5 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) qed thus "isoiec_9798_4_bdkey_composed_typing_state t r s" by unfold_locales auto @@ -504,11 +540,11 @@ s(MV ''Text1'' tid0) |} ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_4_1_bdkey_A_1_hash tid1) note_unified facts = this facts thus ?thesis by (fastforce intro: event_predOrdI split: if_splits) - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_4_bdkey_state) isoiec_9798_4_2_bdkey_B_injective_agreement: @@ -543,11 +579,11 @@ s(MV ''Text2'' tid0) |} ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -584,11 +620,11 @@ s(MV ''Text3'' tid0) |} ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_4_3_bdkey_B_2_hash tid1) note_unified facts = this facts thus ?thesis by (fastforce intro: event_predOrdI split: if_splits) - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_4_bdkey_state) isoiec_9798_4_3_bdkey_B_non_injective_agreement: @@ -614,11 +650,11 @@ s(MV ''Text1'' tid0) |} ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_4_3_bdkey_A_1_hash tid1) note_unified facts = this facts thus ?thesis by (fastforce intro: event_predOrdI split: if_splits) - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_4_bdkey_state) isoiec_9798_4_4_bdkey_A_injective_agreement: @@ -653,7 +689,7 @@ s(MV ''Text4'' tid0) |} ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -667,11 +703,11 @@ s(AV ''B'' tid1), s(MV ''Text2'' tid1) |} ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) next case swapped note_unified facts = this facts thus ?thesis proof(sources! " @@ -680,13 +716,13 @@ s(AV ''A'' tid0), s(MV ''Text2'' tid1) |} ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed (fastforce+)? - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -732,11 +768,11 @@ s(AV ''B'' tid0), s(MV ''Text2'' tid0) |} ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this diff --git a/data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-4-udkey_cert_auto.thy b/data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-4-udkey_cert_auto.thy --- a/data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-4-udkey_cert_auto.thy +++ b/data/examples/iso9798/isabelle-parallel-proofs/isoiec-9798-4-udkey_cert_auto.thy @@ -208,220 +208,256 @@ have "(t,r,s) : approx isoiec_9798_4_udkey_composed_typing" proof(cases rule: reachable_in_approxI_ext [OF isoiec_9798_4_udkey_composed_typing.monoTyp, completeness_cases_rule]) - case (isoiec_9798_4_1_udkey_A_text_1_Text1 t r s tid0) note facts = this + case (isoiec_9798_4_1_udkey_A_text_1_Text1 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_1_udkey_A_text_1_Text1 + thus ?case 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 + case (isoiec_9798_4_1_udkey_A_text_1_Text2 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_1_udkey_A_text_1_Text2 + thus ?case 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 + case (isoiec_9798_4_1_udkey_B_1_A t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_1_udkey_B_1_A + thus ?case 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 + case (isoiec_9798_4_1_udkey_B_1_TNA t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_1_udkey_B_1_TNA + thus ?case 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 + case (isoiec_9798_4_1_udkey_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_1_udkey_B_1_Text1 + thus ?case 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 + case (isoiec_9798_4_1_udkey_B_1_Text2 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_1_udkey_B_1_Text2 + thus ?case 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 + case (isoiec_9798_4_2_udkey_A_1_B t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_udkey_A_1_B + thus ?case 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 + case (isoiec_9798_4_2_udkey_A_1_Rb t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_udkey_A_1_Rb + thus ?case 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 + case (isoiec_9798_4_2_udkey_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_udkey_A_1_Text1 + thus ?case 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 + case (isoiec_9798_4_2_udkey_A_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_udkey_A_text_2_Text2 + thus ?case 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 + case (isoiec_9798_4_2_udkey_A_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_udkey_A_text_2_Text3 + thus ?case 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 + case (isoiec_9798_4_2_udkey_B_2_Text2 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_udkey_B_2_Text2 + thus ?case 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 + case (isoiec_9798_4_2_udkey_B_2_Text3 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_udkey_B_2_Text3 + thus ?case 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 + case (isoiec_9798_4_3_udkey_A_text_1_Text1 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_udkey_A_text_1_Text1 + thus ?case 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 + case (isoiec_9798_4_3_udkey_A_text_1_Text2 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_udkey_A_text_1_Text2 + thus ?case 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 + case (isoiec_9798_4_3_udkey_A_2_TNb t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_udkey_A_2_TNb + thus ?case 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 + case (isoiec_9798_4_3_udkey_A_2_Text3 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_udkey_A_2_Text3 + thus ?case 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 + case (isoiec_9798_4_3_udkey_A_2_Text4 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_udkey_A_2_Text4 + thus ?case 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 + case (isoiec_9798_4_3_udkey_B_1_A t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_udkey_B_1_A + thus ?case 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 + case (isoiec_9798_4_3_udkey_B_1_TNa t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_udkey_B_1_TNa + thus ?case 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 + case (isoiec_9798_4_3_udkey_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_udkey_B_1_Text1 + thus ?case 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 + case (isoiec_9798_4_3_udkey_B_1_Text2 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_udkey_B_1_Text2 + thus ?case 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 + case (isoiec_9798_4_3_udkey_B_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_udkey_B_text_2_Text3 + thus ?case 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 + case (isoiec_9798_4_3_udkey_B_text_2_Text4 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_udkey_B_text_2_Text4 + thus ?case 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 + case (isoiec_9798_4_4_udkey_A_1_B t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_udkey_A_1_B + thus ?case 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 + case (isoiec_9798_4_4_udkey_A_1_Rb t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_udkey_A_1_Rb + thus ?case 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 + case (isoiec_9798_4_4_udkey_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_udkey_A_1_Text1 + thus ?case 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 + case (isoiec_9798_4_4_udkey_A_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_udkey_A_text_2_Text2 + thus ?case 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 + case (isoiec_9798_4_4_udkey_A_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_udkey_A_text_2_Text3 + thus ?case 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 + case (isoiec_9798_4_4_udkey_A_3_Text4 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_udkey_A_3_Text4 + thus ?case 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 + case (isoiec_9798_4_4_udkey_A_3_Text5 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_udkey_A_3_Text5 + thus ?case 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 + case (isoiec_9798_4_4_udkey_B_2_Ra t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_udkey_B_2_Ra + thus ?case 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 + case (isoiec_9798_4_4_udkey_B_2_Text2 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_udkey_B_2_Text2 + thus ?case 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 + case (isoiec_9798_4_4_udkey_B_2_Text3 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_udkey_B_2_Text3 + thus ?case 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 + case (isoiec_9798_4_4_udkey_B_text_3_Text4 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_udkey_B_text_3_Text4 + thus ?case 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 + case (isoiec_9798_4_4_udkey_B_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_4_udkey_composed_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_udkey_B_text_3_Text5 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) qed thus "isoiec_9798_4_udkey_composed_typing_state t r s" by unfold_locales auto @@ -501,11 +537,11 @@ 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 (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_4_1_udkey_A_1_hash tid1) note_unified facts = this facts thus ?thesis by (fastforce intro: event_predOrdI split: if_splits) - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_4_udkey_state) isoiec_9798_4_2_udkey_B_injective_agreement: @@ -539,11 +575,11 @@ 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) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -579,11 +615,11 @@ 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 (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_4_3_udkey_B_2_hash tid1) note_unified facts = this facts thus ?thesis by (fastforce intro: event_predOrdI split: if_splits) - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_4_udkey_state) isoiec_9798_4_3_udkey_B_non_injective_agreement: @@ -608,11 +644,11 @@ 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 (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_4_3_udkey_A_1_hash tid1) note_unified facts = this facts thus ?thesis by (fastforce intro: event_predOrdI split: if_splits) - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_4_udkey_state) isoiec_9798_4_4_udkey_A_injective_agreement: @@ -647,7 +683,7 @@ s(MV ''Text4'' tid0) |} ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_4_4_udkey_B_3_hash tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -656,12 +692,12 @@ s(MV ''Text2'' tid1) |} ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -707,11 +743,11 @@ s(MV ''Text2'' tid0) |} ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this diff --git a/data/examples/iso9798/isabelle-proofs/isoiec-9798-2-bdkey_cert_auto.thy b/data/examples/iso9798/isabelle-proofs/isoiec-9798-2-bdkey_cert_auto.thy --- a/data/examples/iso9798/isabelle-proofs/isoiec-9798-2-bdkey_cert_auto.thy +++ b/data/examples/iso9798/isabelle-proofs/isoiec-9798-2-bdkey_cert_auto.thy @@ -51,50 +51,56 @@ 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 + case (isoiec_9798_2_1_bdkey_A_text_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_1_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_1_bdkey_A_text_1_Text1 + thus ?case 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 + case (isoiec_9798_2_1_bdkey_A_text_1_Text2 t r s tid0) then interpret state: isoiec_9798_2_1_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_1_bdkey_A_text_1_Text2 + thus ?case 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 + case (isoiec_9798_2_1_bdkey_B_1_A t r s tid0) then interpret state: isoiec_9798_2_1_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_1_bdkey_B_1_A + thus ?case 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 + case (isoiec_9798_2_1_bdkey_B_1_TNA t r s tid0) then interpret state: isoiec_9798_2_1_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_1_bdkey_B_1_TNA + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_1_bdkey_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_1_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_1_bdkey_B_1_Text1 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_1_bdkey_B_1_Text2 t r s tid0) then interpret state: isoiec_9798_2_1_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_1_bdkey_B_1_Text2 + thus ?case 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 @@ -175,11 +181,11 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed role isoiec_9798_2_2_bdkey_A @@ -234,51 +240,58 @@ 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 + case (isoiec_9798_2_2_bdkey_A_1_B t r s tid0) then interpret state: isoiec_9798_2_2_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_bdkey_A_1_B + thus ?case 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 + case (isoiec_9798_2_2_bdkey_A_1_RB t r s tid0) then interpret state: isoiec_9798_2_2_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_bdkey_A_1_RB + thus ?case 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 + case (isoiec_9798_2_2_bdkey_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_2_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_bdkey_A_1_Text1 + thus ?case 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 + case (isoiec_9798_2_2_bdkey_A_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_2_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_bdkey_A_text_2_Text2 + thus ?case 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 + case (isoiec_9798_2_2_bdkey_A_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_2_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_bdkey_A_text_2_Text3 + thus ?case 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 + case (isoiec_9798_2_2_bdkey_B_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_2_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_bdkey_B_2_Text2 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_2_bdkey_B_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_2_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_bdkey_B_2_Text3 + thus ?case 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 @@ -368,11 +381,11 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -458,90 +471,101 @@ 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 + case (isoiec_9798_2_3_bdkey_A_text_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_bdkey_A_text_1_Text1 + thus ?case 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 + case (isoiec_9798_2_3_bdkey_A_text_1_Text2 t r s tid0) then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_bdkey_A_text_1_Text2 + thus ?case 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 + case (isoiec_9798_2_3_bdkey_A_2_TNB t r s tid0) then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_bdkey_A_2_TNB + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_3_bdkey_A_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_bdkey_A_2_Text3 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_3_bdkey_A_2_Text4 t r s tid0) then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_bdkey_A_2_Text4 + thus ?case 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 + case (isoiec_9798_2_3_bdkey_B_1_A t r s tid0) then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_bdkey_B_1_A + thus ?case 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 + case (isoiec_9798_2_3_bdkey_B_1_TNA t r s tid0) then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_bdkey_B_1_TNA + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_3_bdkey_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_bdkey_B_1_Text1 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_3_bdkey_B_1_Text2 t r s tid0) then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_bdkey_B_1_Text2 + thus ?case 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 + case (isoiec_9798_2_3_bdkey_B_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_bdkey_B_text_2_Text3 + thus ?case 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 + case (isoiec_9798_2_3_bdkey_B_text_2_Text4 t r s tid0) then interpret state: isoiec_9798_2_3_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_bdkey_B_text_2_Text4 + thus ?case 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 @@ -622,11 +646,11 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_3_bdkey_state) B_non_injective_agreement: @@ -652,11 +676,11 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed role isoiec_9798_2_4_bdkey_A @@ -735,91 +759,103 @@ 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 + case (isoiec_9798_2_4_bdkey_A_1_B t r s tid0) then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_bdkey_A_1_B + thus ?case 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 + case (isoiec_9798_2_4_bdkey_A_1_RB t r s tid0) then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_bdkey_A_1_RB + thus ?case 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 + case (isoiec_9798_2_4_bdkey_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_bdkey_A_1_Text1 + thus ?case 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 + case (isoiec_9798_2_4_bdkey_A_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_bdkey_A_text_2_Text2 + thus ?case 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 + case (isoiec_9798_2_4_bdkey_A_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_bdkey_A_text_2_Text3 + thus ?case 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 + case (isoiec_9798_2_4_bdkey_A_3_Text4 t r s tid0) then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_bdkey_A_3_Text4 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_4_bdkey_A_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_bdkey_A_3_Text5 + thus ?case 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 + case (isoiec_9798_2_4_bdkey_B_2_RA t r s tid0) then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_bdkey_B_2_RA + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_4_bdkey_B_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_bdkey_B_2_Text2 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_4_bdkey_B_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_bdkey_B_2_Text3 + thus ?case 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 + case (isoiec_9798_2_4_bdkey_B_text_3_Text4 t r s tid0) then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_bdkey_B_text_3_Text4 + thus ?case 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 + case (isoiec_9798_2_4_bdkey_B_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_4_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_bdkey_B_text_3_Text5 + thus ?case 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 @@ -909,7 +945,7 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(MV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -923,11 +959,11 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid1) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) next case swapped note_unified facts = this facts thus ?thesis proof(sources! " @@ -936,13 +972,13 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''A'' tid1) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed (fastforce+)? - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -988,11 +1024,11 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -1144,210 +1180,236 @@ 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 + case (isoiec_9798_2_5_bdkey_A_2_Kab t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_A_2_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_bdkey_A_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_A_2_Text3 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_bdkey_A_2_Text4 t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_A_2_Text4 + thus ?case 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 + case (isoiec_9798_2_5_bdkey_A_2_TokenPA_for_B t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_A_2_TokenPA_for_B + thus ?case 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 + case (isoiec_9798_2_5_bdkey_A_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_A_text_3_Text5 + thus ?case 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 + case (isoiec_9798_2_5_bdkey_A_text_3_Text6 t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_A_text_3_Text6 + thus ?case 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 + case (isoiec_9798_2_5_bdkey_A_4_TNb t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_A_4_TNb + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_bdkey_A_4_Text7 t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_A_4_Text7 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_bdkey_A_4_Text8 t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_A_4_Text8 + thus ?case 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 + case (isoiec_9798_2_5_bdkey_B_3_A t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_B_3_A + thus ?case 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 + case (isoiec_9798_2_5_bdkey_B_3_Kab t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_B_3_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_bdkey_B_3_P t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_B_3_P + thus ?case 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 + case (isoiec_9798_2_5_bdkey_B_3_TNa t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_B_3_TNa + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_bdkey_B_3_TNp t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_B_3_TNp + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_bdkey_B_3_Text2 t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_B_3_Text2 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_bdkey_B_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_B_3_Text5 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_bdkey_B_3_Text6 t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_B_3_Text6 + thus ?case 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 + case (isoiec_9798_2_5_bdkey_B_text_4_Text7 t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_B_text_4_Text7 + thus ?case 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 + case (isoiec_9798_2_5_bdkey_B_text_4_Text8 t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_B_text_4_Text8 + thus ?case 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 + case (isoiec_9798_2_5_bdkey_P_1_A t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_P_1_A + thus ?case 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 + case (isoiec_9798_2_5_bdkey_P_1_B t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_P_1_B + thus ?case 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 + case (isoiec_9798_2_5_bdkey_P_1_TVPa t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_P_1_TVPa + thus ?case 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 + case (isoiec_9798_2_5_bdkey_P_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_P_1_Text1 + thus ?case 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 + case (isoiec_9798_2_5_bdkey_P_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_P_text_2_Text2 + thus ?case 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 + case (isoiec_9798_2_5_bdkey_P_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_P_text_2_Text3 + thus ?case 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 + case (isoiec_9798_2_5_bdkey_P_text_2_Text4 t r s tid0) then interpret state: isoiec_9798_2_5_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_bdkey_P_text_2_Text4 + thus ?case 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 @@ -1415,11 +1477,11 @@ 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) + thus ?thesis by (auto 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+)? + thus ?thesis by (auto dest!: ltk_secrecy) +qed (safe?, simp_all?, insert facts, (fastforce+)?) lemma (in restricted_isoiec_9798_2_5_bdkey_state) A_secret_Kab: assumes facts: @@ -1439,11 +1501,11 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_5_bdkey_state) B_secret_Kab: @@ -1464,11 +1526,11 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_5_bdkey_state) A_injective_agreement_B: @@ -1507,7 +1569,7 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_2_5_bdkey_P_2_enc tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -1547,11 +1609,11 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -1590,7 +1652,7 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_2_5_bdkey_P_2_enc_1 tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -1612,9 +1674,9 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_5_bdkey_state) A_injective_agreement_P: @@ -1651,11 +1713,11 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -1694,11 +1756,11 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed role isoiec_9798_2_6_bdkey_A @@ -1840,205 +1902,232 @@ 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 + case (isoiec_9798_2_6_bdkey_A_1_B t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_A_1_B + thus ?case 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 + case (isoiec_9798_2_6_bdkey_A_1_Rb t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_A_1_Rb + thus ?case 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 + case (isoiec_9798_2_6_bdkey_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_A_1_Text1 + thus ?case 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 + case (isoiec_9798_2_6_bdkey_A_3_Kab t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_A_3_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_bdkey_A_3_Text4 t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_A_3_Text4 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_bdkey_A_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_A_3_Text5 + thus ?case 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 + case (isoiec_9798_2_6_bdkey_A_3_TokenPA_for_B t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_A_3_TokenPA_for_B + thus ?case 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 + case (isoiec_9798_2_6_bdkey_A_text_4_Text6 t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_A_text_4_Text6 + thus ?case 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 + case (isoiec_9798_2_6_bdkey_A_text_4_Text7 t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_A_text_4_Text7 + thus ?case 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 + case (isoiec_9798_2_6_bdkey_A_5_Text8 t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_A_5_Text8 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_bdkey_A_5_Text9 t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_A_5_Text9 + thus ?case 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 + case (isoiec_9798_2_6_bdkey_B_4_Kab t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_B_4_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_bdkey_B_4_P t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_B_4_P + thus ?case 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 + case (isoiec_9798_2_6_bdkey_B_4_Rpa t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_B_4_Rpa + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_bdkey_B_4_Text3 t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_B_4_Text3 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_bdkey_B_4_Text6 t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_B_4_Text6 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_bdkey_B_4_Text7 t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_B_4_Text7 + thus ?case 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 + case (isoiec_9798_2_6_bdkey_B_text_5_Text8 t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_B_text_5_Text8 + thus ?case 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 + case (isoiec_9798_2_6_bdkey_B_text_5_Text9 t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_B_text_5_Text9 + thus ?case 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 + case (isoiec_9798_2_6_bdkey_P_2_A t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_P_2_A + thus ?case 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 + case (isoiec_9798_2_6_bdkey_P_2_B t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_P_2_B + thus ?case 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 + case (isoiec_9798_2_6_bdkey_P_2_Ra t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_P_2_Ra + thus ?case 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 + case (isoiec_9798_2_6_bdkey_P_2_Rb t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_P_2_Rb + thus ?case 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 + case (isoiec_9798_2_6_bdkey_P_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_P_2_Text2 + thus ?case 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 + case (isoiec_9798_2_6_bdkey_P_text_3_Text3 t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_P_text_3_Text3 + thus ?case 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 + case (isoiec_9798_2_6_bdkey_P_text_3_Text4 t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_P_text_3_Text4 + thus ?case 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 + case (isoiec_9798_2_6_bdkey_P_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_6_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_bdkey_P_text_3_Text5 + thus ?case 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 @@ -2106,11 +2195,11 @@ 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) + thus ?thesis by (auto 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+)? + thus ?thesis by (auto dest!: ltk_secrecy) +qed (safe?, simp_all?, insert facts, (fastforce+)?) lemma (in restricted_isoiec_9798_2_6_bdkey_state) A_secret_Kab: assumes facts: @@ -2130,11 +2219,11 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_6_bdkey_state) B_secret_Kab: @@ -2155,11 +2244,11 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_6_bdkey_state) A_injective_agreement_B: @@ -2198,7 +2287,7 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_2_6_bdkey_P_3_enc tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -2229,10 +2318,10 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2282,7 +2371,7 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_2_6_bdkey_P_3_enc_1 tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -2304,9 +2393,9 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2354,11 +2443,11 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2406,11 +2495,11 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2572,205 +2661,231 @@ 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 + case (isoiec_9798_2_5_special_TTP_bdkey_A_2_Kab t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_A_2_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_special_TTP_bdkey_A_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_A_2_Text3 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_special_TTP_bdkey_A_2_Text4 t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_A_2_Text4 + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_A_2_TokenPA_for_B t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_A_2_TokenPA_for_B + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_A_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_A_text_3_Text5 + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_A_text_3_Text6 t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_A_text_3_Text6 + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_A_4_TNb t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_A_4_TNb + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_special_TTP_bdkey_A_4_Text7 t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_A_4_Text7 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_special_TTP_bdkey_A_4_Text8 t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_A_4_Text8 + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_B_3_A t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_B_3_A + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_B_3_Kab t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_B_3_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_special_TTP_bdkey_B_3_P t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_B_3_P + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_B_3_TNa t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_B_3_TNa + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_special_TTP_bdkey_B_3_TNp t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_B_3_TNp + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_special_TTP_bdkey_B_3_Text2 t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_B_3_Text2 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_special_TTP_bdkey_B_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_B_3_Text5 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_special_TTP_bdkey_B_3_Text6 t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_B_3_Text6 + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_B_text_4_Text7 t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_B_text_4_Text7 + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_B_text_4_Text8 t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_B_text_4_Text8 + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_P_1_A t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_P_1_A + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_P_1_B t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_P_1_B + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_P_1_TVPa t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_P_1_TVPa + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_P_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_P_1_Text1 + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_P_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_P_text_2_Text2 + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_P_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_P_text_2_Text3 + thus ?case 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 + case (isoiec_9798_2_5_special_TTP_bdkey_P_text_2_Text4 t r s tid0) then interpret state: isoiec_9798_2_5_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_special_TTP_bdkey_P_text_2_Text4 + thus ?case 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 @@ -2839,11 +2954,11 @@ 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) + thus ?thesis by (auto 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+)? + thus ?thesis by (auto dest!: ltk_secrecy) +qed (safe?, simp_all?, insert facts, (fastforce+)?) lemma (in restricted_isoiec_9798_2_5_special_TTP_bdkey_state) A_secret_Kab: assumes facts: @@ -2862,7 +2977,7 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -2875,7 +2990,7 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_5_special_TTP_bdkey_state) B_secret_Kab: @@ -2895,7 +3010,7 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -2908,7 +3023,7 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_5_special_TTP_bdkey_state) A_injective_agreement_B: @@ -2946,7 +3061,7 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -2994,12 +3109,12 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed (fastforce+)? - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -3063,14 +3178,14 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed (fastforce+)? - qed (insert facts, fastforce+)? - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_5_special_TTP_bdkey_state) A_injective_agreement_P: @@ -3106,7 +3221,7 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -3119,7 +3234,7 @@ case swapped note_unified facts = this facts thus ?thesis by (fastforce intro: event_predOrdI split: if_splits) qed (fastforce+)? - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -3157,7 +3272,7 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -3184,13 +3299,13 @@ 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+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed role isoiec_9798_2_6_special_TTP_bdkey_A @@ -3351,201 +3466,228 @@ 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 + case (isoiec_9798_2_6_special_TTP_bdkey_A_1_B t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_A_1_B + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_A_1_Rb t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_A_1_Rb + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_A_1_Text1 + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_A_3_Kab t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_A_3_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_special_TTP_bdkey_A_3_Text4 t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_A_3_Text4 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_special_TTP_bdkey_A_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_A_3_Text5 + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_A_3_TokenPA_for_B t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_A_3_TokenPA_for_B + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_A_text_4_Text6 t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_A_text_4_Text6 + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_A_text_4_Text7 t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_A_text_4_Text7 + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_A_5_Text8 t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_A_5_Text8 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_special_TTP_bdkey_A_5_Text9 t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_A_5_Text9 + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Kab t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_B_4_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_special_TTP_bdkey_B_4_P t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_B_4_P + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Rpa t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_B_4_Rpa + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Text3 t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_B_4_Text3 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Text6 t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_B_4_Text6 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_special_TTP_bdkey_B_4_Text7 t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_B_4_Text7 + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_B_text_5_Text8 t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_B_text_5_Text8 + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_B_text_5_Text9 t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_B_text_5_Text9 + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_P_2_A t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_P_2_A + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_P_2_B t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_P_2_B + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_P_2_Ra t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_P_2_Ra + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_P_2_Rb t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_P_2_Rb + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_P_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_P_2_Text2 + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_P_text_3_Text3 t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_P_text_3_Text3 + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_P_text_3_Text4 t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_P_text_3_Text4 + thus ?case 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 + case (isoiec_9798_2_6_special_TTP_bdkey_P_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_6_special_TTP_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_special_TTP_bdkey_P_text_3_Text5 + thus ?case 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 @@ -3615,11 +3757,11 @@ 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) + thus ?thesis by (auto 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+)? + thus ?thesis by (auto dest!: ltk_secrecy) +qed (safe?, simp_all?, insert facts, (fastforce+)?) lemma (in restricted_isoiec_9798_2_6_special_TTP_bdkey_state) A_secret_Kab: assumes facts: @@ -3638,7 +3780,7 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -3651,7 +3793,7 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_6_special_TTP_bdkey_state) B_secret_Kab: @@ -3671,7 +3813,7 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -3684,7 +3826,7 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_6_special_TTP_bdkey_state) A_injective_agreement_B: @@ -3722,7 +3864,7 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -3769,12 +3911,12 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed (fastforce+)? - qed (insert facts, fastforce+)? - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed (fastforce+)? - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -3823,7 +3965,7 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -3862,10 +4004,10 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed (fastforce+)? - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -3912,7 +4054,7 @@ |} ( Kbd ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -3925,7 +4067,7 @@ case swapped note_unified facts = this facts thus ?thesis by (fastforce intro: event_predOrdI split: if_splits) qed (fastforce+)? - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -3972,7 +4114,7 @@ |} ( Kbd ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -3985,7 +4127,7 @@ case swapped note_unified facts = this facts thus ?thesis by (fastforce intro: event_predOrdI split: if_splits) qed (fastforce+)? - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this diff --git a/data/examples/iso9798/isabelle-proofs/isoiec-9798-2-udkey_cert_auto.thy b/data/examples/iso9798/isabelle-proofs/isoiec-9798-2-udkey_cert_auto.thy --- a/data/examples/iso9798/isabelle-proofs/isoiec-9798-2-udkey_cert_auto.thy +++ b/data/examples/iso9798/isabelle-proofs/isoiec-9798-2-udkey_cert_auto.thy @@ -47,50 +47,56 @@ 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 + case (isoiec_9798_2_1_udkey_A_text_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_1_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_1_udkey_A_text_1_Text1 + thus ?case 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 + case (isoiec_9798_2_1_udkey_A_text_1_Text2 t r s tid0) then interpret state: isoiec_9798_2_1_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_1_udkey_A_text_1_Text2 + thus ?case 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 + case (isoiec_9798_2_1_udkey_B_1_A t r s tid0) then interpret state: isoiec_9798_2_1_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_1_udkey_B_1_A + thus ?case 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 + case (isoiec_9798_2_1_udkey_B_1_TNA t r s tid0) then interpret state: isoiec_9798_2_1_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_1_udkey_B_1_TNA + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_1_udkey_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_1_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_1_udkey_B_1_Text1 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_1_udkey_B_1_Text2 t r s tid0) then interpret state: isoiec_9798_2_1_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_1_udkey_B_1_Text2 + thus ?case 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 @@ -171,11 +177,11 @@ |} ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed role isoiec_9798_2_2_udkey_A @@ -227,50 +233,57 @@ 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 + case (isoiec_9798_2_2_udkey_A_1_B t r s tid0) then interpret state: isoiec_9798_2_2_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_udkey_A_1_B + thus ?case 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 + case (isoiec_9798_2_2_udkey_A_1_RB t r s tid0) then interpret state: isoiec_9798_2_2_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_udkey_A_1_RB + thus ?case 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 + case (isoiec_9798_2_2_udkey_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_2_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_udkey_A_1_Text1 + thus ?case 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 + case (isoiec_9798_2_2_udkey_A_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_2_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_udkey_A_text_2_Text2 + thus ?case 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 + case (isoiec_9798_2_2_udkey_A_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_2_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_udkey_A_text_2_Text3 + thus ?case 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 + case (isoiec_9798_2_2_udkey_B_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_2_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_udkey_B_2_Text2 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_2_udkey_B_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_2_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_2_udkey_B_2_Text3 + thus ?case 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 @@ -359,11 +372,11 @@ |} ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -441,90 +454,101 @@ 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 + case (isoiec_9798_2_3_udkey_A_text_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_udkey_A_text_1_Text1 + thus ?case 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 + case (isoiec_9798_2_3_udkey_A_text_1_Text2 t r s tid0) then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_udkey_A_text_1_Text2 + thus ?case 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 + case (isoiec_9798_2_3_udkey_A_2_TNB t r s tid0) then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_udkey_A_2_TNB + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_3_udkey_A_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_udkey_A_2_Text3 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_3_udkey_A_2_Text4 t r s tid0) then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_udkey_A_2_Text4 + thus ?case 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 + case (isoiec_9798_2_3_udkey_B_1_A t r s tid0) then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_udkey_B_1_A + thus ?case 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 + case (isoiec_9798_2_3_udkey_B_1_TNA t r s tid0) then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_udkey_B_1_TNA + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_3_udkey_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_udkey_B_1_Text1 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_3_udkey_B_1_Text2 t r s tid0) then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_udkey_B_1_Text2 + thus ?case 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 + case (isoiec_9798_2_3_udkey_B_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_udkey_B_text_2_Text3 + thus ?case 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 + case (isoiec_9798_2_3_udkey_B_text_2_Text4 t r s tid0) then interpret state: isoiec_9798_2_3_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_3_udkey_B_text_2_Text4 + thus ?case 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 @@ -605,11 +629,11 @@ |} ( K ( s(AV ''B'' tid0) ) ( s(AV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_3_udkey_state) B_non_injective_agreement: @@ -635,11 +659,11 @@ |} ( K ( s(MV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed role isoiec_9798_2_4_udkey_A @@ -718,91 +742,103 @@ 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 + case (isoiec_9798_2_4_udkey_A_1_B t r s tid0) then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_udkey_A_1_B + thus ?case 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 + case (isoiec_9798_2_4_udkey_A_1_RB t r s tid0) then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_udkey_A_1_RB + thus ?case 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 + case (isoiec_9798_2_4_udkey_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_udkey_A_1_Text1 + thus ?case 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 + case (isoiec_9798_2_4_udkey_A_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_udkey_A_text_2_Text2 + thus ?case 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 + case (isoiec_9798_2_4_udkey_A_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_udkey_A_text_2_Text3 + thus ?case 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 + case (isoiec_9798_2_4_udkey_A_3_Text4 t r s tid0) then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_udkey_A_3_Text4 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_4_udkey_A_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_udkey_A_3_Text5 + thus ?case 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 + case (isoiec_9798_2_4_udkey_B_2_RA t r s tid0) then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_udkey_B_2_RA + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_4_udkey_B_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_udkey_B_2_Text2 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_4_udkey_B_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_udkey_B_2_Text3 + thus ?case 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 + case (isoiec_9798_2_4_udkey_B_text_3_Text4 t r s tid0) then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_udkey_B_text_3_Text4 + thus ?case 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 + case (isoiec_9798_2_4_udkey_B_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_4_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_4_udkey_B_text_3_Text5 + thus ?case 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 @@ -892,7 +928,7 @@ |} ( K ( s(MV ''B'' tid0) ) ( s(AV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_2_4_udkey_B_3_enc tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -901,12 +937,12 @@ |} ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid1) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -952,11 +988,11 @@ |} ( K ( s(AV ''A'' tid0) ) ( s(AV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -1108,205 +1144,231 @@ 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 + case (isoiec_9798_2_5_udkey_A_2_Kab t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_A_2_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_udkey_A_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_A_2_Text3 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_udkey_A_2_Text4 t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_A_2_Text4 + thus ?case 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 + case (isoiec_9798_2_5_udkey_A_2_TokenPA_for_B t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_A_2_TokenPA_for_B + thus ?case 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 + case (isoiec_9798_2_5_udkey_A_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_A_text_3_Text5 + thus ?case 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 + case (isoiec_9798_2_5_udkey_A_text_3_Text6 t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_A_text_3_Text6 + thus ?case 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 + case (isoiec_9798_2_5_udkey_A_4_TNb t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_A_4_TNb + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_udkey_A_4_Text7 t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_A_4_Text7 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_udkey_A_4_Text8 t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_A_4_Text8 + thus ?case 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 + case (isoiec_9798_2_5_udkey_B_3_A t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_B_3_A + thus ?case 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 + case (isoiec_9798_2_5_udkey_B_3_Kab t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_B_3_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_udkey_B_3_P t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_B_3_P + thus ?case 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 + case (isoiec_9798_2_5_udkey_B_3_TNa t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_B_3_TNa + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_udkey_B_3_TNp t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_B_3_TNp + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_udkey_B_3_Text2 t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_B_3_Text2 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_udkey_B_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_B_3_Text5 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_5_udkey_B_3_Text6 t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_B_3_Text6 + thus ?case 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 + case (isoiec_9798_2_5_udkey_B_text_4_Text7 t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_B_text_4_Text7 + thus ?case 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 + case (isoiec_9798_2_5_udkey_B_text_4_Text8 t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_B_text_4_Text8 + thus ?case 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 + case (isoiec_9798_2_5_udkey_P_1_A t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_P_1_A + thus ?case 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 + case (isoiec_9798_2_5_udkey_P_1_B t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_P_1_B + thus ?case 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 + case (isoiec_9798_2_5_udkey_P_1_TVPa t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_P_1_TVPa + thus ?case 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 + case (isoiec_9798_2_5_udkey_P_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_P_1_Text1 + thus ?case 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 + case (isoiec_9798_2_5_udkey_P_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_P_text_2_Text2 + thus ?case 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 + case (isoiec_9798_2_5_udkey_P_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_P_text_2_Text3 + thus ?case 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 + case (isoiec_9798_2_5_udkey_P_text_2_Text4 t r s tid0) then interpret state: isoiec_9798_2_5_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_5_udkey_P_text_2_Text4 + thus ?case 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 @@ -1374,11 +1436,11 @@ 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) + thus ?thesis by (auto 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+)? + thus ?thesis by (auto dest!: ltk_secrecy) +qed (safe?, simp_all?, insert facts, (fastforce+)?) lemma (in restricted_isoiec_9798_2_5_udkey_state) A_secret_Kab: assumes facts: @@ -1397,11 +1459,11 @@ |} ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_5_udkey_state) B_secret_Kab: @@ -1421,11 +1483,11 @@ |} ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_5_udkey_state) A_injective_agreement_B: @@ -1463,7 +1525,7 @@ |} ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_2_5_udkey_P_2_enc tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -1503,11 +1565,11 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -1545,7 +1607,7 @@ |} ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_2_5_udkey_P_2_enc_1 tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -1567,9 +1629,9 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_5_udkey_state) A_injective_agreement_P: @@ -1605,11 +1667,11 @@ |} ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -1647,11 +1709,11 @@ |} ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed role isoiec_9798_2_6_udkey_A @@ -1793,201 +1855,228 @@ 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 + case (isoiec_9798_2_6_udkey_A_1_B t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_A_1_B + thus ?case 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 + case (isoiec_9798_2_6_udkey_A_1_Rb t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_A_1_Rb + thus ?case 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 + case (isoiec_9798_2_6_udkey_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_A_1_Text1 + thus ?case 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 + case (isoiec_9798_2_6_udkey_A_3_Kab t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_A_3_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_udkey_A_3_Text4 t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_A_3_Text4 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_udkey_A_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_A_3_Text5 + thus ?case 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 + case (isoiec_9798_2_6_udkey_A_3_TokenPA_for_B t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_A_3_TokenPA_for_B + thus ?case 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 + case (isoiec_9798_2_6_udkey_A_text_4_Text6 t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_A_text_4_Text6 + thus ?case 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 + case (isoiec_9798_2_6_udkey_A_text_4_Text7 t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_A_text_4_Text7 + thus ?case 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 + case (isoiec_9798_2_6_udkey_A_5_Text8 t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_A_5_Text8 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_udkey_A_5_Text9 t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_A_5_Text9 + thus ?case 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 + case (isoiec_9798_2_6_udkey_B_4_Kab t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_B_4_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_udkey_B_4_P t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_B_4_P + thus ?case 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 + case (isoiec_9798_2_6_udkey_B_4_Rpa t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_B_4_Rpa + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_udkey_B_4_Text3 t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_B_4_Text3 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_udkey_B_4_Text6 t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_B_4_Text6 + thus ?case 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))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_2_6_udkey_B_4_Text7 t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_B_4_Text7 + thus ?case 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 + case (isoiec_9798_2_6_udkey_B_text_5_Text8 t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_B_text_5_Text8 + thus ?case 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 + case (isoiec_9798_2_6_udkey_B_text_5_Text9 t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_B_text_5_Text9 + thus ?case 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 + case (isoiec_9798_2_6_udkey_P_2_A t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_P_2_A + thus ?case 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 + case (isoiec_9798_2_6_udkey_P_2_B t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_P_2_B + thus ?case 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 + case (isoiec_9798_2_6_udkey_P_2_Ra t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_P_2_Ra + thus ?case 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 + case (isoiec_9798_2_6_udkey_P_2_Rb t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_P_2_Rb + thus ?case 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 + case (isoiec_9798_2_6_udkey_P_2_Text2 t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_P_2_Text2 + thus ?case 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 + case (isoiec_9798_2_6_udkey_P_text_3_Text3 t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_P_text_3_Text3 + thus ?case 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 + case (isoiec_9798_2_6_udkey_P_text_3_Text4 t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_P_text_3_Text4 + thus ?case 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 + case (isoiec_9798_2_6_udkey_P_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_2_6_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_2_6_udkey_P_text_3_Text5 + thus ?case 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 @@ -2055,11 +2144,11 @@ 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) + thus ?thesis by (auto 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+)? + thus ?thesis by (auto dest!: ltk_secrecy) +qed (safe?, simp_all?, insert facts, (fastforce+)?) lemma (in restricted_isoiec_9798_2_6_udkey_state) A_secret_Kab: assumes facts: @@ -2078,11 +2167,11 @@ |} ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_6_udkey_state) B_secret_Kab: @@ -2102,11 +2191,11 @@ |} ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_2_6_udkey_state) A_injective_agreement_B: @@ -2144,7 +2233,7 @@ |} ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_2_6_udkey_P_3_enc tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -2175,10 +2264,10 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2227,7 +2316,7 @@ |} ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_2_6_udkey_P_3_enc_1 tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -2249,9 +2338,9 @@ 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2298,11 +2387,11 @@ |} ( K ( s(AV ''A'' tid0) ) ( s(AV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2349,11 +2438,11 @@ |} ( K ( s(AV ''B'' tid0) ) ( s(MV ''P'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this diff --git a/data/examples/iso9798/isabelle-proofs/isoiec-9798-3_cert_auto.thy b/data/examples/iso9798/isabelle-proofs/isoiec-9798-3_cert_auto.thy --- a/data/examples/iso9798/isabelle-proofs/isoiec-9798-3_cert_auto.thy +++ b/data/examples/iso9798/isabelle-proofs/isoiec-9798-3_cert_auto.thy @@ -45,40 +45,46 @@ 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 + case (isoiec_9798_3_1_A_text_1_Text1 t r s tid0) then interpret state: isoiec_9798_3_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_1_A_text_1_Text1 + thus ?case 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 + case (isoiec_9798_3_1_A_text_1_Text2 t r s tid0) then interpret state: isoiec_9798_3_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_1_A_text_1_Text2 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_1_B_1_A t r s tid0) note facts = this + case (isoiec_9798_3_1_B_1_A t r s tid0) then interpret state: isoiec_9798_3_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_1_B_1_A + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_1_B_1_TNA t r s tid0) note facts = this + case (isoiec_9798_3_1_B_1_TNA t r s tid0) then interpret state: isoiec_9798_3_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_1_B_1_TNA + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_1_B_1_Text1 t r s tid0) note facts = this + case (isoiec_9798_3_1_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_3_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_1_B_1_Text1 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_1_B_1_Text2 t r s tid0) note facts = this + case (isoiec_9798_3_1_B_1_Text2 t r s tid0) then interpret state: isoiec_9798_3_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_1_B_1_Text2 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) qed thus "isoiec_9798_3_1_msc_typing_state t r s" by unfold_locales auto @@ -158,11 +164,11 @@ |} ( SK ( s(MV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed role isoiec_9798_3_2_A @@ -212,52 +218,60 @@ 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 + case (isoiec_9798_3_2_A_1_B t r s tid0) then interpret state: isoiec_9798_3_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_2_A_1_B + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_2_A_1_Rb t r s tid0) note facts = this + case (isoiec_9798_3_2_A_1_Rb t r s tid0) then interpret state: isoiec_9798_3_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_2_A_1_Rb + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_2_A_1_Text1 t r s tid0) note facts = this + case (isoiec_9798_3_2_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_3_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_2_A_1_Text1 + thus ?case 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 + case (isoiec_9798_3_2_A_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_3_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_2_A_text_2_Text2 + thus ?case 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 + case (isoiec_9798_3_2_A_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_3_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_2_A_text_2_Text3 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_2_B_2_Ra t r s tid0) note facts = this + case (isoiec_9798_3_2_B_2_Ra t r s tid0) then interpret state: isoiec_9798_3_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_2_B_2_Ra + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_2_B_2_Text2 t r s tid0) note facts = this + case (isoiec_9798_3_2_B_2_Text2 t r s tid0) then interpret state: isoiec_9798_3_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_2_B_2_Text2 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_2_B_2_Text3 t r s tid0) note facts = this + case (isoiec_9798_3_2_B_2_Text3 t r s tid0) then interpret state: isoiec_9798_3_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_2_B_2_Text3 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) qed thus "isoiec_9798_3_2_msc_typing_state t r s" by unfold_locales auto @@ -346,11 +360,11 @@ |} ( SK ( s(AV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -425,70 +439,81 @@ 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 + case (isoiec_9798_3_3_A_text_1_Text1 t r s tid0) then interpret state: isoiec_9798_3_3_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_3_A_text_1_Text1 + thus ?case 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 + case (isoiec_9798_3_3_A_text_1_Text2 t r s tid0) then interpret state: isoiec_9798_3_3_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_3_A_text_1_Text2 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_3_A_2_TNB t r s tid0) note facts = this + case (isoiec_9798_3_3_A_2_TNB t r s tid0) then interpret state: isoiec_9798_3_3_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_3_A_2_TNB + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_3_A_2_Text3 t r s tid0) note facts = this + case (isoiec_9798_3_3_A_2_Text3 t r s tid0) then interpret state: isoiec_9798_3_3_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_3_A_2_Text3 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_3_A_2_Text4 t r s tid0) note facts = this + case (isoiec_9798_3_3_A_2_Text4 t r s tid0) then interpret state: isoiec_9798_3_3_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_3_A_2_Text4 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_3_B_1_A t r s tid0) note facts = this + case (isoiec_9798_3_3_B_1_A t r s tid0) then interpret state: isoiec_9798_3_3_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_3_B_1_A + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_3_B_1_TNA t r s tid0) note facts = this + case (isoiec_9798_3_3_B_1_TNA t r s tid0) then interpret state: isoiec_9798_3_3_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_3_B_1_TNA + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_3_B_1_Text1 t r s tid0) note facts = this + case (isoiec_9798_3_3_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_3_3_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_3_B_1_Text1 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_3_B_1_Text2 t r s tid0) note facts = this + case (isoiec_9798_3_3_B_1_Text2 t r s tid0) then interpret state: isoiec_9798_3_3_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_3_B_1_Text2 + thus ?case 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 + case (isoiec_9798_3_3_B_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_3_3_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_3_B_text_2_Text3 + thus ?case 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 + case (isoiec_9798_3_3_B_text_2_Text4 t r s tid0) then interpret state: isoiec_9798_3_3_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_3_B_text_2_Text4 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) qed thus "isoiec_9798_3_3_msc_typing_state t r s" by unfold_locales auto @@ -568,11 +593,11 @@ |} ( SK ( s(AV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_3_3_state) B_non_injective_agreement: @@ -597,11 +622,11 @@ |} ( SK ( s(MV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed role isoiec_9798_3_4_A @@ -668,76 +693,88 @@ 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 + case (isoiec_9798_3_4_A_1_B t r s tid0) then interpret state: isoiec_9798_3_4_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_4_A_1_B + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_4_A_1_RB t r s tid0) note facts = this + case (isoiec_9798_3_4_A_1_RB t r s tid0) then interpret state: isoiec_9798_3_4_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_4_A_1_RB + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_4_A_1_Text1 t r s tid0) note facts = this + case (isoiec_9798_3_4_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_3_4_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_4_A_1_Text1 + thus ?case 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 + case (isoiec_9798_3_4_A_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_3_4_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_4_A_text_2_Text2 + thus ?case 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 + case (isoiec_9798_3_4_A_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_3_4_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_4_A_text_2_Text3 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_4_A_3_Text4 t r s tid0) note facts = this + case (isoiec_9798_3_4_A_3_Text4 t r s tid0) then interpret state: isoiec_9798_3_4_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_4_A_3_Text4 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_4_A_3_Text5 t r s tid0) note facts = this + case (isoiec_9798_3_4_A_3_Text5 t r s tid0) then interpret state: isoiec_9798_3_4_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_4_A_3_Text5 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_4_B_2_RA t r s tid0) note facts = this + case (isoiec_9798_3_4_B_2_RA t r s tid0) then interpret state: isoiec_9798_3_4_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_4_B_2_RA + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_4_B_2_Text2 t r s tid0) note facts = this + case (isoiec_9798_3_4_B_2_Text2 t r s tid0) then interpret state: isoiec_9798_3_4_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_4_B_2_Text2 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_4_B_2_Text3 t r s tid0) note facts = this + case (isoiec_9798_3_4_B_2_Text3 t r s tid0) then interpret state: isoiec_9798_3_4_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_4_B_2_Text3 + thus ?case 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 + case (isoiec_9798_3_4_B_text_3_Text4 t r s tid0) then interpret state: isoiec_9798_3_4_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_4_B_text_3_Text4 + thus ?case 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 + case (isoiec_9798_3_4_B_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_3_4_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_4_B_text_3_Text5 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) qed thus "isoiec_9798_3_4_msc_typing_state t r s" by unfold_locales auto @@ -827,7 +864,7 @@ |} ( SK ( s(MV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_3_4_B_3_enc tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -836,12 +873,12 @@ |} ( SK ( s(AV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -886,11 +923,11 @@ |} ( SK ( s(AV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -973,82 +1010,95 @@ 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 + case (isoiec_9798_3_5_A_2_RB t r s tid0) then interpret state: isoiec_9798_3_5_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_A_2_RB + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_5_A_2_Text2 t r s tid0) note facts = this + case (isoiec_9798_3_5_A_2_Text2 t r s tid0) then interpret state: isoiec_9798_3_5_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_A_2_Text2 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_5_A_3_Text5 t r s tid0) note facts = this + case (isoiec_9798_3_5_A_3_Text5 t r s tid0) then interpret state: isoiec_9798_3_5_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_A_3_Text5 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_5_A_3_Text6 t r s tid0) note facts = this + case (isoiec_9798_3_5_A_3_Text6 t r s tid0) then interpret state: isoiec_9798_3_5_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_A_3_Text6 + thus ?case 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 + case (isoiec_9798_3_5_A_text_4_Text3 t r s tid0) then interpret state: isoiec_9798_3_5_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_A_text_4_Text3 + thus ?case 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 + case (isoiec_9798_3_5_A_text_4_Text4 t r s tid0) then interpret state: isoiec_9798_3_5_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_A_text_4_Text4 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_5_B_1_A t r s tid0) note facts = this + case (isoiec_9798_3_5_B_1_A t r s tid0) then interpret state: isoiec_9798_3_5_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_B_1_A + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_5_B_1_RA t r s tid0) note facts = this + case (isoiec_9798_3_5_B_1_RA t r s tid0) then interpret state: isoiec_9798_3_5_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_B_1_RA + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_5_B_1_Text1 t r s tid0) note facts = this + case (isoiec_9798_3_5_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_3_5_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_B_1_Text1 + thus ?case 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 + case (isoiec_9798_3_5_B_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_3_5_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_B_text_3_Text5 + thus ?case 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 + case (isoiec_9798_3_5_B_text_3_Text6 t r s tid0) then interpret state: isoiec_9798_3_5_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_B_text_3_Text6 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_5_B_4_Text3 t r s tid0) note facts = this + case (isoiec_9798_3_5_B_4_Text3 t r s tid0) then interpret state: isoiec_9798_3_5_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_B_4_Text3 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (isoiec_9798_3_5_B_4_Text4 t r s tid0) note facts = this + case (isoiec_9798_3_5_B_4_Text4 t r s tid0) then interpret state: isoiec_9798_3_5_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_5_B_4_Text4 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) qed thus "isoiec_9798_3_5_msc_typing_state t r s" by unfold_locales auto @@ -1137,11 +1187,11 @@ |} ( SK ( s(AV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -1187,7 +1237,7 @@ |} ( SK ( s(MV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_3_5_A_4_enc tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -1196,12 +1246,12 @@ |} ( SK ( s(AV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -1344,52 +1394,60 @@ 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 + case (isoiec_9798_3_6_1_A_2_Rb t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_A_2_Rb + thus ?case 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 + case (isoiec_9798_3_6_1_A_2_Text3 t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_A_2_Text3 + thus ?case 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 + case (isoiec_9798_3_6_1_A_2_TokenBA t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_A_2_TokenBA + thus ?case 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 + case (isoiec_9798_3_6_1_A_4_Text6 t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_A_4_Text6 + thus ?case 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 + case (isoiec_9798_3_6_1_A_4_Text7 t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_A_4_Text7 + thus ?case 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 + case (isoiec_9798_3_6_1_A_4_TokenTA_for_B t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_A_4_TokenTA_for_B + thus ?case 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 + case (isoiec_9798_3_6_1_A_4_pkB t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_A_4_pkB + thus ?case 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 + case (isoiec_9798_3_6_1_A_check_4_in_Text2 t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_A_check_4_in_Text2 + thus ?case proof(sources! " Enc {| LC ''check_4'', {| LC ''isoiec_9798_3_6_opt_1_sig_2'', s(AV ''B'' tid0), LN ''Ra'' tid0, @@ -1401,126 +1459,146 @@ ( inv(s(MV ''pkB'' tid0)) ) |} ( LN ''check_nonce_4'' tid0 ) ") - qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_3_6_1_A_text_5_Text8 t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_A_text_5_Text8 + thus ?case 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 + case (isoiec_9798_3_6_1_A_text_5_Text9 t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_A_text_5_Text9 + thus ?case 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 + case (isoiec_9798_3_6_1_B_1_A t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_B_1_A + thus ?case 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 + case (isoiec_9798_3_6_1_B_1_Ra t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_B_1_Ra + thus ?case 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 + case (isoiec_9798_3_6_1_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_B_1_Text1 + thus ?case 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 + case (isoiec_9798_3_6_1_B_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_B_text_2_Text2 + thus ?case 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 + case (isoiec_9798_3_6_1_B_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_B_text_2_Text3 + thus ?case 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 + case (isoiec_9798_3_6_1_B_5_T t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_B_5_T + thus ?case 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 + case (isoiec_9798_3_6_1_B_5_Text5 t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_B_5_Text5 + thus ?case 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 + case (isoiec_9798_3_6_1_B_5_Text8 t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_B_5_Text8 + thus ?case 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 + case (isoiec_9798_3_6_1_B_5_Text9 t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_B_5_Text9 + thus ?case 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 + case (isoiec_9798_3_6_1_B_5_pkA t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_B_5_pkA + thus ?case 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 + case (isoiec_9798_3_6_1_T_3_A t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_T_3_A + thus ?case 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 + case (isoiec_9798_3_6_1_T_3_B t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_T_3_B + thus ?case 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 + case (isoiec_9798_3_6_1_T_3_Rb t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_T_3_Rb + thus ?case 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 + case (isoiec_9798_3_6_1_T_3_Rpa t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_T_3_Rpa + thus ?case 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 + case (isoiec_9798_3_6_1_T_3_Text4 t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_T_3_Text4 + thus ?case 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 + case (isoiec_9798_3_6_1_T_text_4_Text5 t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_T_text_4_Text5 + thus ?case 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 + case (isoiec_9798_3_6_1_T_text_4_Text6 t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_T_text_4_Text6 + thus ?case 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 + case (isoiec_9798_3_6_1_T_text_4_Text7 t r s tid0) then interpret state: isoiec_9798_3_6_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_1_T_text_4_Text7 + thus ?case 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 @@ -1617,7 +1695,7 @@ ( 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+)? + qed (safe?, simp_all?, 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! " @@ -1632,16 +1710,16 @@ |} ( SK ( s(AV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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+)? + thus ?thesis by (auto dest!: ltk_secrecy) + qed (safe?, simp_all?, 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -1687,7 +1765,7 @@ |} ( SK ( s(MV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_3_6_1_T_4_enc_1 tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -1697,12 +1775,12 @@ |} ( SK ( s(MV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -1747,11 +1825,11 @@ |} ( SK ( s(AV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -1796,11 +1874,11 @@ |} ( SK ( s(MV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -1945,46 +2023,53 @@ 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 + case (isoiec_9798_3_6_2_A_2_Rb t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_A_2_Rb + thus ?case 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 + case (isoiec_9798_3_6_2_A_2_Text3 t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_A_2_Text3 + thus ?case 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 + case (isoiec_9798_3_6_2_A_2_TokenBA t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_A_2_TokenBA + thus ?case 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 + case (isoiec_9798_3_6_2_A_4_Text7 t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_A_4_Text7 + thus ?case 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 + case (isoiec_9798_3_6_2_A_4_TokenTA t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_A_4_TokenTA + thus ?case 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 + case (isoiec_9798_3_6_2_A_4_pkB t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_A_4_pkB + thus ?case 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 + case (isoiec_9798_3_6_2_A_check_4_in_Text2 t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_A_check_4_in_Text2 + thus ?case proof(sources! " Enc {| LC ''check_4'', {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0, @@ -2006,12 +2091,13 @@ ( inv(s(MV ''pkB'' tid0)) ) |} ( LN ''check_nonce_4'' tid0 ) ") - qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_3_6_2_A_check_4_in_Text5 t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_A_check_4_in_Text5 + thus ?case proof(sources! " Enc {| LC ''check_4'', {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0, @@ -2033,12 +2119,13 @@ ( inv(s(MV ''pkB'' tid0)) ) |} ( LN ''check_nonce_4'' tid0 ) ") - qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_3_6_2_A_check_4_in_pkA t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_A_check_4_in_pkA + thus ?case proof(sources! " Enc {| LC ''check_4'', {| {| LC ''isoiec_9798_3_6_opt_2_sig_4'', LN ''Rpa'' tid0, @@ -2060,132 +2147,153 @@ ( inv(s(MV ''pkB'' tid0)) ) |} ( LN ''check_nonce_4'' tid0 ) ") - qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_3_6_2_A_text_5_Text8 t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_A_text_5_Text8 + thus ?case 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 + case (isoiec_9798_3_6_2_A_text_5_Text9 t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_A_text_5_Text9 + thus ?case 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 + case (isoiec_9798_3_6_2_B_1_A t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_B_1_A + thus ?case 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 + case (isoiec_9798_3_6_2_B_1_Ra t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_B_1_Ra + thus ?case 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 + case (isoiec_9798_3_6_2_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_B_1_Text1 + thus ?case 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 + case (isoiec_9798_3_6_2_B_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_B_text_2_Text2 + thus ?case 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 + case (isoiec_9798_3_6_2_B_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_B_text_2_Text3 + thus ?case 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 + case (isoiec_9798_3_6_2_B_5_Rpa t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_B_5_Rpa + thus ?case 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 + case (isoiec_9798_3_6_2_B_5_T t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_B_5_T + thus ?case 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 + case (isoiec_9798_3_6_2_B_5_Text5 t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_B_5_Text5 + thus ?case 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 + case (isoiec_9798_3_6_2_B_5_Text8 t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_B_5_Text8 + thus ?case 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 + case (isoiec_9798_3_6_2_B_5_Text9 t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_B_5_Text9 + thus ?case 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 + case (isoiec_9798_3_6_2_B_5_pkA t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_B_5_pkA + thus ?case 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 + case (isoiec_9798_3_6_2_B_5_pkB t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_B_5_pkB + thus ?case 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 + case (isoiec_9798_3_6_2_T_3_A t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_T_3_A + thus ?case 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 + case (isoiec_9798_3_6_2_T_3_B t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_T_3_B + thus ?case 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 + case (isoiec_9798_3_6_2_T_3_Rb t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_T_3_Rb + thus ?case 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 + case (isoiec_9798_3_6_2_T_3_Rpa t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_T_3_Rpa + thus ?case 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 + case (isoiec_9798_3_6_2_T_3_Text4 t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_T_3_Text4 + thus ?case 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 + case (isoiec_9798_3_6_2_T_text_4_Text5 t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_T_text_4_Text5 + thus ?case 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 + case (isoiec_9798_3_6_2_T_text_4_Text7 t r s tid0) then interpret state: isoiec_9798_3_6_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_6_2_T_text_4_Text7 + thus ?case 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 @@ -2292,7 +2400,7 @@ ( 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+)? + qed (safe?, simp_all?, 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! " @@ -2308,16 +2416,16 @@ |} ( SK ( s(AV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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+)? + thus ?thesis by (auto dest!: ltk_secrecy) + qed (safe?, simp_all?, 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2364,7 +2472,7 @@ |} ( SK ( s(MV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_3_6_2_T_4_enc tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -2374,12 +2482,12 @@ |} ( SK ( s(MV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2443,7 +2551,7 @@ ( 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+)? + qed (safe?, simp_all?, 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! " @@ -2453,12 +2561,12 @@ |} ( SK ( s(AV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2506,11 +2614,11 @@ |} ( SK ( s(MV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2645,166 +2753,193 @@ 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 + case (isoiec_9798_3_7_1_A_1_B t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_A_1_B + thus ?case 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 + case (isoiec_9798_3_7_1_A_1_Rb t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_A_1_Rb + thus ?case 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 + case (isoiec_9798_3_7_1_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_A_1_Text1 + thus ?case 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 + case (isoiec_9798_3_7_1_A_3_Text4 t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_A_3_Text4 + thus ?case 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 + case (isoiec_9798_3_7_1_A_3_Text5 t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_A_3_Text5 + thus ?case 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 + case (isoiec_9798_3_7_1_A_3_TokenTA_for_B t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_A_3_TokenTA_for_B + thus ?case 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 + case (isoiec_9798_3_7_1_A_3_pkB t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_A_3_pkB + thus ?case 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 + case (isoiec_9798_3_7_1_A_text_4_Text6 t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_A_text_4_Text6 + thus ?case 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 + case (isoiec_9798_3_7_1_A_text_4_Text7 t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_A_text_4_Text7 + thus ?case 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 + case (isoiec_9798_3_7_1_A_5_Text8 t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_A_5_Text8 + thus ?case 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 + case (isoiec_9798_3_7_1_A_5_Text9 t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_A_5_Text9 + thus ?case 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 + case (isoiec_9798_3_7_1_B_4_Ra t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_B_4_Ra + thus ?case 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 + case (isoiec_9798_3_7_1_B_4_Rpa t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_B_4_Rpa + thus ?case 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 + case (isoiec_9798_3_7_1_B_4_T t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_B_4_T + thus ?case 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 + case (isoiec_9798_3_7_1_B_4_Text3 t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_B_4_Text3 + thus ?case 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 + case (isoiec_9798_3_7_1_B_4_Text6 t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_B_4_Text6 + thus ?case 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 + case (isoiec_9798_3_7_1_B_4_Text9 t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_B_4_Text9 + thus ?case 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 + case (isoiec_9798_3_7_1_B_4_pkA t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_B_4_pkA + thus ?case 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 + case (isoiec_9798_3_7_1_B_text_5_Text8 t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_B_text_5_Text8 + thus ?case 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 + case (isoiec_9798_3_7_1_T_2_A t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_T_2_A + thus ?case 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 + case (isoiec_9798_3_7_1_T_2_B t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_T_2_B + thus ?case 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 + case (isoiec_9798_3_7_1_T_2_Rb t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_T_2_Rb + thus ?case 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 + case (isoiec_9798_3_7_1_T_2_Rpa t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_T_2_Rpa + thus ?case 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 + case (isoiec_9798_3_7_1_T_2_Text2 t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_T_2_Text2 + thus ?case 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 + case (isoiec_9798_3_7_1_T_text_3_Text3 t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_T_text_3_Text3 + thus ?case 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 + case (isoiec_9798_3_7_1_T_text_3_Text4 t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_T_text_3_Text4 + thus ?case 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 + case (isoiec_9798_3_7_1_T_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_3_7_1_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_1_T_text_3_Text5 + thus ?case 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 @@ -2894,7 +3029,7 @@ |} ( SK ( s(AV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_3_7_1_T_3_enc tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -2904,12 +3039,12 @@ |} ( SK ( s(MV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -2955,7 +3090,7 @@ |} ( SK ( s(MV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_3_7_1_T_3_enc_1 tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -2965,12 +3100,12 @@ |} ( SK ( s(AV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -3015,11 +3150,11 @@ |} ( SK ( s(AV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -3064,11 +3199,11 @@ |} ( SK ( s(MV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -3208,46 +3343,53 @@ 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 + case (isoiec_9798_3_7_2_A_1_B t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_A_1_B + thus ?case 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 + case (isoiec_9798_3_7_2_A_1_Rb t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_A_1_Rb + thus ?case 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 + case (isoiec_9798_3_7_2_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_A_1_Text1 + thus ?case 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 + case (isoiec_9798_3_7_2_A_3_Text5 t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_A_3_Text5 + thus ?case 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 + case (isoiec_9798_3_7_2_A_3_TokenTA t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_A_3_TokenTA + thus ?case 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 + case (isoiec_9798_3_7_2_A_3_pkB t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_A_3_pkB + thus ?case 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 + case (isoiec_9798_3_7_2_A_check_3_in_Text3 t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_A_check_3_in_Text3 + thus ?case proof(sources! " Enc {| LC ''check_4'', {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0, @@ -3261,12 +3403,13 @@ ( SK ( s(AV ''T'' tid0) ) ) |} ( LN ''check_nonce_4'' tid0 ) ") - qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_3_7_2_A_check_3_in_pkA t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_A_check_3_in_pkA + thus ?case proof(sources! " Enc {| LC ''check_4'', {| LC ''isoiec_9798_3_7_opt_2_sig_3'', LN ''Rpa'' tid0, @@ -3280,126 +3423,146 @@ ( SK ( s(AV ''T'' tid0) ) ) |} ( LN ''check_nonce_4'' tid0 ) ") - qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)? + qed (safe?, simp_all?, 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 + case (isoiec_9798_3_7_2_A_text_4_Text6 t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_A_text_4_Text6 + thus ?case 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 + case (isoiec_9798_3_7_2_A_text_4_Text7 t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_A_text_4_Text7 + thus ?case 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 + case (isoiec_9798_3_7_2_A_5_Text8 t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_A_5_Text8 + thus ?case 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 + case (isoiec_9798_3_7_2_A_5_Text9 t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_A_5_Text9 + thus ?case 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 + case (isoiec_9798_3_7_2_B_4_Ra t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_B_4_Ra + thus ?case 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 + case (isoiec_9798_3_7_2_B_4_Rpa t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_B_4_Rpa + thus ?case 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 + case (isoiec_9798_3_7_2_B_4_T t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_B_4_T + thus ?case 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 + case (isoiec_9798_3_7_2_B_4_Text3 t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_B_4_Text3 + thus ?case 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 + case (isoiec_9798_3_7_2_B_4_Text6 t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_B_4_Text6 + thus ?case 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 + case (isoiec_9798_3_7_2_B_4_Text9 t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_B_4_Text9 + thus ?case 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 + case (isoiec_9798_3_7_2_B_4_pkA t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_B_4_pkA + thus ?case 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 + case (isoiec_9798_3_7_2_B_4_pkB t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_B_4_pkB + thus ?case 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 + case (isoiec_9798_3_7_2_B_text_5_Text8 t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_B_text_5_Text8 + thus ?case 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 + case (isoiec_9798_3_7_2_T_2_A t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_T_2_A + thus ?case 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 + case (isoiec_9798_3_7_2_T_2_B t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_T_2_B + thus ?case 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 + case (isoiec_9798_3_7_2_T_2_Rb t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_T_2_Rb + thus ?case 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 + case (isoiec_9798_3_7_2_T_2_Rpa t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_T_2_Rpa + thus ?case 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 + case (isoiec_9798_3_7_2_T_2_Text2 t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_T_2_Text2 + thus ?case 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 + case (isoiec_9798_3_7_2_T_text_3_Text3 t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_T_text_3_Text3 + thus ?case 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 + case (isoiec_9798_3_7_2_T_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_3_7_2_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_3_7_2_T_text_3_Text5 + thus ?case 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 @@ -3498,7 +3661,7 @@ ( 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+)? + qed (safe?, simp_all?, 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! " @@ -3508,7 +3671,7 @@ |} ( SK ( s(AV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_3_7_2_T_3_enc tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -3518,13 +3681,13 @@ |} ( SK ( s(MV ''B'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -3571,7 +3734,7 @@ |} ( SK ( s(MV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_3_7_2_T_3_enc tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -3581,12 +3744,12 @@ |} ( SK ( s(AV ''A'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -3642,7 +3805,7 @@ ( 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+)? + qed (safe?, simp_all?, 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! " @@ -3652,12 +3815,12 @@ |} ( SK ( s(AV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -3705,11 +3868,11 @@ |} ( SK ( s(MV ''T'' tid0) ) ) ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this diff --git a/data/examples/iso9798/isabelle-proofs/isoiec-9798-4-bdkey_cert_auto.thy b/data/examples/iso9798/isabelle-proofs/isoiec-9798-4-bdkey_cert_auto.thy --- a/data/examples/iso9798/isabelle-proofs/isoiec-9798-4-bdkey_cert_auto.thy +++ b/data/examples/iso9798/isabelle-proofs/isoiec-9798-4-bdkey_cert_auto.thy @@ -51,40 +51,46 @@ have "(t,r,s) : approx isoiec_9798_4_1_bdkey_msc_typing" proof(cases rule: reachable_in_approxI_ext [OF isoiec_9798_4_1_bdkey_msc_typing.monoTyp, completeness_cases_rule]) - case (isoiec_9798_4_1_bdkey_A_text_1_Text1 t r s tid0) note facts = this + case (isoiec_9798_4_1_bdkey_A_text_1_Text1 t r s tid0) then interpret state: isoiec_9798_4_1_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_1_bdkey_A_text_1_Text1 + thus ?case 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 + case (isoiec_9798_4_1_bdkey_A_text_1_Text2 t r s tid0) then interpret state: isoiec_9798_4_1_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_1_bdkey_A_text_1_Text2 + thus ?case 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 + case (isoiec_9798_4_1_bdkey_B_1_A t r s tid0) then interpret state: isoiec_9798_4_1_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_1_bdkey_B_1_A + thus ?case 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 + case (isoiec_9798_4_1_bdkey_B_1_TNA t r s tid0) then interpret state: isoiec_9798_4_1_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_1_bdkey_B_1_TNA + thus ?case 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 + case (isoiec_9798_4_1_bdkey_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_4_1_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_1_bdkey_B_1_Text1 + thus ?case 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 + case (isoiec_9798_4_1_bdkey_B_1_Text2 t r s tid0) then interpret state: isoiec_9798_4_1_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_1_bdkey_B_1_Text2 + thus ?case 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 @@ -165,11 +171,11 @@ s(MV ''Text1'' tid0) |} ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_4_1_bdkey_A_1_hash tid1) note_unified facts = this facts thus ?thesis by (fastforce intro: event_predOrdI split: if_splits) - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed role isoiec_9798_4_2_bdkey_A @@ -225,46 +231,53 @@ have "(t,r,s) : approx isoiec_9798_4_2_bdkey_msc_typing" proof(cases rule: reachable_in_approxI_ext [OF isoiec_9798_4_2_bdkey_msc_typing.monoTyp, completeness_cases_rule]) - case (isoiec_9798_4_2_bdkey_A_1_B t r s tid0) note facts = this + case (isoiec_9798_4_2_bdkey_A_1_B t r s tid0) then interpret state: isoiec_9798_4_2_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_bdkey_A_1_B + thus ?case 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 + case (isoiec_9798_4_2_bdkey_A_1_Rb t r s tid0) then interpret state: isoiec_9798_4_2_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_bdkey_A_1_Rb + thus ?case 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 + case (isoiec_9798_4_2_bdkey_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_4_2_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_bdkey_A_1_Text1 + thus ?case 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 + case (isoiec_9798_4_2_bdkey_A_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_4_2_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_bdkey_A_text_2_Text2 + thus ?case 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 + case (isoiec_9798_4_2_bdkey_A_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_4_2_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_bdkey_A_text_2_Text3 + thus ?case 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 + case (isoiec_9798_4_2_bdkey_B_2_Text2 t r s tid0) then interpret state: isoiec_9798_4_2_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_bdkey_B_2_Text2 + thus ?case 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 + case (isoiec_9798_4_2_bdkey_B_2_Text3 t r s tid0) then interpret state: isoiec_9798_4_2_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_bdkey_B_2_Text3 + thus ?case 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 @@ -354,11 +367,11 @@ s(MV ''Text2'' tid0) |} ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -444,70 +457,81 @@ have "(t,r,s) : approx isoiec_9798_4_3_bdkey_msc_typing" proof(cases rule: reachable_in_approxI_ext [OF isoiec_9798_4_3_bdkey_msc_typing.monoTyp, completeness_cases_rule]) - case (isoiec_9798_4_3_bdkey_A_text_1_Text1 t r s tid0) note facts = this + case (isoiec_9798_4_3_bdkey_A_text_1_Text1 t r s tid0) then interpret state: isoiec_9798_4_3_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_A_text_1_Text1 + thus ?case 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 + case (isoiec_9798_4_3_bdkey_A_text_1_Text2 t r s tid0) then interpret state: isoiec_9798_4_3_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_A_text_1_Text2 + thus ?case 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 + case (isoiec_9798_4_3_bdkey_A_2_TNb t r s tid0) then interpret state: isoiec_9798_4_3_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_A_2_TNb + thus ?case 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 + case (isoiec_9798_4_3_bdkey_A_2_Text3 t r s tid0) then interpret state: isoiec_9798_4_3_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_A_2_Text3 + thus ?case 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 + case (isoiec_9798_4_3_bdkey_A_2_Text4 t r s tid0) then interpret state: isoiec_9798_4_3_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_A_2_Text4 + thus ?case 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 + case (isoiec_9798_4_3_bdkey_B_1_A t r s tid0) then interpret state: isoiec_9798_4_3_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_B_1_A + thus ?case 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 + case (isoiec_9798_4_3_bdkey_B_1_TNa t r s tid0) then interpret state: isoiec_9798_4_3_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_B_1_TNa + thus ?case 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 + case (isoiec_9798_4_3_bdkey_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_4_3_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_B_1_Text1 + thus ?case 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 + case (isoiec_9798_4_3_bdkey_B_1_Text2 t r s tid0) then interpret state: isoiec_9798_4_3_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_B_1_Text2 + thus ?case 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 + case (isoiec_9798_4_3_bdkey_B_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_4_3_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_B_text_2_Text3 + thus ?case 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 + case (isoiec_9798_4_3_bdkey_B_text_2_Text4 t r s tid0) then interpret state: isoiec_9798_4_3_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_bdkey_B_text_2_Text4 + thus ?case 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 @@ -588,11 +612,11 @@ s(MV ''Text3'' tid0) |} ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_4_3_bdkey_B_2_hash tid1) note_unified facts = this facts thus ?thesis by (fastforce intro: event_predOrdI split: if_splits) - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_4_3_bdkey_state) B_non_injective_agreement: @@ -618,11 +642,11 @@ s(MV ''Text1'' tid0) |} ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_4_3_bdkey_A_1_hash tid1) note_unified facts = this facts thus ?thesis by (fastforce intro: event_predOrdI split: if_splits) - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed role isoiec_9798_4_4_bdkey_A @@ -700,76 +724,88 @@ have "(t,r,s) : approx isoiec_9798_4_4_bdkey_msc_typing" proof(cases rule: reachable_in_approxI_ext [OF isoiec_9798_4_4_bdkey_msc_typing.monoTyp, completeness_cases_rule]) - case (isoiec_9798_4_4_bdkey_A_1_B t r s tid0) note facts = this + case (isoiec_9798_4_4_bdkey_A_1_B t r s tid0) then interpret state: isoiec_9798_4_4_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_A_1_B + thus ?case 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 + case (isoiec_9798_4_4_bdkey_A_1_Rb t r s tid0) then interpret state: isoiec_9798_4_4_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_A_1_Rb + thus ?case 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 + case (isoiec_9798_4_4_bdkey_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_4_4_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_A_1_Text1 + thus ?case 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 + case (isoiec_9798_4_4_bdkey_A_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_4_4_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_A_text_2_Text2 + thus ?case 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 + case (isoiec_9798_4_4_bdkey_A_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_4_4_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_A_text_2_Text3 + thus ?case 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 + case (isoiec_9798_4_4_bdkey_A_3_Text4 t r s tid0) then interpret state: isoiec_9798_4_4_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_A_3_Text4 + thus ?case 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 + case (isoiec_9798_4_4_bdkey_A_3_Text5 t r s tid0) then interpret state: isoiec_9798_4_4_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_A_3_Text5 + thus ?case 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 + case (isoiec_9798_4_4_bdkey_B_2_Ra t r s tid0) then interpret state: isoiec_9798_4_4_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_B_2_Ra + thus ?case 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 + case (isoiec_9798_4_4_bdkey_B_2_Text2 t r s tid0) then interpret state: isoiec_9798_4_4_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_B_2_Text2 + thus ?case 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 + case (isoiec_9798_4_4_bdkey_B_2_Text3 t r s tid0) then interpret state: isoiec_9798_4_4_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_B_2_Text3 + thus ?case 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 + case (isoiec_9798_4_4_bdkey_B_text_3_Text4 t r s tid0) then interpret state: isoiec_9798_4_4_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_B_text_3_Text4 + thus ?case 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 + case (isoiec_9798_4_4_bdkey_B_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_4_4_bdkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_bdkey_B_text_3_Text5 + thus ?case 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 @@ -859,7 +895,7 @@ s(MV ''Text4'' tid0) |} ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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) ) @@ -873,11 +909,11 @@ s(AV ''B'' tid1), s(MV ''Text2'' tid1) |} ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) next case swapped note_unified facts = this facts thus ?thesis proof(sources! " @@ -886,13 +922,13 @@ s(AV ''A'' tid0), s(MV ''Text2'' tid1) |} ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed (fastforce+)? - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -938,11 +974,11 @@ s(AV ''B'' tid0), s(MV ''Text2'' tid0) |} ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this diff --git a/data/examples/iso9798/isabelle-proofs/isoiec-9798-4-udkey_cert_auto.thy b/data/examples/iso9798/isabelle-proofs/isoiec-9798-4-udkey_cert_auto.thy --- a/data/examples/iso9798/isabelle-proofs/isoiec-9798-4-udkey_cert_auto.thy +++ b/data/examples/iso9798/isabelle-proofs/isoiec-9798-4-udkey_cert_auto.thy @@ -51,40 +51,46 @@ have "(t,r,s) : approx isoiec_9798_4_1_udkey_msc_typing" proof(cases rule: reachable_in_approxI_ext [OF isoiec_9798_4_1_udkey_msc_typing.monoTyp, completeness_cases_rule]) - case (isoiec_9798_4_1_udkey_A_text_1_Text1 t r s tid0) note facts = this + case (isoiec_9798_4_1_udkey_A_text_1_Text1 t r s tid0) then interpret state: isoiec_9798_4_1_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_1_udkey_A_text_1_Text1 + thus ?case 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 + case (isoiec_9798_4_1_udkey_A_text_1_Text2 t r s tid0) then interpret state: isoiec_9798_4_1_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_1_udkey_A_text_1_Text2 + thus ?case 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 + case (isoiec_9798_4_1_udkey_B_1_A t r s tid0) then interpret state: isoiec_9798_4_1_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_1_udkey_B_1_A + thus ?case 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 + case (isoiec_9798_4_1_udkey_B_1_TNA t r s tid0) then interpret state: isoiec_9798_4_1_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_1_udkey_B_1_TNA + thus ?case 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 + case (isoiec_9798_4_1_udkey_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_4_1_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_1_udkey_B_1_Text1 + thus ?case 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 + case (isoiec_9798_4_1_udkey_B_1_Text2 t r s tid0) then interpret state: isoiec_9798_4_1_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_1_udkey_B_1_Text2 + thus ?case 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 @@ -164,11 +170,11 @@ 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 (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_4_1_udkey_A_1_hash tid1) note_unified facts = this facts thus ?thesis by (fastforce intro: event_predOrdI split: if_splits) - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed role isoiec_9798_4_2_udkey_A @@ -224,46 +230,53 @@ have "(t,r,s) : approx isoiec_9798_4_2_udkey_msc_typing" proof(cases rule: reachable_in_approxI_ext [OF isoiec_9798_4_2_udkey_msc_typing.monoTyp, completeness_cases_rule]) - case (isoiec_9798_4_2_udkey_A_1_B t r s tid0) note facts = this + case (isoiec_9798_4_2_udkey_A_1_B t r s tid0) then interpret state: isoiec_9798_4_2_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_udkey_A_1_B + thus ?case 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 + case (isoiec_9798_4_2_udkey_A_1_Rb t r s tid0) then interpret state: isoiec_9798_4_2_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_udkey_A_1_Rb + thus ?case 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 + case (isoiec_9798_4_2_udkey_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_4_2_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_udkey_A_1_Text1 + thus ?case 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 + case (isoiec_9798_4_2_udkey_A_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_4_2_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_udkey_A_text_2_Text2 + thus ?case 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 + case (isoiec_9798_4_2_udkey_A_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_4_2_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_udkey_A_text_2_Text3 + thus ?case 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 + case (isoiec_9798_4_2_udkey_B_2_Text2 t r s tid0) then interpret state: isoiec_9798_4_2_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_udkey_B_2_Text2 + thus ?case 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 + case (isoiec_9798_4_2_udkey_B_2_Text3 t r s tid0) then interpret state: isoiec_9798_4_2_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_2_udkey_B_2_Text3 + thus ?case 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 @@ -352,11 +365,11 @@ 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) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -442,70 +455,81 @@ have "(t,r,s) : approx isoiec_9798_4_3_udkey_msc_typing" proof(cases rule: reachable_in_approxI_ext [OF isoiec_9798_4_3_udkey_msc_typing.monoTyp, completeness_cases_rule]) - case (isoiec_9798_4_3_udkey_A_text_1_Text1 t r s tid0) note facts = this + case (isoiec_9798_4_3_udkey_A_text_1_Text1 t r s tid0) then interpret state: isoiec_9798_4_3_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_udkey_A_text_1_Text1 + thus ?case 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 + case (isoiec_9798_4_3_udkey_A_text_1_Text2 t r s tid0) then interpret state: isoiec_9798_4_3_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_udkey_A_text_1_Text2 + thus ?case 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 + case (isoiec_9798_4_3_udkey_A_2_TNb t r s tid0) then interpret state: isoiec_9798_4_3_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_udkey_A_2_TNb + thus ?case 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 + case (isoiec_9798_4_3_udkey_A_2_Text3 t r s tid0) then interpret state: isoiec_9798_4_3_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_udkey_A_2_Text3 + thus ?case 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 + case (isoiec_9798_4_3_udkey_A_2_Text4 t r s tid0) then interpret state: isoiec_9798_4_3_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_udkey_A_2_Text4 + thus ?case 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 + case (isoiec_9798_4_3_udkey_B_1_A t r s tid0) then interpret state: isoiec_9798_4_3_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_udkey_B_1_A + thus ?case 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 + case (isoiec_9798_4_3_udkey_B_1_TNa t r s tid0) then interpret state: isoiec_9798_4_3_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_udkey_B_1_TNa + thus ?case 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 + case (isoiec_9798_4_3_udkey_B_1_Text1 t r s tid0) then interpret state: isoiec_9798_4_3_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_udkey_B_1_Text1 + thus ?case 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 + case (isoiec_9798_4_3_udkey_B_1_Text2 t r s tid0) then interpret state: isoiec_9798_4_3_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_udkey_B_1_Text2 + thus ?case 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 + case (isoiec_9798_4_3_udkey_B_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_4_3_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_udkey_B_text_2_Text3 + thus ?case 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 + case (isoiec_9798_4_3_udkey_B_text_2_Text4 t r s tid0) then interpret state: isoiec_9798_4_3_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_3_udkey_B_text_2_Text4 + thus ?case 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 @@ -585,11 +609,11 @@ 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 (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_4_3_udkey_B_2_hash tid1) note_unified facts = this facts thus ?thesis by (fastforce intro: event_predOrdI split: if_splits) - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed lemma (in restricted_isoiec_9798_4_3_udkey_state) B_non_injective_agreement: @@ -614,11 +638,11 @@ 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 (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_4_3_udkey_A_1_hash tid1) note_unified facts = this facts thus ?thesis by (fastforce intro: event_predOrdI split: if_splits) - qed (insert facts, fastforce+)? + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed role isoiec_9798_4_4_udkey_A @@ -694,76 +718,88 @@ have "(t,r,s) : approx isoiec_9798_4_4_udkey_msc_typing" proof(cases rule: reachable_in_approxI_ext [OF isoiec_9798_4_4_udkey_msc_typing.monoTyp, completeness_cases_rule]) - case (isoiec_9798_4_4_udkey_A_1_B t r s tid0) note facts = this + case (isoiec_9798_4_4_udkey_A_1_B t r s tid0) then interpret state: isoiec_9798_4_4_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_udkey_A_1_B + thus ?case 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 + case (isoiec_9798_4_4_udkey_A_1_Rb t r s tid0) then interpret state: isoiec_9798_4_4_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_udkey_A_1_Rb + thus ?case 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 + case (isoiec_9798_4_4_udkey_A_1_Text1 t r s tid0) then interpret state: isoiec_9798_4_4_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_udkey_A_1_Text1 + thus ?case 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 + case (isoiec_9798_4_4_udkey_A_text_2_Text2 t r s tid0) then interpret state: isoiec_9798_4_4_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_udkey_A_text_2_Text2 + thus ?case 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 + case (isoiec_9798_4_4_udkey_A_text_2_Text3 t r s tid0) then interpret state: isoiec_9798_4_4_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_udkey_A_text_2_Text3 + thus ?case 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 + case (isoiec_9798_4_4_udkey_A_3_Text4 t r s tid0) then interpret state: isoiec_9798_4_4_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_udkey_A_3_Text4 + thus ?case 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 + case (isoiec_9798_4_4_udkey_A_3_Text5 t r s tid0) then interpret state: isoiec_9798_4_4_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_udkey_A_3_Text5 + thus ?case 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 + case (isoiec_9798_4_4_udkey_B_2_Ra t r s tid0) then interpret state: isoiec_9798_4_4_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_udkey_B_2_Ra + thus ?case 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 + case (isoiec_9798_4_4_udkey_B_2_Text2 t r s tid0) then interpret state: isoiec_9798_4_4_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_udkey_B_2_Text2 + thus ?case 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 + case (isoiec_9798_4_4_udkey_B_2_Text3 t r s tid0) then interpret state: isoiec_9798_4_4_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_udkey_B_2_Text3 + thus ?case 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 + case (isoiec_9798_4_4_udkey_B_text_3_Text4 t r s tid0) then interpret state: isoiec_9798_4_4_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_udkey_B_text_3_Text4 + thus ?case 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 + case (isoiec_9798_4_4_udkey_B_text_3_Text5 t r s tid0) then interpret state: isoiec_9798_4_4_udkey_msc_typing_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = isoiec_9798_4_4_udkey_B_text_3_Text5 + thus ?case 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 @@ -853,7 +889,7 @@ s(MV ''Text4'' tid0) |} ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto dest!: ltk_secrecy) next case (isoiec_9798_4_4_udkey_B_3_hash tid1) note_unified facts = this facts thus ?thesis proof(sources! " @@ -862,12 +898,12 @@ s(MV ''Text2'' tid1) |} ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) + qed (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this @@ -913,11 +949,11 @@ s(MV ''Text2'' tid0) |} ") case fake note_unified facts = this facts - thus ?thesis by (fastforce dest!: ltk_secrecy) + thus ?thesis by (auto 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 (safe?, simp_all?, insert facts, (fastforce+)?) qed } note niagree = this diff --git a/data/examples/iso9798/isabelle-proofs/isoiec-9798_cert_auto.thy b/data/examples/iso9798/isabelle-proofs/isoiec-9798_cert_auto.thy --- a/data/examples/iso9798/isabelle-proofs/isoiec-9798_cert_auto.thy +++ b/data/examples/iso9798/isabelle-proofs/isoiec-9798_cert_auto.thy @@ -219,402 +219,456 @@ have "(t,r,s) : approx typing_2_6" proof(cases rule: reachable_in_approxI_ext [OF typing_2_6.monoTyp, completeness_cases_rule]) - case (A_1_B t r s tid0) note facts = this + case (A_1_B t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = A_1_B + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (A_1_Rb t r s tid0) note facts = this + case (A_1_Rb t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = A_1_Rb + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (A_1_Text1 t r s tid0) note facts = this + case (A_1_Text1 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = A_1_Text1 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (A_3_Kab t r s tid0) note facts = this + case (A_3_Kab t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = A_3_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, insert facts, (((fastforce intro: event_predOrdI split: if_splits))+)?) next - case (A_3_Text4 t r s tid0) note facts = this + case (A_3_Text4 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = A_3_Text4 + thus ?case 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))+)? + qed (safe?, simp_all?, insert facts, (((fastforce intro: event_predOrdI split: if_splits))+)?) next - case (A_3_Text5 t r s tid0) note facts = this + case (A_3_Text5 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = A_3_Text5 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (A_3_TokenPA_for_B t r s tid0) note facts = this + case (A_3_TokenPA_for_B t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = A_3_TokenPA_for_B + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (A_text4_Text6 t r s tid0) note facts = this + case (A_text4_Text6 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = A_text4_Text6 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (A_text4_Text7 t r s tid0) note facts = this + case (A_text4_Text7 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = A_text4_Text7 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (A_5_Text8 t r s tid0) note facts = this + case (A_5_Text8 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = A_5_Text8 + thus ?case 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))+)? + qed (safe?, simp_all?, insert facts, (((fastforce intro: event_predOrdI split: if_splits))+)?) next - case (A_5_Text9 t r s tid0) note facts = this + case (A_5_Text9 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = A_5_Text9 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (Abd_1_Bbd t r s tid0) note facts = this + case (Abd_1_Bbd t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Abd_1_Bbd + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (Abd_1_Rb t r s tid0) note facts = this + case (Abd_1_Rb t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Abd_1_Rb + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (Abd_1_Text1 t r s tid0) note facts = this + case (Abd_1_Text1 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Abd_1_Text1 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (Abd_3_Kab t r s tid0) note facts = this + case (Abd_3_Kab t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Abd_3_Kab + thus ?case proof(sources! " Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0, s(MV ''Kab'' tid0), s(AV ''Abd'' tid0), s(MV ''Bbd'' tid0), s(MV ''Text4'' tid0) |} ( Kbd ( s(AV ''Abd'' tid0) ) ( s(AV ''Pbd'' tid0) ) ) ") - qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)? + qed (safe?, simp_all?, insert facts, (((fastforce intro: event_predOrdI split: if_splits))+)?) next - case (Abd_3_Text4 t r s tid0) note facts = this + case (Abd_3_Text4 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Abd_3_Text4 + thus ?case proof(sources! " Enc {| LC ''isoiec_9798_2_6_enc_3_1'', LN ''Ra'' tid0, s(MV ''Kab'' tid0), s(AV ''Abd'' tid0), s(MV ''Bbd'' tid0), s(MV ''Text4'' tid0) |} ( Kbd ( s(AV ''Abd'' tid0) ) ( s(AV ''Pbd'' tid0) ) ) ") - qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)? + qed (safe?, simp_all?, insert facts, (((fastforce intro: event_predOrdI split: if_splits))+)?) next - case (Abd_3_Text5 t r s tid0) note facts = this + case (Abd_3_Text5 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Abd_3_Text5 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (Abd_3_TokenPA_for_B t r s tid0) note facts = this + case (Abd_3_TokenPA_for_B t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Abd_3_TokenPA_for_B + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (Abd_text4_Text6 t r s tid0) note facts = this + case (Abd_text4_Text6 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Abd_text4_Text6 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (Abd_text4_Text7 t r s tid0) note facts = this + case (Abd_text4_Text7 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Abd_text4_Text7 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (Abd_5_Text8 t r s tid0) note facts = this + case (Abd_5_Text8 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Abd_5_Text8 + thus ?case 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))+)? + qed (safe?, simp_all?, insert facts, (((fastforce intro: event_predOrdI split: if_splits))+)?) next - case (Abd_5_Text9 t r s tid0) note facts = this + case (Abd_5_Text9 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Abd_5_Text9 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (B_4_Kab t r s tid0) note facts = this + case (B_4_Kab t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = B_4_Kab + thus ?case 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))+)? + qed (safe?, simp_all?, insert facts, (((fastforce intro: event_predOrdI split: if_splits))+)?) next - case (B_4_P t r s tid0) note facts = this + case (B_4_P t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = B_4_P + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (B_4_Rpa t r s tid0) note facts = this + case (B_4_Rpa t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = B_4_Rpa + thus ?case 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))+)? + qed (safe?, simp_all?, insert facts, (((fastforce intro: event_predOrdI split: if_splits))+)?) next - case (B_4_Text3 t r s tid0) note facts = this + case (B_4_Text3 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = B_4_Text3 + thus ?case 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))+)? + qed (safe?, simp_all?, insert facts, (((fastforce intro: event_predOrdI split: if_splits))+)?) next - case (B_4_Text6 t r s tid0) note facts = this + case (B_4_Text6 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = B_4_Text6 + thus ?case 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))+)? + qed (safe?, simp_all?, insert facts, (((fastforce intro: event_predOrdI split: if_splits))+)?) next - case (B_4_Text7 t r s tid0) note facts = this + case (B_4_Text7 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = B_4_Text7 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (B_text5_Text8 t r s tid0) note facts = this + case (B_text5_Text8 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = B_text5_Text8 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (B_text5_Text9 t r s tid0) note facts = this + case (B_text5_Text9 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = B_text5_Text9 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (Bbd_4_Kab t r s tid0) note facts = this + case (Bbd_4_Kab t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Bbd_4_Kab + thus ?case proof(sources! " Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0, s(MV ''Kab'' tid0), s(AV ''Abd'' tid0), s(AV ''Bbd'' tid0), s(MV ''Text3'' tid0) |} ( Kbd ( s(AV ''Bbd'' tid0) ) ( s(MV ''Pbd'' tid0) ) ) ") - qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)? + qed (safe?, simp_all?, insert facts, (((fastforce intro: event_predOrdI split: if_splits))+)?) next - case (Bbd_4_Pbd t r s tid0) note facts = this + case (Bbd_4_Pbd t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Bbd_4_Pbd + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (Bbd_4_Rpa t r s tid0) note facts = this + case (Bbd_4_Rpa t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Bbd_4_Rpa + thus ?case 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))+)? + qed (safe?, simp_all?, insert facts, (((fastforce intro: event_predOrdI split: if_splits))+)?) next - case (Bbd_4_Text3 t r s tid0) note facts = this + case (Bbd_4_Text3 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Bbd_4_Text3 + thus ?case proof(sources! " Enc {| LC ''isoiec_9798_2_6_enc_3_2'', LN ''Rb'' tid0, s(MV ''Kab'' tid0), s(AV ''Abd'' tid0), s(AV ''Bbd'' tid0), s(MV ''Text3'' tid0) |} ( Kbd ( s(AV ''Bbd'' tid0) ) ( s(MV ''Pbd'' tid0) ) ) ") - qed (insert facts, ((fastforce intro: event_predOrdI split: if_splits))+)? + qed (safe?, simp_all?, insert facts, (((fastforce intro: event_predOrdI split: if_splits))+)?) next - case (Bbd_4_Text6 t r s tid0) note facts = this + case (Bbd_4_Text6 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Bbd_4_Text6 + thus ?case 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))+)? + qed (safe?, simp_all?, insert facts, (((fastforce intro: event_predOrdI split: if_splits))+)?) next - case (Bbd_4_Text7 t r s tid0) note facts = this + case (Bbd_4_Text7 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Bbd_4_Text7 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (Bbd_text5_Text8 t r s tid0) note facts = this + case (Bbd_text5_Text8 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Bbd_text5_Text8 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (Bbd_text5_Text9 t r s tid0) note facts = this + case (Bbd_text5_Text9 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Bbd_text5_Text9 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (P_2_A t r s tid0) note facts = this + case (P_2_A t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = P_2_A + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (P_2_B t r s tid0) note facts = this + case (P_2_B t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = P_2_B + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (P_2_Ra t r s tid0) note facts = this + case (P_2_Ra t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = P_2_Ra + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (P_2_Rb t r s tid0) note facts = this + case (P_2_Rb t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = P_2_Rb + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (P_2_Text2 t r s tid0) note facts = this + case (P_2_Text2 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = P_2_Text2 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (P_text3_Text3 t r s tid0) note facts = this + case (P_text3_Text3 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = P_text3_Text3 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (P_text3_Text4 t r s tid0) note facts = this + case (P_text3_Text4 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = P_text3_Text4 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (P_text3_Text5 t r s tid0) note facts = this + case (P_text3_Text5 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = P_text3_Text5 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (Pbd_2_Abd t r s tid0) note facts = this + case (Pbd_2_Abd t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Pbd_2_Abd + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (Pbd_2_Bbd t r s tid0) note facts = this + case (Pbd_2_Bbd t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Pbd_2_Bbd + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (Pbd_2_Ra t r s tid0) note facts = this + case (Pbd_2_Ra t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Pbd_2_Ra + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (Pbd_2_Rb t r s tid0) note facts = this + case (Pbd_2_Rb t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Pbd_2_Rb + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (Pbd_2_Text2 t r s tid0) note facts = this + case (Pbd_2_Text2 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Pbd_2_Text2 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (Pbd_text3_Text3 t r s tid0) note facts = this + case (Pbd_text3_Text3 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Pbd_text3_Text3 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (Pbd_text3_Text4 t r s tid0) note facts = this + case (Pbd_text3_Text4 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Pbd_text3_Text4 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) next - case (Pbd_text3_Text5 t r s tid0) note facts = this + case (Pbd_text3_Text5 t r s tid0) then interpret state: typing_2_6_state t r s by unfold_locales auto - show ?case using facts + note_prefix_closed (state) facts = Pbd_text3_Text5 + thus ?case by (fastforce intro: event_predOrdI split: if_splits) qed thus "typing_2_6_state t r s" by unfold_locales auto diff --git a/data/isabelle/README b/data/isabelle/README --- a/data/isabelle/README +++ b/data/isabelle/README @@ -1,10 +1,12 @@ -README: The scyther-proof security protocol verification tool -============================================================= +The scyther-proof security protocol verification tool +===================================================== -Authors: Simon Meier -Creation Date: 2011-05-13 -Last Updated: 2014-01-31 by Andreas Lochbihler +![master branch build-status](https://travis-ci.org/meiersi/scyther-proof.svg?branch=master) +- Authors: Simon Meier , Andreas Lochbihler +- Creation Date: 2011-05-13 +- Last Updated: 2015-02-20 by Andreas Lochbihler + 1. Introduction =============== @@ -55,55 +57,16 @@ 2.2 Installing the Isabelle/HOL theories ---------------------------------------- -Download and install full Isabelle2013-2 according to the installation +Download and install full Isabelle2014 according to the installation instructions at - http://isabelle.in.tum.de/website-Isabelle2013-2/ + http://isabelle.in.tum.de/website-Isabelle2014/ 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`. -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 ----------------------- - -Copy the Emacs keywords file provided with the ESPL distribution at - - $SCYTHER_PROOF_HOME/data/isabelle/src/isar-keywords.el - -to your local Isabelle configuration in - - $ISABELLE_HOME_USER/etc - -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_USER/etc/isar-keywords-ESPL.el - -and start Isabelle using the -k switch as follows. - - isabelle emacs -k ESPL - - - 3. Usage ======== @@ -147,20 +110,6 @@ 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 /src - isabelle emacs Tutorial.thy - - or if you've chosen the elegant variant for the keywords file - - isabelle emacs -k ESPL Tutorial.thy - Using the Isabelle/jEdit Prover IDE ----------------------------------- diff --git a/data/isabelle/document/root.tex b/data/isabelle/document/root.tex --- a/data/isabelle/document/root.tex +++ b/data/isabelle/document/root.tex @@ -1,46 +1,25 @@ \documentclass[11pt,a4paper]{article} \usepackage{isabelle,isabellesym} -% further packages required for unusual symbols (see also -% isabellesym.sty), use only when needed - -%\usepackage{amssymb} - %for \, \, \, \, \, \, - %\, \, \, \, \, - %\, \, \ - -%\usepackage[greek,english]{babel} - %option greek for \ - %option english (default language) for \, \ - -%\usepackage[latin1]{inputenc} - %for \, \, \, \, - %\, \, \ - -%\usepackage[only,bigsqcap]{stmaryrd} - %for \ - -%\usepackage{eufrak} - %for \ ... \, \ ... \ (also included in amssymb) - -%\usepackage{textcomp} - %for \, \ - -% this should be the last package used \usepackage{pdfsetup} % urls in roman style, theory text in math-similar italics \urlstyle{rm} \isabellestyle{it} -% for uniform font size -%\renewcommand{\isastyle}{\isastyleminor} +\renewcommand{\isamarkupchapter}[1]{\section{#1}} +\renewcommand{\isamarkupsection}[1]{\subsection{#1}} +\renewcommand{\isamarkupsubsection}[1]{\subsubsection{#1}} +\renewcommand{\isamarkupsubsubsection}[1]{\subsubsection{#1}} +\renewcommand{\isamarkupsect}[1]{\subsection{#1}} +\renewcommand{\isamarkupsubsect}[1]{\subsubsection{#1}} +\renewcommand{\isamarkupsubsubsect}[1]{\subsubsubsection{#1}} \begin{document} -\title{ESPL} -\author{By simon} +\title{Embedded Security Protocol Logic} +\author{Simon Meier} \maketitle \tableofcontents diff --git a/data/isabelle/src/ESPLogic/Automation.thy b/data/isabelle/src/ESPLogic/Automation.thy --- a/data/isabelle/src/ESPLogic/Automation.thy +++ b/data/isabelle/src/ESPLogic/Automation.thy @@ -31,7 +31,7 @@ method_setup sources = {* ESPL_Methods.sourcesP >> (fn ((minimal, msg_t), opt_rule) => fn ctxt => - METHOD_CASES (fn facts => + METHOD_CASES (fn facts => Seq.DETERM (HEADGOAL ( ESPL_Methods.sources_tac ctxt minimal msg_t opt_rule facts)))) diff --git a/data/isabelle/src/ESPLogic/Capabilities.thy b/data/isabelle/src/ESPLogic/Capabilities.thy --- a/data/isabelle/src/ESPLogic/Capabilities.thy +++ b/data/isabelle/src/ESPLogic/Capabilities.thy @@ -27,10 +27,10 @@ "unionPart P1 P2 q = P1 q \ P2 q" notation (xsymbols) - unionPart (infix "\\<^isub>P" 65) + unionPart (infix "\\<^sub>P" 65) lemma union_unionPart_conv: - "(a \ ((P1 \\<^isub>P P2) q)) = (a \ (P1 q \ P2 q))" + "(a \ ((P1 \\<^sub>P P2) q)) = (a \ (P1 q \ P2 q))" by (fastforce simp add: unionPart_def) @@ -90,21 +90,21 @@ "interCap C1 C2 = (\ q. C1 q \ C2 q)" notation (xsymbols) - interCap (infix "\\<^isub>C" 65) + interCap (infix "\\<^sub>C" 65) definition unionCap :: "capability \ capability \ capability" (infix "UNC" 65) where "unionCap C1 C2 = (\ q. C1 q \ C2 q)" notation (xsymbols) - unionCap (infix "\\<^isub>C" 65) + unionCap (infix "\\<^sub>C" 65) lemma union_unionCap_conv: - "(a \ ((C1 \\<^isub>C C2) q)) = (a \ (C1 q \ C2 q))" + "(a \ ((C1 \\<^sub>C C2) q)) = (a \ (C1 q \ C2 q))" by (fastforce simp add: unionCap_def) lemma inter_interCap_conv: - "(a \ ((C1 \\<^isub>C C2) q)) = (a \ (C1 q \ C2 q))" + "(a \ ((C1 \\<^sub>C C2) q)) = (a \ (C1 q \ C2 q))" by (fastforce simp add: interCap_def) diff --git a/data/isabelle/src/ESPLogic/DistinctList.thy b/data/isabelle/src/ESPLogic/DistinctList.thy --- a/data/isabelle/src/ESPLogic/DistinctList.thy +++ b/data/isabelle/src/ESPLogic/DistinctList.thy @@ -95,7 +95,7 @@ qed -text{* Specialized instances of nextRel_rev for Snoc appends *} +text{* Specialized instances of @{text "nextRel_rev"} for Snoc appends *} lemma nextRel_Snoc_simps: "nextRel (xs@[a]) x y = nextRel (a#rev xs) y x" "nextRel (xs@[a,b]) x y = nextRel (b#a#rev xs) y x" diff --git a/data/isabelle/src/ESPLogic/ExecMessage.thy b/data/isabelle/src/ESPLogic/ExecMessage.thy --- a/data/isabelle/src/ESPLogic/ExecMessage.thy +++ b/data/isabelle/src/ESPLogic/ExecMessage.thy @@ -11,7 +11,8 @@ * All rights reserved. See file LICENCE for more information. ******************************************************************************) theory ExecMessage -imports +imports + HOL_ext Protocol begin @@ -87,15 +88,15 @@ (Kbd a b = Kbd x y) = (a = x \ b = y \ a = y \ b = x)" apply(clarsimp simp: Kbd_def Agent_def agents_def set_eq_iff) apply(rule iffI) - apply(rename_tac a b x y) + apply(rename_tac a' b' x' y') apply(safe) - apply(drule_tac x="a" in spec) + apply(drule_tac x="a'" in spec) apply(simp) - apply(drule_tac x="y" in spec) + apply(drule_tac x="y'" in spec) apply(simp) - apply(drule_tac x="x" in spec) + apply(drule_tac x="x'" in spec) apply(simp) - apply(drule_tac x="b" in spec) + apply(drule_tac x="b'" in spec) apply(simp) done @@ -128,6 +129,7 @@ type_synonym store = "varid \ tid \ execmsg" +text{* Key inversion *} fun inv :: "execmsg \ execmsg" where "inv (PK m) = SK m" @@ -138,34 +140,8 @@ "\ a \ Agent; b \ Agent \ \ inv (Kbd a b) = Kbd a b" by(auto simp: Kbd_def) -(* TODO: Move *) -fun opt_map2 :: "('a \ 'b \ 'c) \ 'a option \ 'b option \ 'c option" -where - "opt_map2 f (Some x) (Some y) = Some (f x y)" -| "opt_map2 f _ _ = None" -lemma Some_opt_map2 [simp]: - "(Some x = opt_map2 f a b) = - (\ y z. x = f y z \ Some y = a \ Some z = b)" - "(opt_map2 f a b = Some x) = - (\ y z. x = f y z \ Some y = a \ Some z = b)" - by (cases a, simp, cases b, simp_all add: eq_commute)+ - -lemma Some_if_pushL [simp]: - "(Some x = (if b then Some y else None)) = (b \ x = y)" - "((if b then Some y else None) = Some x) = (b \ x = y)" - by (auto split: if_splits) - -lemma Some_if_pushR [simp]: - "(Some x = (if b then None else Some y)) = (\b \ x = y)" - "((if b then None else Some y) = Some x) = (\b \ x = y)" - by (auto split: if_splits) - -lemma Some_Option_map [simp]: - "(Some x = Option.map f a) = (\y. x = f y \ Some y = a)" - "(Option.map f a = Some x) = (\y. x = f y \ Some y = a)" - by (cases a, auto)+ - +text{* Instantiating a pattern *} fun inst :: "store \ tid \ pattern \ execmsg option" where "inst s i (PConst c) = Some (Lit (EConst c))" @@ -175,16 +151,36 @@ | "inst s i (PEnc m k) = opt_map2 Enc (inst s i m) (inst s i k)" | "inst s i (PSign m k) = opt_map2 Tup (inst s i m) - (opt_map2 Enc (inst s i m) (Option.map inv (inst s i k)))" -| "inst s i (PHash m) = Option.map Hash (inst s i m)" + (opt_map2 Enc (inst s i m) (map_option inv (inst s i k)))" +| "inst s i (PHash m) = map_option Hash (inst s i m)" | "inst s i (PSymK a b) = opt_map2 K (inst s i a) (inst s i b)" -| "inst s i (PAsymPK a) = Option.map PK (inst s i a)" -| "inst s i (PAsymSK a) = Option.map SK (inst s i a)" +| "inst s i (PAsymPK a) = map_option PK (inst s i a)" +| "inst s i (PAsymSK a) = map_option SK (inst s i a)" | "inst s i (PShrK V) = (if (\ v \ V. s (v, i) \ Agent) then Some (KShr (agents {s (v, i) | v. v \ V})) else None)" +| "inst s i (PAny) = None" +text{* Instantiate a pattern and export wildcards *} +fun any_inst :: "store \ tid \ pattern \ (execmsg, execmsg option) varfun" +where + "any_inst s i (PConst c) = Val (Some (Lit (EConst c)))" +| "any_inst s i (PFresh n) = Val (Some (Lit (ENonce n i)))" +| "any_inst s i (PVar v) = Val (Some (s (v, i)))" +| "any_inst s i (PTup x y) = var_lift2 (opt_map2 Tup) (any_inst s i x) (any_inst s i y)" +| "any_inst s i (PEnc m k) = var_lift2 (opt_map2 Enc) (any_inst s i m) (any_inst s i k)" +| "any_inst s i (PSign m k) = var_lift2 + (\m' k'. opt_map2 Tup m' (opt_map2 Enc m' (map_option inv k'))) + (any_inst s i m) (any_inst s i k)" +| "any_inst s i (PHash m) = var_map (map_option Hash) (any_inst s i m)" +| "any_inst s i (PSymK a b) = var_lift2 (opt_map2 K) (any_inst s i a) (any_inst s i b)" +| "any_inst s i (PAsymPK a) = var_map (map_option PK) (any_inst s i a)" +| "any_inst s i (PAsymSK a) = var_map (map_option SK) (any_inst s i a)" +| "any_inst s i (PShrK V) = Val (inst s i (PShrK V))" +| "any_inst s i (PAny) = Fun (\m. Val (Some m))" + + text{* We assume that recipients making use of shared keys look them up in a table. This lookup only succeeds if agent identities are given. @@ -304,8 +300,6 @@ lemma inv_inj [iff]: "(inv x = inv y) = (x = y)" by (auto) (induct x, auto) - - subsubsection{* @{term subterms} *} diff --git a/data/isabelle/src/ESPLogic/ExplicitModel.thy b/data/isabelle/src/ESPLogic/ExplicitModel.thy --- a/data/isabelle/src/ESPLogic/ExplicitModel.thy +++ b/data/isabelle/src/ESPLogic/ExplicitModel.thy @@ -111,6 +111,11 @@ type_synonym state = "explicit_trace \ threadpool \ store" + +definition exec_match :: "store \ tid \ varid \ pattern \ bool" +where + "exec_match s i v pt = var_fold Ex (var_map (op = (Some (s (v, i)))) (any_inst s i pt))" + inductive_set reachable :: "proto \ state set" for P :: "proto" @@ -149,6 +154,12 @@ \ \ (t @ [Step (i, Recv l pt)], r(i \ (done @ [Recv l pt], todo, skipped)), s) \ reachable P" +| match: "\ (t, r, s) \ reachable P; + r i = Some (done, Match l eq mv pt # todo, skipped); + exec_match s i mv pt = eq + \ + \ (t @ [Step (i, Match l eq mv pt)], r(i \ (done @ [Match l eq mv pt], todo, skipped)), s) \ reachable P" + | hash: "\ (t, r, s) \ reachable P; m \ knows t; Hash m \ knows t @@ -169,7 +180,6 @@ \ \ (t @ [Learns {Enc m k}], r, s) \ reachable P" - | decr: "\ (t, r, s) \ reachable P; Enc m k \ knows t; inv k \ knows t @@ -187,7 +197,7 @@ [ OF reachable , rule_format , consumes 0 - , case_names init compr skip lkr send recv hash tuple encr decr + , case_names init compr skip lkr send recv match hash tuple encr decr ] end @@ -342,6 +352,11 @@ "Recv l pt \ skipped" by (auto dest!: note_in_skipped) +lemma match_notin_skipped [iff]: + "Match l eq mv pt \ skipped" + by (auto dest!: note_in_skipped) + + lemma in_steps_conv_done_skipped: "(i, step) \ steps t = (step \ set done \ step \ skipped)" @@ -372,13 +387,23 @@ using recv `i = i'` by fastforce qed auto next + case (match t r s i "done" l eq mv pt todo skipped i' done' todo' skipped') + thus ?case + proof(cases "i = i'") + case True + then interpret thread: + reachable_thread P t r s i "done" "Match l eq mv pt # todo" skipped' + using match by unfold_locales auto + show ?thesis using match `i = i'` by fastforce + qed auto +next case (compr t r s i "done" l ty pt todo skipped m i' done' todo' skipped') thus ?case proof(cases "i = i'") case True thus ?thesis using compr `i = i'` proof(cases "step = Note l ty pt") - case True + case True interpret thread: reachable_thread P t r s i "done" "Note l ty pt # todo" skipped' using compr `i = i'` by unfold_locales auto @@ -417,11 +442,27 @@ thus "?case" by fastforce qed ((unfold map_upd_Some_unfold)?, auto)+ +lemma in_steps_match: + "((Match l eq mv pt) \ set done) = ((i, Match l eq mv pt) \ steps t)" +using thread_exists +proof(induct arbitrary: i "done" todo skipped rule rule: reachable_induct) + case init + thus ?case by fastforce +qed ((unfold map_upd_Some_unfold)?, auto)+ + lemmas send_steps_in_done [elim!] = iffD1[OF in_steps_send, rule_format] lemmas send_done_in_steps [elim!] = iffD2[OF in_steps_send, rule_format] lemmas recv_steps_in_done [elim!] = iffD1[OF in_steps_recv, rule_format] lemmas recv_done_in_steps [elim!] = iffD2[OF in_steps_recv, rule_format] +lemmas match_steps_in_done [elim!] = iffD1[OF in_steps_match, rule_format] +lemmas match_done_in_steps [elim!] = iffD2[OF in_steps_match, rule_format] +lemma not_note_done_in_steps: + assumes "step \ set done" + and "\ noteStep step" + shows "(i, step) \ steps t" +using assms +by (cases step, auto) lemma in_steps_eq_in_done: "step \ skipped \ ((i, step) \ steps t) = (step \ set done)" @@ -462,13 +503,16 @@ shows "step \ set done" proof(cases step) - case (Send l pt) + case Send thus ?thesis using inSteps by (fastforce dest: in_steps_send[THEN iffD2]) next - case (Recv l pt) + case Recv thus ?thesis using inSteps by (fastforce dest: in_steps_recv[THEN iffD2]) next - case (Note l ty pt) + case Match + thus ?thesis using inSteps by (fastforce dest: in_steps_match[THEN iffD2]) +next + case Note thus ?thesis using inSteps by (fastforce simp add: in_steps_conv_done_skipped) qed @@ -533,6 +577,16 @@ by fastforce qed fastforce next + case (match t r s i "done" l eq mv pt todo skipped i' done' todo' skipped') + from match show ?case + proof(cases "i = i'") + case True + interpret this_thread: + reachable_thread P t r s i' "done" "Match l eq mv pt # todo'" skipped' + using match `i = i'` by unfold_locales auto + show ?thesis using match `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 proof(cases "i = i'") @@ -576,6 +630,16 @@ using facts by(auto dest: in_set_listOrd1 todo_notin_doneD listOrd_done_imp_listOrd_trace in_set_listOrd2 listOrd_append[THEN iffD1] in_steps_conv_done_skipped[THEN iffD1]) +lemma listOrd_match_role_imp_listOrd_trace: + assumes facts: + "(i, step) \ steps t" + "listOrd (done @ todo) (Match l eq mv pt) step" + shows + "listOrd t (Step (i, Match l eq mv pt)) (Step (i, step))" +using distinct +using facts +by(auto dest: in_set_listOrd1 todo_notin_doneD listOrd_done_imp_listOrd_trace in_set_listOrd2 listOrd_append[THEN iffD1] in_steps_conv_done_skipped[THEN iffD1]) + lemma roleOrd_notSkipped_imp_listOrd_trace: assumes facts: "(i, step) \ steps t" @@ -613,44 +677,29 @@ end (* reachable_state *) -lemma (in reachable_state) send_step_FV: - assumes thread_exists: "r i = Some (done, Send l msg # todo, skipped)" - and FV: "MVar n \ FV msg" - shows "\ l' msg'. (i, Recv l' msg') \ steps t \ MVar n \ FV msg'" -proof - - interpret this_thread: reachable_thread P t r s i "done" "Send l msg # todo" skipped - using thread_exists by unfold_locales auto - let ?role = "done @ Send l msg # todo" - have "Send l msg \ set ?role" by simp - then obtain l' msg' - where "listOrd ?role (Recv l' msg') (Send l msg)" - and "MVar n \ FV msg'" - using FV by(fast dest!: this_thread.Send_FV) - thus ?thesis using this_thread.distinct - by(auto dest: in_set_listOrd1 in_set_listOrd2) -qed - -lemma (in reachable_state) note_step_FV: - assumes thread_exists: "r i = Some (done, Note l ty msg # todo, skipped)" - and FV: "MVar n \ FV msg" - shows "\ l' msg'. (i, Recv l' msg') \ steps t \ MVar n \ FV msg'" +lemma (in reachable_state) source_step: + assumes thread_exists: "r i = Some (done, ustep # todo, skipped)" + and useV: "v \ used_vars ustep" + shows "\ sstep. (i, sstep) \ steps t \ v \ sourced_vars sstep" proof - - interpret this_thread: reachable_thread P t r s i "done" "Note l ty msg # todo" skipped + interpret this_thread: reachable_thread P t r s i "done" "ustep # todo" skipped using thread_exists by unfold_locales auto - let ?role = "done @ Note l ty msg # todo" - have "Note l ty msg \ set ?role" by simp - then obtain l' msg' - where "listOrd ?role (Recv l' msg') (Note l ty msg)" - and "MVar n \ FV msg'" - using FV by(fast dest!: this_thread.Note_FV) - thus ?thesis using this_thread.distinct - by(auto dest: in_set_listOrd1 in_set_listOrd2) + let ?role = "done @ ustep # todo" + have "ustep \ set ?role" by simp + then obtain sstep + where "listOrd ?role sstep ustep" + and is_source: "v \ sourced_vars sstep" + using useV by (fast dest!: this_thread.source_use_ord) + hence "sstep \ set done" using this_thread.distinct + by (auto dest: in_set_listOrd1 in_set_listOrd2) + moreover have "\ noteStep sstep" using is_source by auto + ultimately show ?thesis using is_source + by (auto intro: this_thread.not_note_done_in_steps) qed - +(* subsubsection{* The Effect of a Step on the Intruder Knowledge *} - context reachable_state begin @@ -661,7 +710,7 @@ qed auto end - +*) subsection{* Almost Distinct Traces *} @@ -697,6 +746,13 @@ show ?case using `distinct' t` this_thread.distinct by(fastforce dest: this_thread.in_steps_in_done) next + case (match t r s i "done" l eq mv pt todo skipped) + then interpret this_thread: + reachable_thread P t r s i "done" "Match l eq mv pt # todo" skipped + by unfold_locales auto + show ?case using `distinct' t` this_thread.distinct + 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 @@ -910,40 +966,40 @@ next case (Cons e xs) thus ?case proof(cases e) - case (Step st) thus ?thesis - proof(cases "x = St st") - case True hence "?decomp (e#xs) [e] xs" - using Step Cons by auto - thus ?thesis by blast - next - case False - hence "predOrd xs x y" - using Step Cons by auto - then obtain ys zs where "?decomp xs ys zs" - using Cons by blast - hence "?decomp (e#xs) (e#ys) zs" - using Step Cons by auto - thus ?thesis by blast - qed + case (Step st) thus ?thesis + proof(cases "x = St st") + case True hence "?decomp (e#xs) [e] xs" + using Step Cons by auto + thus ?thesis by blast + next + case False + hence "predOrd xs x y" + using Step Cons by auto + then obtain ys zs where "?decomp xs ys zs" + using Cons by blast + hence "?decomp (e#xs) (e#ys) zs" + using Step Cons by auto + thus ?thesis by blast + qed next - case (Learns M) thus ?thesis - proof(cases "\ m \ M. x = Ln m") - case True - then obtain m where "m \ M" and "x = Ln m" - by auto - hence "?decomp (e#xs) [e] xs" - using Learns Cons by auto - thus ?thesis by blast - next - case False - hence "predOrd xs x y" - using Learns Cons by auto - then obtain ys zs where "?decomp xs ys zs" - using Cons by blast - hence "?decomp (e#xs) (e#ys) zs" - using Learns Cons by auto - thus ?thesis by blast - qed + case (Learns M) thus ?thesis + proof(cases "\ m \ M. x = Ln m") + case True + then obtain m where "m \ M" and "x = Ln m" + by auto + hence "?decomp (e#xs) [e] xs" + using Learns Cons by auto + thus ?thesis by blast + next + case False + hence "predOrd xs x y" + using Learns Cons by auto + then obtain ys zs where "?decomp xs ys zs" + using Cons by blast + hence "?decomp (e#xs) (e#ys) zs" + using Learns Cons by auto + thus ?thesis by blast + qed next case (LKReveal a) thus ?thesis proof(cases "x = LKR (Lit (EAgent a))") @@ -970,46 +1026,46 @@ next case (Cons e xs) then obtain ys zs where decomp1: "?decomp (e#xs) ys zs" - by blast + by fast hence "ys = [] \ e # xs = zs \ (\ys'. e # ys' = ys \ xs = ys' @ zs)" - (is "?nil \ ?non_nil") - by (simp add: Cons_eq_append_conv) + (is "?nil \ ?non_nil") + by (simp add: Cons_eq_append_conv) moreover { assume ?nil hence ?case using decomp1 by auto } moreover { assume ?non_nil - then obtain ys' where decomp2: "ys = e # ys'" and "xs = ys' @ zs" - by auto - hence ?case - proof(cases e) - case (Step st) thus ?thesis - proof(cases "x = St st") - case True thus ?thesis - using Step decomp1 decomp2 by auto - next - case False - hence "?decomp xs ys' zs" - using Step decomp1 decomp2 by auto - hence "predOrd xs x y" - using Cons by auto - thus ?thesis - using Step by auto - qed - next - case (Learns M) thus ?thesis - proof(cases "\ m \ M. x = Ln m") - case True thus ?thesis - using Learns decomp1 decomp2 by auto - next - case False - hence "?decomp xs ys' zs" - using Learns decomp1 decomp2 by auto - hence "predOrd xs x y" - using Cons by auto - thus ?thesis - using Learns by auto - qed + then obtain ys' where decomp2: "ys = e # ys'" and "xs = ys' @ zs" + by auto + hence ?case + proof(cases e) + case (Step st) thus ?thesis + proof(cases "x = St st") + case True thus ?thesis + using Step decomp1 decomp2 by auto + next + case False + hence "?decomp xs ys' zs" + using Step decomp1 decomp2 by auto + hence "predOrd xs x y" + using Cons by auto + thus ?thesis + using Step by auto + qed next + case (Learns M) thus ?thesis + proof(cases "\ m \ M. x = Ln m") + case True thus ?thesis + using Learns decomp1 decomp2 by auto + next + case False + hence "?decomp xs ys' zs" + using Learns decomp1 decomp2 by auto + hence "predOrd xs x y" + using Cons by auto + thus ?thesis + using Learns by auto + qed + next case (LKReveal a) thus ?thesis proof(cases "x = LKR (Lit (EAgent a))") case True thus ?thesis @@ -1023,7 +1079,7 @@ thus ?thesis using LKReveal by auto qed - qed + qed } ultimately show ?case by fast qed @@ -1102,6 +1158,12 @@ from recv show ?case by (fastforce dest: s1.rev_knows_pairParts_closedD) next + case (match t r s i "done" l eq mv pt todo) + then interpret s1: reachable_state P t r s + by unfold_locales + from match show ?case + by (fastforce dest: s1.rev_knows_pairParts_closedD) +next case (init r s) thus ?case by simp next case (lkr t r s a) @@ -1142,6 +1204,14 @@ text{* Three of the lemmas for the reasoning technique. *} lemmas Input = Ln_before_inp +lemma match_eq_rule: + "(i, Match l True v pt) \ steps t \ exec_match s i v pt" +by (induct rule: reachable_induct) (fastforce+) + +lemma not_match_rule: + "(i, Match l False v pt) \ steps t \ \ exec_match s i v pt" +by (induct rule: reachable_induct) (fastforce+) + lemma split_before: "Ln (Tup m m') \ y \ Ln m \ y \ Ln m' \ y" by (fastforce intro: pairParts_before) @@ -1262,12 +1332,12 @@ { assume "?tup" hence "?thesis" by fastforce } moreover { assume "?chain t r s" hence "?chain (t@t') r s" - by (fastforce 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 (fastforce intro!: decrChain_append) + by (fastforce intro!: decrChain_append) hence "?thesis" by blast } moreover { assume "?keys" hence "?thesis" by auto } @@ -1287,7 +1357,7 @@ using hash by fastforce moreover { assume "?new" hence ?case - using `m \ knows t` by fastforce + using `m \ knows t` by fastforce } moreover { assume "?old" @@ -1302,7 +1372,7 @@ using encr by fastforce moreover { assume "?new" hence ?case - using `m \ knows t` and `k \ knows t` by fastforce + using `m \ knows t` and `k \ knows t` by fastforce } moreover { assume "?old" @@ -1317,7 +1387,7 @@ using tuple by fastforce moreover { assume "?new" hence ?case - using `x \ knows t` and `y \ knows t` by fastforce + using `x \ knows t` and `y \ knows t` by fastforce } moreover { assume "?old" @@ -1380,6 +1450,61 @@ } ultimately show ?case by fastforce next + case (match t r s i "done" l eq mv pt todo skipped) + hence "?cases m' t r s" + (is "?ik0 \ ?hash \ ?enc \ ?tup \ ?chain t r s \ ?note t r s \ ?keys") + by clarsimp + moreover + { assume "?ik0" hence "?case" by blast } 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, Match l eq mv pt)]" + and ?r' = "r(i \ (done @ [Match l eq mv 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' \ set done'" + and msg: "Some m = inst s i' pt'" + 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 match by unfold_locales auto + obtain done'' todo'' skipped'' + where "Send l' pt' \ set done''" + and "?r' i' = Some (done'', todo'', skipped'')" + using `r i = Some (done, Match l eq mv 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 + { let ?t' = "t@[Step (i, Match l eq mv pt)]" + and ?r' = "r(i \ (done @ [Match l eq mv 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' \ set done'" + and notSkipped: "Note l' ty' pt' \ skipped'" + and msg: "Some m = inst s i' pt'" + 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 match by unfold_locales auto + obtain done'' todo'' skipped'' + where "Note l' ty' pt' \ set done''" + and "Note l' ty' pt' \ skipped'' " + and "?r' i' = Some (done'', todo'', skipped'')" + using `r i = Some (done, Match l eq mv 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 fastforce + next case (send t r s i "done" l pt todo skipped m) then interpret th1: reachable_thread P t r s i "done" "Send l pt # todo" skipped @@ -1392,10 +1517,10 @@ moreover { assume "?new" hence "decrChain [] ?t' {St (i, Send l pt)} m m'" - by (fastforce 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 + using th1.thread_exists by auto ultimately have ?case using `Some m = inst s i pt` apply- @@ -1405,13 +1530,13 @@ apply(rule disjI2) apply(rule disjI1) apply(fastforce) - done + done } moreover { assume "?old" hence "?cases m' t r s" (is "?ik0 \ ?hash \ ?enc \ ?tup \ ?chain t r s \ ?note t r s \ ?keys") - using send by clarsimp + using send by clarsimp moreover { assume "?ik0" hence "?case" by blast } moreover { assume "?hash" hence "?case" by fastforce } moreover @@ -1419,38 +1544,38 @@ { 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')" - and send: "Send l' pt' \ set done'" - and msg: "Some m = inst s i' pt'" - and chain: "decrChain [] t {St (i', Send l' pt')} m m'" - by auto - obtain done'' todo'' skipped'' - where "Send l' pt' \ set done''" - and "(r(i \ (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'") (fastforce+) - hence "?chain ?t' ?r' s" - using chain msg - by (fast intro!: decrChain_append) - hence "?case" by auto + obtain i' done' todo' l' pt' skipped' m + where thread': "r i' = Some (done', todo',skipped')" + and send: "Send l' pt' \ set done'" + and msg: "Some m = inst s i' pt'" + and chain: "decrChain [] t {St (i', Send l' pt')} m m'" + by auto + obtain done'' todo'' skipped'' + where "Send l' pt' \ set done''" + and "(r(i \ (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'") (fastforce+) + hence "?chain ?t' ?r' s" + using chain msg + by (fast intro!: decrChain_append) + hence "?case" by auto } moreover { 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' \ set done'" + where thread': "r i' = Some (done', todo', skipped')" + and inDone: "Note l' ty' pt' \ set done'" and notSkipped: "Note l' ty' pt' \ 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 obtain done'' todo'' skipped'' - where "Note l' ty' pt' \ set done''" + where "Note l' ty' pt' \ set done''" and "Note l' ty' pt' \ 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'") (fastforce+) + and "?r' i' = Some (done'', todo'', skipped'')" + using `r i = Some (done, Send l pt # todo, skipped)` thread' inDone notSkipped + by (cases "i = i'") (fastforce+) hence "?note ?t' ?r' s" using chain notSkipped inDone msg - by(fast intro!: decrChain_append) + by(fast intro!: decrChain_append) hence "?case" by auto } ultimately have ?case by fast @@ -1469,53 +1594,53 @@ { assume "?new" hence "m' \ pairParts m" and "m' \ knows t" by auto hence - "(predOrd t (Ln m) (Ln (Enc m k)) \ predOrd t (Ln k) (Ln (Enc m k))) \ + "(predOrd t (Ln m) (Ln (Enc m k)) \ predOrd t (Ln k) (Ln (Enc m k))) \ ((\i done todo skipped. r i = Some (done, todo,skipped) \ (\l pt ms. Send l pt \ set done \ Some ms = inst s i pt \ - decrChain [] t {St (i, Send l pt)} ms (Enc m k)))) \ + decrChain [] t {St (i, Send l pt)} ms (Enc m k)))) \ ((\i done todo skipped. r i = Some (done, todo,skipped) \ (\l ty pt ms. Note l ty pt \ set done \ Note l ty pt \ skipped \ - Some ms = inst s i pt \ - decrChain [] t {St (i, Note l ty pt)} ms (Enc m k))))" - (is "?fake_enc \ ?decchain t (Enc m k) \ ?notechain t (Enc m k)") - using IH[OF `Enc m k \ knows t`] by auto + Some ms = inst s i pt \ + decrChain [] t {St (i, Note l ty pt)} ms (Enc m k))))" + (is "?fake_enc \ ?decchain t (Enc m k) \ ?notechain t (Enc m k)") + using IH[OF `Enc m k \ knows t`] by auto moreover { assume "?fake_enc" - hence "?case" using `?new` - by (auto dest!: in_knows_predOrd1 s1.rev_knows_pairParts_closedD) + hence "?case" using `?new` + by (auto dest!: in_knows_predOrd1 s1.rev_knows_pairParts_closedD) } moreover { assume "?decchain t (Enc m k)" then - obtain i' done' todo' l' pt' skipped' ms - where thread': "r i' = Some (done', todo',skipped')" - and send: "Send l' pt' \ set done'" - and msg: "Some ms = inst s i' pt'" - and chain: "decrChain [] t {St (i', Send l' pt')} ms (Enc m k)" - by auto - moreover - hence "decrChain [] ?t' {St (i', Send l' pt')} ms m'" - using `?new` `Enc m k \ knows t` `inv k \ knows t` - by (fastforce intro!: decrChain_decrypt) - ultimately - have "?decchain ?t' m'" by fastforce - hence "?case" by blast + obtain i' done' todo' l' pt' skipped' ms + where thread': "r i' = Some (done', todo',skipped')" + and send: "Send l' pt' \ set done'" + and msg: "Some ms = inst s i' pt'" + and chain: "decrChain [] t {St (i', Send l' pt')} ms (Enc m k)" + by auto + moreover + hence "decrChain [] ?t' {St (i', Send l' pt')} ms m'" + using `?new` `Enc m k \ knows t` `inv k \ knows t` + by (fastforce intro!: decrChain_decrypt) + ultimately + have "?decchain ?t' m'" by fastforce + hence "?case" by blast } moreover { assume "?notechain t (Enc m k)" then - obtain i' done' todo' l' ty' pt' skipped' ms - where thread': "r i' = Some (done', todo',skipped')" - and inDone: "Note l' ty' pt' \ set done'" - and notSkipped: "Note l' ty' pt' \ skipped'" - and msg: "Some ms = inst s i' pt'" - and chain: "decrChain [] t {St (i', Note l' ty' pt')} ms (Enc m k)" - by auto - moreover - hence "decrChain [] ?t' {St (i', Note l' ty' pt')} ms m'" - using `?new` `Enc m k \ knows t` `inv k \ knows t` - by (fastforce intro!: decrChain_decrypt) - ultimately - have "?notechain ?t' m'" by fastforce - hence "?case" by blast + obtain i' done' todo' l' ty' pt' skipped' ms + where thread': "r i' = Some (done', todo',skipped')" + and inDone: "Note l' ty' pt' \ set done'" + and notSkipped: "Note l' ty' pt' \ skipped'" + and msg: "Some ms = inst s i' pt'" + and chain: "decrChain [] t {St (i', Note l' ty' pt')} ms (Enc m k)" + by auto + moreover + hence "decrChain [] ?t' {St (i', Note l' ty' pt')} ms m'" + using `?new` `Enc m k \ knows t` `inv k \ knows t` + by (fastforce intro!: decrChain_decrypt) + ultimately + have "?notechain ?t' m'" by fastforce + hence "?case" by blast } ultimately have ?case by fast } @@ -1545,61 +1670,63 @@ } ultimately show "?case" by fast next - 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 \ (done @ [Note l ty pt], todo, insert (Note l ty pt) skipped))" - have "m' \ knows t" using skip by fastforce - hence "?cases m' t r s" - (is "?ik0 \ ?hash \ ?enc \ ?tup \ ?chain t r s \ ?note t r s \ ?keys") - using skip by clarsimp - moreover - { assume "?ik0" hence "?case" by blast } 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 + 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 \ (done @ [Note l ty pt], todo, insert (Note l ty pt) skipped))" + have "m' \ knows t" using skip by fastforce + hence "?cases m' t r s" + (is "?ik0 \ ?hash \ ?enc \ ?tup \ ?chain t r s \ ?note t r s \ ?keys") + using skip by clarsimp + moreover + { assume "?ik0" hence "?case" by blast } 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')" and send: "Send l' pt' \ set done'" and msg: "Some m = inst s i' pt'" and chain: "decrChain [] t {St (i', Send l' pt')} m m'" by auto - obtain done'' todo'' skipped'' + obtain done'' todo'' skipped'' where "Send l' pt' \ set done''" and "?r' i' = Some (done'', todo'',skipped'')" using skip(3) thread' send by (cases "i = i'") (fastforce+) - hence "?chain t ?r' s" + hence "?chain t ?r' s" using chain msg by fast - hence "?case" by auto - } - moreover - { 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' \ set done'" - and notSkipped: "Note l' ty' pt' \ skipped'" - and msg: "Some m = inst s i' pt'" - and chain: "decrChain [] t {St (i', Note l' ty' pt')} m m'" - by auto + hence "?case" by auto + } + moreover + { 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' \ set done'" + and notSkipped: "Note l' ty' pt' \ skipped'" + and msg: "Some m = inst s i' pt'" + and chain: "decrChain [] t {St (i', Note l' ty' pt')} m m'" + by auto obtain done'' todo'' skipped'' - where "Note l' ty' pt' \ set done''" - and "Note l' ty' pt' \ 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'") (force dest: this_thread.done_notin_todoD)+ - hence "?note t ?r' s" + where "Note l' ty' pt' \ set done''" + and "Note l' ty' pt' \ 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'") (force dest: this_thread.done_notin_todoD)+ + hence "?note t ?r' s" using chain notSkipped inDone msg by fast hence "?case" by auto - } moreover - { assume "?keys" hence "?case" by fastforce } - ultimately - show "?case" by fastforce + } moreover + { assume "?keys" hence "?case" by fastforce } + ultimately + show "?case" by fastforce next - case(compr t r s i "done" l ty pt todo skipped m m') - then interpret th1: + case(compr t r s i "done" l ty pt todo skipped m m') + then interpret th1: reachable_thread P t r s i "done" "Note l ty pt # todo" skipped by unfold_locales let ?r' = "r(i \ (done @ [Note l ty pt], todo, skipped))" @@ -1609,12 +1736,8 @@ using compr by fastforce moreover { assume "?new" - (* - hence "m' \ pairParts (inst s i pt)" and "m' \ knows t" using `m = inst s i pt` - by auto -*) - hence "decrChain [] ?t' {St (i, Note l ty pt)} m m'" - by (fastforce intro!: decrChain_unpair) + hence "decrChain [] ?t' {St (i, Note l ty pt)} m m'" + by (fastforce intro!: decrChain_unpair) moreover have "?r' i = Some (done @ [Note l ty pt], todo, skipped)" using th1.thread_exists by auto @@ -1625,7 +1748,7 @@ by (fastforce dest: th1.todo_notin_skippedD) ultimately have ?case using `Some m = inst s i pt` - apply- + apply- apply(rule disjI2) apply(rule disjI2) apply(rule disjI2) @@ -1638,7 +1761,7 @@ { assume "?old" hence "?cases m' t r s" (is "?ik0 \ ?hash \ ?enc \ ?tup \ ?chain t r s \ ?note t r s \ ?keys") - using compr by clarsimp + using compr by clarsimp moreover { assume "?ik0" hence "?case" by blast } moreover { assume "?hash" hence "?case" by fastforce } moreover @@ -1646,35 +1769,35 @@ { 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')" - and send: "Send l' pt' \ set done'" - and msg: "Some m = inst s i' pt'" - and chain: "decrChain [] t {St (i', Send l' pt')} m m'" - by auto - obtain done'' todo'' skipped'' - where "Send l' pt' \ set done''" - and "(r(i \ (done @ [Note l ty pt], todo, skipped))) i' = Some (done'', todo'',skipped'')" - using compr(3) thread' send - by (cases "i = i'") (fastforce+) - hence "?chain ?t' ?r' s" using chain msg - by(fast intro!: decrChain_append) - hence "?case" by auto + obtain i' done' todo' l' pt' skipped' m + where thread': "r i' = Some (done', todo',skipped')" + and send: "Send l' pt' \ set done'" + and msg: "Some m = inst s i' pt'" + and chain: "decrChain [] t {St (i', Send l' pt')} m m'" + by auto + obtain done'' todo'' skipped'' + where "Send l' pt' \ set done''" + and "(r(i \ (done @ [Note l ty pt], todo, skipped))) i' = Some (done'', todo'',skipped'')" + using compr(3) 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 { 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' \ set done'" + where thread': "r i' = Some (done', todo', skipped')" + and inDone: "Note l' ty' pt' \ set done'" and notSkipped: "Note l' ty' pt' \ 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 obtain done'' todo'' skipped'' - where "Note l' ty' pt' \ set done''" + where "Note l' ty' pt' \ set done''" and "Note l' ty' pt' \ 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'") (fastforce+) + 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'") (fastforce+) hence "?note ?t' ?r' s" using chain notSkipped inDone msg by(fast intro!: decrChain_append) diff --git a/data/isabelle/src/ESPLogic/HOL_ext.thy b/data/isabelle/src/ESPLogic/HOL_ext.thy --- a/data/isabelle/src/ESPLogic/HOL_ext.thy +++ b/data/isabelle/src/ESPLogic/HOL_ext.thy @@ -29,6 +29,70 @@ "\ \ x y. m x = Some y \ m' x = Some y \ \ m \\<^sub>m m'" by(force simp: map_le_def) + +section{* Option *} + +fun opt_map2 :: "('a \ 'b \ 'c) \ 'a option \ 'b option \ 'c option" +where + "opt_map2 f (Some x) (Some y) = Some (f x y)" +| "opt_map2 f _ _ = None" + +lemma Some_opt_map2 [simp]: + "(Some x = opt_map2 f a b) = + (\ y z. x = f y z \ Some y = a \ Some z = b)" + "(opt_map2 f a b = Some x) = + (\ y z. x = f y z \ Some y = a \ Some z = b)" + by (cases a, simp, cases b, simp_all add: eq_commute)+ + +lemma Some_if_pushL [simp]: + "(Some x = (if b then Some y else None)) = (b \ x = y)" + "((if b then Some y else None) = Some x) = (b \ x = y)" + by (auto split: if_splits) + +lemma Some_if_pushR [simp]: + "(Some x = (if b then None else Some y)) = (\b \ x = y)" + "((if b then None else Some y) = Some x) = (\b \ x = y)" + by (auto split: if_splits) + +lemma Some_Option_map [simp]: + "(Some x = map_option f a) = (\y. x = f y \ Some y = a)" + "(map_option f a = Some x) = (\y. x = f y \ Some y = a)" + by (cases a, auto)+ + + +section{* Variadic Functions *} + +datatype ('a, 'b) varfun = Val 'b | Fun "'a \ ('a, 'b) varfun" + +primrec var_map :: "('b \ 'c) \ ('a, 'b) varfun \ ('a, 'c) varfun" +where + "var_map f (Val x) = Val (f x)" +| "var_map f (Fun g) = Fun (\x. var_map f (g x))" + +primrec var_apply :: "('a, 'b \ 'c) varfun \ ('a, 'b) varfun \ ('a, 'c) varfun" +where + "var_apply (Val f) v = var_map f v" +| "var_apply (Fun g) v = Fun (\x. var_apply (g x) v)" + +abbreviation var_lift2 :: "('b \ 'c \ 'd) \ ('a, 'b) varfun \ ('a, 'c) varfun \ ('a, 'd) varfun" +where "var_lift2 f v1 v2 \ var_apply (var_map f v1) v2" + +primrec var_fold :: "(('a \ 'b) \ 'b) \ ('a, 'b) varfun \ 'b" +where + "var_fold f (Val x) = x" +| "var_fold f (Fun g) = f (\x. var_fold f (g x))" + + +lemma var_map_map [simp]: "var_map f (var_map g v) = var_map (f o g) v" +by (induct v) (auto) + +lemma var_fold_not_all: "(\ var_fold All v) = var_fold Ex (var_map Not v)" +by (induct v) (auto) + +lemma var_fold_not_ex: "(\ var_fold Ex v) = var_fold All (var_map Not v)" +by (induct v) (auto) + + section{* Finite Sets *} text{* diff --git a/data/isabelle/src/ESPLogic/Hints.thy b/data/isabelle/src/ESPLogic/Hints.thy --- a/data/isabelle/src/ESPLogic/Hints.thy +++ b/data/isabelle/src/ESPLogic/Hints.thy @@ -79,7 +79,7 @@ val hint_ct = mk_hint name t |> HOLogic.mk_Trueprop |> Thm.cterm_of (Proof_Context.theory_of ctxt); in - Goal.prove_internal [] hint_ct (K (ALLGOALS (remove_all_hints_tac ctxt))) + Goal.prove_internal ctxt [] hint_ct (K (ALLGOALS (remove_all_hints_tac ctxt))) end; end; diff --git a/data/isabelle/src/ESPLogic/InferenceRules.thy b/data/isabelle/src/ESPLogic/InferenceRules.thy --- a/data/isabelle/src/ESPLogic/InferenceRules.thy +++ b/data/isabelle/src/ESPLogic/InferenceRules.thy @@ -75,6 +75,8 @@ (\ st st'. (nextRel (filter (\ x. \ (noteStep x)) (takeWhile (\ x. x \ step) R) @ [step]) st st') \ ((recvStep st \ (\ m. Some m = inst s i (stepPat st) \ predOrd t (Ln m) (St (i, st)))) \ + (matchEqStep st \ exec_match s i (matchVar st) (stepPat st)) \ + (notMatchStep st \ \ exec_match s i (matchVar st) (stepPat st)) \ predOrd t (St (i, st)) (St (i, st'))) )" @@ -232,6 +234,14 @@ \ nextRel (filter (\ x. \ (noteStep x)) (takeWhile (\ x. x \ step) R) @ [step]) st st'; recvStep st \ \ \ m. Some m = inst s i (stepPat st) \ Ln m \ St (i, st)" + and "\ st st'. + \ nextRel (filter (\ x. \ (noteStep x)) (takeWhile (\ x. x \ step) R) @ [step]) st st'; + matchEqStep st + \ \ exec_match s i (matchVar st) (stepPat st)" + and "\ st st'. + \ nextRel (filter (\ x. \ (noteStep x)) (takeWhile (\ x. x \ step) R) @ [step]) st st'; + notMatchStep st + \ \ \ exec_match s i (matchVar st) (stepPat st)" and "\ st st'. \ nextRel (filter (\ x. \ (noteStep x)) (takeWhile (\ x. x \ step) R) @ [step]) st st' \ \ St (i, st) \ St (i, st')" @@ -246,7 +256,7 @@ from role_exists obtain "done" todo skipped where R_split: "R = done @ todo" - and "r i = Some (done, todo,skipped)" + and thread_state: "r i = Some (done, todo,skipped)" by (auto elim!: roleMap_SomeE) moreover then interpret this_thread: @@ -285,12 +295,23 @@ by(fastforce dest!: this_thread.note_in_skipped note_filtered_revRole) hence steps: "(i, st) \ steps t" "(i, st') \ steps t" by(auto dest: this_thread.in_steps_conv_done_skipped[THEN iffD1]) - { assume "recvStep st" then - obtain l pt where "st = Recv l pt" by (cases st) auto + { assume "recvStep st" hence "\ m. Some m = inst s i (stepPat st) \ Ln m \ St (i, st)" - using steps by(auto intro!: Ln_before_inp) + using steps by (auto dest!: recvStepD Ln_before_inp) } note input = this + { + assume "matchEqStep st" + hence "exec_match s i (matchVar st) (stepPat st)" + using steps by (auto dest!: matchEqStepD match_eq_rule) + } + note match_eq = this + { + assume "notMatchStep st" + hence "\ exec_match s i (matchVar st) (stepPat st)" + using steps by (auto dest!: notMatchStepD not_match_rule) + } + note not_match = this have "listOrd R st st'" using nextRel and R_split and done_split @@ -300,7 +321,7 @@ apply - apply(drule this_thread.in_steps_conv_done_skipped[THEN iffD1]) by(fastforce dest!: this_thread.roleOrd_notSkipped_imp_listOrd_trace dest:listOrd_imp_predOrd)+ - note input and this + note input and match_eq and not_match and this } ultimately show ?thesis by (auto simp: prefixClose_def) @@ -310,15 +331,18 @@ lemma ext_prefixClose: "\ (i, step) \ steps t; roleMap r i = Some R \ \ - prefixClose s t R step i \ - (recvStep step \ (\ m. Some m = inst s i (stepPat step) \ Ln m \ St (i, step)))" - by (cases step) (fastforce intro!: prefixCloseI Ln_before_inp)+ + prefixClose s t R step i \ + (recvStep step \ (\ m. Some m = inst s i (stepPat step) \ Ln m \ St (i, step))) \ + (matchEqStep step \ exec_match s i (matchVar step) (stepPat step)) \ + (notMatchStep step \ \ exec_match s i (matchVar step) (stepPat step))" +by (cases step) + (auto dest: prefixCloseI Ln_before_inp matchEqStepD match_eq_rule notMatchStepD not_match_rule) text{* Used for prefix closing assumptions corresponding to a case of an annotation completeness induction proof. *} -lemma thread_prefixClose: +lemma thread_prefixClose: assumes thread_exists: "r i = Some (step#done, todo, skipped)" and not_skipped: "step \ skipped" shows @@ -326,21 +350,29 @@ ((recvStep st \ (\ m. Some m = inst s i (stepPat st) \ predOrd t (Ln m) (St (i, st))) ) \ - predOrd t (St (i, st)) (St (i, st'))) + (matchEqStep st \ exec_match s i (matchVar st) (stepPat st)) \ + (notMatchStep st \ \ exec_match s i (matchVar st) (stepPat st)) \ + predOrd t (St (i, st)) (St (i, st'))) ) \ (recvStep (last (step#done)) \ - (\ m. Some m = inst s i (stepPat (last (step#done))) \ + (\ m. Some m = inst s i (stepPat (last (step#done))) \ predOrd t (Ln m) (St (i, (last (step#done)))) ) + ) \ + (matchEqStep (last (step#done)) \ + exec_match s i (matchVar (last (step#done))) (stepPat (last (step#done))) + ) \ + (notMatchStep (last (step#done)) \ + \ exec_match s i (matchVar (last (step#done))) (stepPat (last (step#done))) )" - (is "?prefix \ ?inp_last") + (is "?prefix \ ?inp_last \ ?match_eq_last \ ?not_match_last") proof - interpret this_thread: reachable_thread P t r s i "step#done" todo skipped using thread_exists by unfold_locales auto { assume recv: "recvStep (last (step#done))" hence last_step: "(i, last (step#done)) \ steps t" - proof + proof - obtain l pt where recv_eq: "(Recv l pt) = (last (step # done))" using recv by (fastforce dest!: recvStepD) @@ -349,10 +381,39 @@ using thread_exists recv_eq by(fastforce dest!: this_thread.in_steps_recv[THEN iffD1]) qed - hence "?inp_last" - by (cases "last (step # done)") (fastforce dest!: Ln_before_inp)+ + hence "?inp_last" by (fastforce dest: recvStepD Ln_before_inp) } moreover + { + assume match: "matchEqStep (last (step#done))" + hence last_step: "(i, last (step#done)) \ steps t" + proof - + obtain l v pt + where match_eq: "(Match l True v pt) = (last (step # done))" + using match by (fastforce dest!: matchEqStepD) + hence "Match l True v pt \ set (step # done)" by auto + thus ?thesis + using thread_exists match_eq + by(fastforce dest!: this_thread.in_steps_recv[THEN iffD1]) + qed + hence "?match_eq_last" by (fastforce dest: matchEqStepD match_eq_rule) + } + moreover + { + assume match: "notMatchStep (last (step#done))" + hence last_step: "(i, last (step#done)) \ steps t" + proof - + obtain l v pt + where match_eq: "(Match l False v pt) = (last (step # done))" + using match by (fastforce dest!: notMatchStepD) + hence "Match l False v pt \ set (step # done)" by auto + thus ?thesis + using thread_exists match_eq + by(fastforce dest!: this_thread.in_steps_recv[THEN iffD1]) + qed + hence "?not_match_last" by (fastforce dest: notMatchStepD not_match_rule) + } + moreover { fix st st' assume "nextRel (step # (filter (\ x. \ (noteStep x)) done)) st st'" @@ -403,19 +464,25 @@ hence recv: "recvStep st \ \ m. Some m = inst s i (stepPat st) \ predOrd t (Ln m) (St (i, st))" using this_thread.roleMap - by (cases st) (auto intro!: Ln_before_inp dest: in_steps_predOrd1) - note step_ord recv + by (cases st) (auto dest: Ln_before_inp in_steps_predOrd1) + from step_ord have matchEq: + "matchEqStep st \ exec_match s i (matchVar st) (stepPat st)" + by (cases st) (auto dest: in_steps_predOrd1 matchEqStepD match_eq_rule) + from step_ord have notMatch: + "notMatchStep st \ \ exec_match s i (matchVar st) (stepPat st)" + by (cases st) (auto dest: in_steps_predOrd1 notMatchStepD not_match_rule) + note step_ord recv matchEq notMatch } ultimately - show ?thesis by fast + show ?thesis by blast qed end -text{* +(* TODO: Find the right place for this lemma. It is used only in the "prefix\_close" command. -*} +*) lemma steps_in_steps: "(i,step) \ steps t \ (i,step) \ steps t" by auto diff --git a/data/isabelle/src/ESPLogic/Protocol.thy b/data/isabelle/src/ESPLogic/Protocol.thy --- a/data/isabelle/src/ESPLogic/Protocol.thy +++ b/data/isabelle/src/ESPLogic/Protocol.thy @@ -30,15 +30,16 @@ | PFresh id | PVar varid | PHash pattern - | PTup pattern pattern - | PEnc pattern pattern + | PTup pattern pattern + | PEnc pattern pattern | PSign pattern pattern - | PSymK pattern pattern - | PShrK "varid set" (* variables denoting a set of agents sharing a key *) - | PAsymPK pattern - | PAsymSK pattern + | PSymK pattern pattern + | PShrK "varid set" --{* variables denoting a set of agents sharing a key *} + | PAsymPK pattern + | PAsymSK pattern + | PAny --{* wildcard for matching *} -(* bi-directional keys between two agents referenced by variables *) +text{* Bi-directional keys between two agents referenced by variables *} definition sKbd :: "varid \ varid \ pattern" where "sKbd a b = PShrK {a, b}" @@ -79,6 +80,7 @@ by (auto simp: sKbd_def) +text{* Free agent variables *} fun FAV :: "pattern \ id set" where "FAV (PVar (AVar a)) = {a}" @@ -97,13 +99,19 @@ by (auto simp: sKbd_def) -subsubsection{* Roles *} +subsubsection{* Role Steps *} text{* - Roles are non-empty lists of unique send and receive steps - such that no long-term keys are used in message texts and all + Roles are non-empty lists of unique send and receive steps + such that no long-term keys are used in message texts and all nonce variables are received before they are sent. + Additionally, match steps can be used to express local constraints + on variables and messages. Matching may be positive (equality + must hold in order to execute the step) or negative. + Note steps indicate possible points of dynamic information + leakage. + The labels allow to make steps with identical message unique. They are currently defaulted to strings, but could be anything. *} @@ -112,33 +120,105 @@ datatype notetype = RandGen | State | SessKey -datatype rolestep = Send lbl pattern | Recv lbl pattern | Note lbl notetype pattern +datatype rolestep = Send lbl pattern +| Recv lbl pattern +| Match lbl bool varid pattern +| Note lbl notetype pattern +text {* + Free message variables guaranteed to be instantiated (having + a semantic source) after a role step was executed. +*} +fun sourced_vars :: "rolestep \ id set" +where + "sourced_vars (Recv lbl pt) = FMV pt" +| "sourced_vars (Match lbl True v pt) = FMV pt" +| "sourced_vars _ = {}" + +text {* + Free message variables which must have been obtained previously + when performing a role step. +*} +fun used_vars :: "rolestep \ id set" +where + "used_vars (Send lbl msg) = FMV msg" +| "used_vars (Recv lbl pt) = {}" +| "used_vars (Match lbl True v pt) = {m. v = MVar m}" +| "used_vars (Match lbl False v pt) = {m. v = MVar m} \ FMV pt" +| "used_vars (Note lbl ty msg) = FMV msg" + +text {* Free variables of a role step *} +fun FV_rolestep :: "rolestep \ varid set" +where + "FV_rolestep (Send lbl pt) = FV pt" +| "FV_rolestep (Recv lbl pt) = FV pt" +| "FV_rolestep (Match lbl eq v pt) = {v} \ FV pt" +| "FV_rolestep (Note lbl ty pt) = FV pt" + +text {* Free agent variables of a role step *} +fun FAV_rolestep :: "rolestep \ id set" +where + "FAV_rolestep (Send lbl pt) = FAV pt" +| "FAV_rolestep (Recv lbl pt) = FAV pt" +| "FAV_rolestep (Match lbl eq v pt) = {a. v = AVar a} \ FAV pt" +| "FAV_rolestep (Note lbl ty pt) = FAV pt" + +text {* The pattern of a rolestep *} fun stepPat :: "rolestep \ pattern" where - "stepPat (Send lbl msg) = msg" -| "stepPat (Recv lbl msg) = msg" -| "stepPat (Note lbl ty msg) = msg" + "stepPat (Send lbl pt) = pt" +| "stepPat (Recv lbl pt) = pt" +| "stepPat (Match lbl eq v pt) = pt" +| "stepPat (Note lbl ty pt) = pt" +text {* The variable to match with (or not) *} +fun matchVar :: "rolestep \ varid" +where + "matchVar (Match l eq v pt) = v" +| "matchVar _ = undefined" + +text {* The type of possible information leakage *} fun noteType :: "rolestep \ notetype" where "noteType (Note l ty pt) = ty" +| "noteType _ = undefined" + +text {* Predicates for step types *} + fun sendStep :: "rolestep \ bool" where - "sendStep (Send lbl msg) = True" -| "sendStep (Recv lbl msg) = False" -| "sendStep (Note lbl ty msg) = False" + "sendStep (Send lbl pt) = True" +| "sendStep _ = False" fun noteStep :: "rolestep \ bool" where - "noteStep (Send lbl msg) = False" -| "noteStep (Recv lbl msg) = False" -| "noteStep (Note lbl ty msg) = True" + "noteStep (Note lbl ty pt) = True" +| "noteStep _ = False" +fun recvStep :: "rolestep \ bool" +where + "recvStep (Recv lbl pt) = True" +| "recvStep _ = False" -abbreviation recvStep where "recvStep x \ \sendStep x \ \ noteStep x" +fun matchStep :: "rolestep \ bool" +where + "matchStep (Match lbl eq v pt) = True" +| "matchStep _ = False" +text {* Distinguishing positive and negative match steps *} + +fun matchEqStep :: "rolestep \ bool" +where + "matchEqStep (Match lbl True v pt) = True" +| "matchEqStep _ = False" + +fun notMatchStep :: "rolestep \ bool" +where + "notMatchStep (Match lbl False v pt) = True" +| "notMatchStep _ = False" + + lemma sendStepD [simp]: assumes inStep: "sendStep step" shows "\ l pt. step = (Send l pt)" @@ -148,11 +228,36 @@ lemma recvStepD [simp]: assumes inStep: "recvStep step" - shows "\ l pt. step = (Recv l pt)" + shows "\ l v. step = (Recv l v)" using inStep proof(cases step) qed auto +lemma matchStepD [simp]: + assumes inStep: "matchStep step" + shows "\ l eq v pt. step = (Match l eq v pt)" +using inStep +proof (cases step) +qed auto + +lemma matchEqStepD [simp]: + assumes inStep: "matchEqStep step" + shows "\ l v pt. step = (Match l True v pt)" +using inStep +proof (cases step) + case (Match lbl eq v pt) + thus ?thesis using inStep by (cases eq, auto) +qed auto + +lemma notMatchStepD [simp]: + assumes inStep: "notMatchStep step" + shows "\ l v pt. step = (Match l False v pt)" +using inStep +proof (cases step) + case (Match lbl eq v pt) + thus ?thesis using inStep by (cases eq, auto) +qed auto + lemma noteStepD [simp]: assumes inStep: "noteStep step" shows "\ l ty pt. step = (Note l ty pt)" @@ -161,24 +266,28 @@ qed auto +subsubsection{* Roles *} + type_synonym "role" = "rolestep list" -fun recv_before :: "id set \ role \ bool" +text{* + Message variables whose values are semantically used in a + role step, i.e., sent or matched against, must have been + instantiated in an earlier step of the role. +*} +fun source_before_use :: "id set \ role \ bool" where - "recv_before bound [] = True" -| "recv_before bound (Recv _ msg # xs) = - recv_before (bound \ FMV msg) xs" -| "recv_before bound (Note _ _ msg # xs) = - ((\ v. v \ FMV msg \ v \ bound) \ recv_before bound xs)" -| "recv_before bound (Send _ msg # xs) = - ((\ v. v \ FMV msg \ v \ bound) \ recv_before bound xs)" + "source_before_use bound [] = True" +| "source_before_use bound (step # xs) = + ((used_vars step \ bound) + \ source_before_use (bound \ sourced_vars step) xs)" locale wf_role = distinct_list R for R :: "role" + - assumes recv_msgVar_first [iff]: "recv_before {} R" + assumes source_msgVar_first [iff]: "source_before_use {} R" - + subsubsection{* Protocols *} type_synonym proto = "role set" @@ -192,80 +301,44 @@ subsubsection{* Well-Formed Roles *} -lemma recv_before_sent_distinct_Send_FV: - "\ recv_before V (R@ Send lbl pt # R'); - distinct (R @ Send lbl pt # R'); - v \ FMV pt; v \ V +lemma source_before_use_distinct: + "\ source_before_use V (R @ step # R'); + distinct (R @ step # R'); + v \ used_vars step; v \ V \ \ - \ lbl' pt'. Recv lbl' pt' \ set R \ v \ FMV pt'" -proof(induct R arbitrary: V) - case (Cons step R) note IH = this show ?case - proof(cases step) - case (Send lbl pt) thus ?thesis using IH by auto - next - case (Recv lbl pt) thus ?thesis using IH by (auto, fast) + (\ step'. step' \ set R \ v \ sourced_vars step')" +proof (induct R arbitrary: V) + case (Cons step R) + note IH = this show ?case + proof (cases step) + case Send thus ?thesis using IH by fastforce next - case (Note lbl ty pt) thus ?thesis using IH by auto - qed -qed simp - -lemma recv_before_note_distinct_Note_FV: - "\ recv_before V (R@ Note lbl ty pt # R'); - distinct (R @ Note lbl ty pt # R'); - v \ FMV pt; v \ V - \ \ - \ lbl' pt'. Recv lbl' pt' \ set R \ v \ FMV pt'" -proof(induct R arbitrary: V) - case (Cons Note R) - note IH = this show ?case - proof(cases Note) - case (Send lbl pt) thus ?thesis using IH by auto + case Recv thus ?thesis using IH by fastforce next - case (Recv lbl pt) thus ?thesis using IH by (auto, fast) + case Match thus ?thesis using IH by fastforce next - case (Note lbl ty pt) thus ?thesis using IH by auto + case Note thus ?thesis using IH by fastforce qed -qed simp - +qed auto -lemma (in wf_role) Send_FV: - assumes Send: "Send lbl pt \ set R" (is "?send \ set R") - and FV: "v \ FMV pt" - shows "\ lbl' pt'. listOrd R (Recv lbl' pt') (Send lbl pt) \ v \ FMV pt'" -using Send +lemma (in wf_role) source_use_ord: + assumes useR: "ustep \ set R" + and useV: "v \ used_vars ustep" + shows "\ sstep. v \ sourced_vars sstep \ listOrd R sstep ustep" (is "\ sstep. ?source sstep") +using useR proof - - let ?send = "Send lbl pt" - and "\ lbl' pt'. ?received lbl' pt'" = ?thesis - assume "?send \ set R" then - obtain ys zs - where split: "R = ys @ ?send # zs" by (blast dest!: split_list) - moreover have "distinct R" and "recv_before {} R" by auto - ultimately obtain lbl' pt' where "Recv lbl' pt' \ set ys" - and "v \ FMV pt'" - by (fastforce dest!: recv_before_sent_distinct_Send_FV intro!: FV) - hence "?received lbl' pt'" using split by auto + assume "ustep \ set R" + then obtain ys zs + where split: "R = ys @ ustep # zs" by (blast dest!: split_list) + moreover have "distinct R" and "source_before_use {} R" by auto + ultimately obtain sstep where "v \ sourced_vars sstep" and "sstep \ set ys" + by (fastforce dest!: source_before_use_distinct intro!: useV) + hence "?source sstep" using split by fastforce thus ?thesis by blast qed -lemma (in wf_role) Note_FV: - assumes Note: "Note lbl ty pt \ set R" (is "?note \ set R") - and FV: "v \ FMV pt" - shows "\ lbl' pt'. listOrd R (Recv lbl' pt') (Note lbl ty pt) \ v \ FMV pt'" -using Note -proof - - let ?send = "Note lbl ty pt" - and "\ lbl' pt'. ?received lbl' pt'" = ?thesis - assume "?note \ set R" then - obtain ys zs - where split: "R = ys @ ?note # zs" by (blast dest!: split_list) - moreover have "distinct R" and "recv_before {} R" by auto - ultimately obtain lbl' pt' where "Recv lbl' pt' \ set ys" - and "v \ FMV pt'" - by (fastforce dest!: recv_before_note_distinct_Note_FV intro!: FV) - hence "?received lbl' pt'" using split by auto - thus ?thesis by blast -qed +subsubsection{* Auxiliary Lemmas *} lemma FV_FAV_conv[iff]: "(a \ FAV pt) = ((AVar a) \ FV pt)" @@ -283,11 +356,30 @@ by(cases vid) auto qed auto +lemma sourced_imp_FV[dest]: + "v \ sourced_vars st \ MVar v \ FV_rolestep st" +proof (cases st) + case (Match lbl eq mv pt) + assume "v \ sourced_vars st" + thus ?thesis using Match by (cases eq, auto) +qed auto +lemma used_imp_FV[dest]: + "v \ used_vars st \ MVar v \ FV_rolestep st" +proof (cases st) + case (Match lbl eq mv pt) + assume "v \ used_vars st" + thus ?thesis using Match by (cases eq, auto) +qed auto +lemma source_noteD[dest]: + "\ v \ sourced_vars st; noteStep st \ \ False" +by (auto dest: noteStepD) + + definition aVars:: "role \ varid set" where - "aVars role = foldr (\ st se. (AVar ` FAV (stepPat st)) \ se) role {}" + "aVars role = foldr (\ st se. (AVar ` FAV_rolestep st) \ se) role {}" lemma aVars_singleton[iff]: "AVar a \ aVars []" @@ -296,11 +388,11 @@ lemma aVars_Nil [iff]: "aVars [] = {}" by (auto simp: aVars_def) -lemma aVars_Cons [simp]: "aVars (s#xs) = (AVar ` FAV (stepPat s) \ aVars xs)" +lemma aVars_Cons [simp]: "aVars (s#xs) = (AVar ` FAV_rolestep s \ aVars xs)" by (auto simp: aVars_def) lemma aVars_FAV_conv: - "(AVar a \ aVars R) = (\ s \ set R. \ pt. (stepPat s = pt \ a \ FAV pt))" + "(AVar a \ aVars R) = (\ s \ set R. a \ FAV_rolestep s)" by (induct R) ( fastforce simp add: aVars_def)+ @@ -347,8 +439,6 @@ )" proof (cases "[s\xs . \ noteStep s]") qed (fastforce simp add: firstComStep_def)+ - - end diff --git a/data/isabelle/src/ESPLogic/Syntax.thy b/data/isabelle/src/ESPLogic/Syntax.thy --- a/data/isabelle/src/ESPLogic/Syntax.thy +++ b/data/isabelle/src/ESPLogic/Syntax.thy @@ -29,7 +29,7 @@ subsubsection{* General Cryptographic Messages *} -notation (xsymbols) ExecMessage.inv ("[_]\<^isup>-\<^isup>1" [60] 58) +notation (xsymbols) ExecMessage.inv ("[_]\<^sup>-\<^sup>1" [60] 58) subsubsection{* Specification Messages *} @@ -63,6 +63,12 @@ translations "<|x, y, z|>" == "<|x, <|y, z|> |>" "<|x, y|>" == "CONST PTup x y" + + +subsubsection{* Protocol Role Steps *} + +abbreviation "MatchEq" where "MatchEq lbl \ Match lbl True" +abbreviation "NotMatch" where "NotMatch lbl \ Match lbl False" subsubsection{* Execution Messages *} diff --git a/data/isabelle/src/ESPLogic/Unify.thy b/data/isabelle/src/ESPLogic/Unify.thy --- a/data/isabelle/src/ESPLogic/Unify.thy +++ b/data/isabelle/src/ESPLogic/Unify.thy @@ -205,7 +205,7 @@ (* TODO: Remove hack by using Named_Thms data functor. *) val thm_by_name = Proof_Context.get_thm ctxt; val ss = ctxt - delsimps map thm_by_name ["tid_eq_commute", "reorient_store_eq_store"]; + delsimps map thm_by_name ["tid_eq_commute"]; (* substitute an equality theorem in the given list of 'done' and 'todo' theorems. The changed theorems from 'done' are readded @@ -316,10 +316,15 @@ local fun define_cmd name info f = Outer_Syntax.command name info - (Parse_Spec.name_facts >> (Toplevel.print oo (Toplevel.proof o (note_modified_thmss f)))); + (Parse_Spec.name_facts >> (Toplevel.proof o (note_modified_thmss f))); + + fun define_qualified_cmd name info f = + Outer_Syntax.command name info + (Parse.parname -- Parse_Spec.name_facts >> (fn (qualifier, args) => + args |> note_modified_thmss (f qualifier) |> Toplevel.proof)); in val _ = - define_cmd @{command_spec "note_prefix_closed"} + define_qualified_cmd @{command_spec "note_prefix_closed"} "prefix close facts and store them under the given name" ESPL_Methods.prefix_close_thms; diff --git a/data/isabelle/src/ESPLogic/WeakTyping.thy b/data/isabelle/src/ESPLogic/WeakTyping.thy --- a/data/isabelle/src/ESPLogic/WeakTyping.thy +++ b/data/isabelle/src/ESPLogic/WeakTyping.thy @@ -43,7 +43,7 @@ where "approx typing \ {q. case q of (t,r,s) \ \ (i,step) \ steps t. \ R. roleMap r i = Some R \ - (\ n. MVar n \ FV (stepPat step) \ + (\ n. MVar n \ FV_rolestep step \ s (MVar n, i) \ typing (R, n) i (t,r,s) )}" @@ -63,7 +63,7 @@ "((t,r,s) \ approx typing) = (\ (i,step) \ steps t. \ R. roleMap r i = Some R \ - (\ n. MVar n \ FV (stepPat step) \ + (\ n. MVar n \ FV_rolestep step \ s (MVar n, i) \ typing (R, n) i (t,r,s)))" by (auto simp: approx_def) @@ -72,7 +72,7 @@ "\ i step R n. \ (i,step) \ steps t; roleMap r i = Some R; - MVar n \ FV (stepPat step) + MVar n \ FV_rolestep step \ \ s (MV n i) \ typing (R, n) i (t,r,s)" shows "(t,r,s) \ approx typing" @@ -82,7 +82,7 @@ assumes approx: "(t,r,s) \ approx typing" and asms: "(i,step) \ steps t" "roleMap r i = Some R" - "MVar n \ FV (stepPat step)" + "MVar n \ FV_rolestep step" shows "s (MV n i) \ typing (R, n) i (t,r,s)" using approx asms by (auto simp: approx_unfold) @@ -247,23 +247,70 @@ by (rule monoTyp_freeD) auto +lemma (in reachable_thread) step_done_typing: + assumes typ_rule: + "\ step. + \ (i, step) \ steps t; + MVar v \ FV_rolestep step + \ \ s (MV v i) \ typing (done @ todo, v) i (t, r, s)" + and step_done: "step \ set done" + and step_var: "MVar v \ FV_rolestep step" + shows "s (MV v i) \ typing (done @ todo, v) i (t, r, s)" +proof (cases "step \ skipped") + case False + thus ?thesis using assms by auto +next + case True + note inSkipped = this + then obtain l ty pt + where noteEq: "(Note l ty pt) = step" + by(auto dest!: note_in_skipped) + hence "\ step'. listOrd (done@todo) step' (Note l ty pt) \ v \ sourced_vars step'" + using inSkipped step_done step_var + apply - + apply(subgoal_tac "v \ used_vars step") + apply(subgoal_tac "Note l ty pt \ set (done@todo)") + apply(drule source_use_ord) + by auto + then obtain step' + where roleBefore: "listOrd (done@todo) step' (Note l ty pt)" + and varSourced: "v \ sourced_vars step'" + by auto + have notNote: "\ noteStep step'" using varSourced by auto + have "step' \ set done" + using roleBefore step_done noteEq + apply - + apply(drule listOrd_append[THEN iffD1]) + apply(case_tac "listOrd done step' (Note l ty pt)") + apply(fastforce dest: in_set_listOrd1) + apply(case_tac "listOrd todo step' (Note l ty pt)") + apply(fastforce dest: in_set_listOrd2 done_notin_todoD) + apply(case_tac "step' \ set done \ Note l ty pt \ set todo") + by(auto dest: done_notin_todoD) + hence "(i, step') \ steps t" using notNote by (cases step', auto) + thus ?thesis + using varSourced by (auto intro!: typ_rule thread_exists) +qed + + lemma (in reachable_state) reachable_in_approxI: assumes monoTyp: "monoTyp typing" - and recv_case: + and source_case: "\ t r s i done todo skipped m R step n. \ R \ P; roleMap r i = Some R; (done, step # todo) \ set (splits R); - recvStep step; - MVar n \ FV (stepPat step); - \ step' \ set done. MVar n \ FV (stepPat step'); + \ sendStep step; \ noteStep step; + n \ sourced_vars step; + \ step' \ set done. MVar n \ FV_rolestep step'; hint ''completenessCase'' (step, n); (t,r,s) \ reachable P; (t,r,s) \ approx typing; r i = Some (done, step # todo, skipped); - Some m = inst s i (stepPat step); - m \ knows t + + recvStep step \ Some m = inst s i (stepPat step) \ m \ knows t; + matchEqStep step \ exec_match s i (matchVar step) (stepPat step) \ \ s (MV n i) \ typing (R, n) i (t @ [Step (i, step)], r(i \ (done @ [step], todo, skipped)), s)" shows "(t,r,s) \ approx typing" @@ -272,34 +319,33 @@ have "\ r i = Some (done, todo, skipped); (i,step) \ steps t; - MVar n \ FV (stepPat step) + MVar n \ FV_rolestep step \ \ s (MV n i) \ typing (done@todo, n) i (t,r,s)" proof(induct arbitrary: i "done" todo step n skipped rule: reachable_induct) case (send t r s i "done" l pt todo skipped m i' done' todo' step n skipped') then interpret th1: - reachable_thread P t r s i "done" "Send l pt # todo" skipped - by unfold_locales auto + reachable_thread P t r s i "done" "Send l pt # todo" skipped + by unfold_locales auto from send have "(i', step) \ steps t \ (i' = i) \ step = Send l pt" - (is "?old \ ?new") by auto + (is "?old \ ?new") by auto moreover { assume ?old - hence "s(MV n i') \ typing (done'@todo', n) i' (t,r,s)" - using send by (auto split: if_splits) - hence ?case - proof(rule monoTyp_freeD[OF monoTyp]) - qed (auto simp: th1.thread_exists) + hence "s(MV n i') \ typing (done'@todo', n) i' (t,r,s)" + using send by (auto split: if_splits) + hence ?case + proof(rule monoTyp_freeD[OF monoTyp]) + qed (auto simp: th1.thread_exists) } moreover { let ?role = "done @ Send l pt # todo" - note IH = send(2) - assume "?new" - hence "MVar n \ FV pt" - using send by auto - then obtain l' msg' - where "(i, Recv l' msg') \ steps t" - "MVar n \ FV msg'" - by (fastforce dest!: th1.send_step_FV[OF th1.thread_exists]) + note IH = send(2) + assume "?new" + moreover hence "n \ used_vars step" using send by auto + ultimately obtain step' + where "(i, step') \ steps t" + "n \ sourced_vars step'" + by (fastforce dest!: th1.source_step[OF th1.thread_exists]) hence typed: "s (MV n i) \ typing (?role, n) i (t, r, s)" by (auto dest: IH[OF th1.thread_exists]) have "done'@todo' = ?role" @@ -313,16 +359,16 @@ next case (recv t r s i "done" l pt todo skipped m i' done' todo' step n skipped') then interpret th1: - reachable_thread P t r s i "done" "Recv l pt # todo" skipped - by unfold_locales auto + reachable_thread P t r s i "done" "Recv l pt # todo" skipped + by unfold_locales auto from recv have "(i', step) \ steps t \ (i' = i) \ step = Recv l pt" - (is "?old \ ?new") by auto + (is "?old \ ?new") by auto moreover { assume ?old - hence "s(MV n i') \ typing (done'@todo', n) i' (t,r,s)" - using recv by (auto split: if_splits) - hence ?case using `?old` + hence "s(MV n i') \ typing (done'@todo', n) i' (t,r,s)" + using recv by (auto split: if_splits) + hence ?case using `?old` apply - apply(rule monoTyp_freeD[OF monoTyp]) apply(auto simp: th1.thread_exists) @@ -331,86 +377,31 @@ moreover { let ?role = "done @ Recv l pt # todo" note IH = recv(2) - assume "?new" + assume "?new" hence cur_thread: "?role = done' @ todo'" "i = i'" using recv by auto have ?case - proof(cases "\ step' \ set done. MVar n \ FV (stepPat step')") + proof(cases "\ step' \ set done. MVar n \ FV_rolestep step'") case True with recv - obtain step'' - where FV: "MVar n \ FV (stepPat step'')" - and step'': "step'' \ set done" + obtain step' + where FV: "MVar n \ FV_rolestep step'" + and step': "step' \ set done" by auto - thus ?thesis - proof(cases "step'' \ skipped") - case False - then obtain step' - where FV: "MVar n \ FV (stepPat step')" - and notinSkipped: "step' \ skipped" - and step': "(i,step') \ steps t" - using FV step'' - by(auto simp add: th1.in_steps_conv_done_skipped) - hence "s (MV n i) \ typing (?role, n) i (t, r, s)" - by (auto intro!: IH th1.thread_exists) - hence "s (MV n i') \ typing (done'@todo', n) i' (t, r, s)" - using cur_thread by simp - thus ?thesis - apply - - apply(rule monoTyp_freeD[OF monoTyp]) - apply(auto simp: th1.thread_exists) - done - next - case True - then obtain step' - where FV: "MVar n \ FV (stepPat step')" - and inSkipped: "step' \ skipped" - and inDone: "step' \ set done" - using FV step'' - by auto - then obtain l' ty' pt' - where noteEq: "(Note l' ty' pt') = step'" - by(auto dest!: th1.note_in_skipped) - - hence "\ l'' pt''. listOrd ?role (Recv l'' pt'') (Note l' ty' pt') \ MVar n \ FV (stepPat (Recv l'' pt''))" - using FV inSkipped inDone - apply - - apply(drule FV_FMV_conv[THEN iffD2]) - apply(subgoal_tac "Note l' ty' pt' \ set ?role") - apply(drule th1.Note_FV) - by (auto dest: FV_FMV_conv[THEN iffD1]) - then obtain l'' pt'' - where roleBefore: "listOrd ?role (Recv l'' pt'') (Note l' ty' pt')" - and varOfRecv: "MVar n \ FV (stepPat (Recv l'' pt''))" - by auto - hence "Recv l'' pt'' \ set done" - using inDone noteEq - apply - - apply(drule listOrd_append[THEN iffD1]) - apply(case_tac "listOrd done (Recv l'' pt'') (Note l' ty' pt')") - apply(fastforce dest: in_set_listOrd1) - apply(case_tac "listOrd (Recv l pt # todo) (Recv l'' pt'') (Note l' ty' pt')") - apply(fastforce dest: in_set_listOrd2 th1.done_notin_todoD) - apply(case_tac "Recv l'' pt'' \ set done \ Note l' ty' pt' \ set (Recv l pt # todo)") - by(auto dest: th1.done_notin_todoD) - hence "(i, Recv l'' pt'') \ steps t" by auto - - hence "s (MV n i) \ typing (?role, n) i (t, r, s)" - using varOfRecv by (auto intro!: IH th1.thread_exists) - hence "s (MV n i') \ typing (done'@todo', n) i' (t, r, s)" - using cur_thread by simp - thus ?thesis - apply - - apply(rule monoTyp_freeD[OF monoTyp]) - apply(auto simp: th1.thread_exists) - done - qed + hence "s (MV n i) \ typing (done'@todo', n) i (t, r, s)" + using th1.thread_exists cur_thread IH + by (metis th1.step_done_typing) + thus ?thesis using `?new` + apply - + apply(rule monoTyp_freeD[OF monoTyp]) + apply(auto simp: th1.thread_exists) + done next case False moreover have "(t, r, s) \ approx typing" by (auto simp: approx_unfold dest!: IH roleMap_SomeD) - moreover have "MVar n \ FV pt" - using `MVar n \ FV (stepPat step)` `?new` by auto + moreover note `?new` + moreover note `MVar n \ FV_rolestep step` moreover note `Some m = inst s i pt` moreover note `m \ knows t` moreover note cur_thread[symmetric] @@ -418,9 +409,9 @@ ultimately show ?thesis apply - apply(clarsimp simp del: fun_upd_apply) - apply(rule recv_case) + apply(rule source_case) apply(simp_all add: th1.role_in_P th1.roleMap th1.thread_exists - in_set_splits_conv remove_hints) + in_set_splits_conv remove_hints) done qed } @@ -428,30 +419,31 @@ next case (compr t r s i "done" l ty pt todo skipped m i' done' todo' step n skipped') then interpret th1: - reachable_thread P t r s i "done" "Note l ty pt # todo" skipped - by unfold_locales auto + reachable_thread P t r s i "done" "Note l ty pt # todo" skipped + by unfold_locales auto from compr have "(i', step) \ steps t \ (i' = i) \ step = Note l ty pt" - (is "?old \ ?new") by auto + (is "?old \ ?new") by auto moreover { assume ?old - hence "s(MV n i') \ typing (done'@todo', n) i' (t,r,s)" - using compr by (auto split: if_splits) - hence ?case - proof(rule monoTyp_freeD[OF monoTyp]) - qed (auto simp: th1.thread_exists) + hence "s(MV n i') \ typing (done'@todo', n) i' (t,r,s)" + using compr by (auto split: if_splits) + hence ?case + proof(rule monoTyp_freeD[OF monoTyp]) + qed (auto simp: th1.thread_exists) } moreover { let ?role = "done @ Note l ty pt # todo" - note IH = compr(2) - assume "?new" - hence "MVar n \ FV pt" + note IH = compr(2) + assume "?new" + hence "n \ used_vars (Note l ty pt)" using compr by auto - then obtain l' msg' - where "(i, Recv l' msg') \ steps t" - "MVar n \ FV msg'" - by (fastforce dest!: th1.note_step_FV[OF th1.thread_exists]) - hence typed: "s (MV n i) \ typing (?role, n) i (t, r, s)" + then obtain step' + where "(i, step') \ steps t" + "n \ sourced_vars step'" + by (fastforce dest!: th1.source_step[OF th1.thread_exists]) + moreover hence "MVar n \ FV_rolestep step'" by auto + ultimately have typed: "s (MV n i) \ typing (?role, n) i (t, r, s)" by (auto dest: IH[OF th1.thread_exists]) have "done'@todo' = ?role" using compr `?new` by auto @@ -464,15 +456,110 @@ next case (skip t r s i "done" l ty pt todo skipped i' done' todo' step n skipped') then interpret th1: - reachable_thread P t r s i "done" "Note l ty pt # todo" skipped - by unfold_locales auto + reachable_thread P t r s i "done" "Note l ty pt # todo" skipped + by unfold_locales auto from skip have "(i', step) \ steps t" (is "?old") by auto - hence "s(MV n i') \ typing (done'@todo', n) i' (t,r,s)" - using skip by (auto split: if_splits) - thus ?case - proof(rule monoTyp_freeD[OF monoTyp]) - qed (auto simp: th1.thread_exists) + hence "s(MV n i') \ typing (done'@todo', n) i' (t,r,s)" + using skip by (auto split: if_splits) + thus ?case + proof(rule monoTyp_freeD[OF monoTyp]) + qed (auto simp: th1.thread_exists) + next + case (match t r s i "done" l eq mv pt todo skipped i' done' todo' step n skipped') then + interpret th1: + reachable_thread P t r s i "done" "Match l eq mv pt # todo" skipped + by unfold_locales auto + from match + have "(i', step) \ steps t \ (i' = i) \ step = Match l eq mv pt" + (is "?old \ ?new") by auto + moreover + { assume ?old + hence "s (MV n i') \ typing (done'@todo', n) i' (t,r,s)" + using match by (auto split: if_splits) + hence ?case + proof (rule monoTyp_freeD[OF monoTyp]) + qed (auto simp: th1.thread_exists) + } + moreover + { let ?role = "done @ Match l eq mv pt # todo" + note IH = match(2) + assume "?new" + have ?case proof (cases eq) + case True + note eq_case = this + hence cur_thread: "?role = done' @ todo'" "i = i'" and + match_FV: "n \ used_vars step \ n \ sourced_vars step" + using `?new` match by auto + from match_FV show ?thesis proof + assume "n \ used_vars step" + with `?new` obtain step' + where "(i, step') \ steps t" + "n \ sourced_vars step'" + by (fastforce dest!: th1.source_step[OF th1.thread_exists]) + hence typed: "s (MV n i) \ typing (?role, n) i (t, r, s)" + by (auto dest: IH[OF th1.thread_exists]) + thus ?thesis using `?new` cur_thread(1) + apply - + apply(rule monoTyp_freeD[OF monoTyp]) + by (auto intro!: typed simp: th1.thread_exists) + next + assume "n \ sourced_vars step" + thus ?thesis + proof (cases "\ step' \ set done. MVar n \ FV_rolestep step'") + case True + with match + obtain step' + where FV: "MVar n \ FV_rolestep step'" + and step': "step' \ set done" + by auto + hence "s (MV n i) \ typing (done'@todo', n) i (t, r, s)" + using th1.thread_exists cur_thread IH + by (metis th1.step_done_typing) + thus ?thesis using `?new` + apply - + apply(rule monoTyp_freeD[OF monoTyp]) + apply(auto simp: th1.thread_exists) + done + next + case False + moreover have "(t, r, s) \ approx typing" + by (auto simp: approx_unfold dest!: IH roleMap_SomeD) + moreover note `?new` + moreover note `n \ sourced_vars step` + moreover have "exec_match s i mv pt" + using match eq_case by simp + moreover note cur_thread[symmetric] + + ultimately show ?thesis + apply - + apply(clarsimp simp del: fun_upd_apply) + apply(rule source_case) + apply(simp_all add: th1.role_in_P th1.roleMap th1.thread_exists + in_set_splits_conv remove_hints) + done + qed + qed + + next + case False note notMatch = this + moreover note `?new` + moreover hence "n \ used_vars step" using match notMatch by auto + ultimately obtain step' + where "(i, step') \ steps t" + "n \ sourced_vars step'" + by (fastforce dest!: th1.source_step[OF th1.thread_exists]) + hence typed: "s (MV n i) \ typing (?role, n) i (t, r, s)" + by (auto dest: IH[OF th1.thread_exists]) + have "done'@todo' = ?role" using match `?new` by auto + thus ?thesis using `?new` + apply - + apply(rule monoTyp_freeD[OF monoTyp]) + by (auto intro!: typed simp: th1.thread_exists) + qed + } + ultimately show ?case by fastforce + qed (auto intro: monoTyp_appendD[OF monoTyp]) } thus ?thesis unfolding approx_unfold by(auto elim!: roleMap_SomeE) @@ -487,37 +574,46 @@ *} lemma (in reachable_state) reachable_in_approxI_ext: assumes monoTyp: "monoTyp typing" - and recv_case: + and source_case: "\ t r s i done todo skipped m R step n. \ R \ P; roleMap r i = Some R; (done, step # todo) \ set (splits R); - recvStep step; - MVar n \ foldl (\ fv step'. fv - FV (stepPat step')) (FV (stepPat step)) done; + \ sendStep step; \ noteStep step; + n \ foldl (\ fv step'. fv - sourced_vars step') (sourced_vars step) done; hint ''completenessCase'' (step, n); (t,r,s) \ reachable P; (t,r,s) \ approx typing; - r i = Some (done, step # todo ,skipped); - Some m = inst s i (stepPat step); - m \ knows t - \ \ + r i = Some (done, step # todo, skipped); + \ st'. st' \ set done \ \ noteStep st' \ (i, st') \ steps t; + + recvStep step \ Some m = inst s i (stepPat step) \ m \ knows t; + matchEqStep step \ exec_match s i (matchVar step) (stepPat step) + \ \ s (MV n i) \ typing (R, n) i ( t @ [Step (i, step)], r(i \ (done @ [step], todo, skipped)), s)" shows "(t,r,s) \ approx typing" proof(induct rule: reachable_in_approxI[OF monoTyp]) case (1 t r s i "done" todo skipped m R step n) { fix v V assume "v \ V" - and "\step'\set done. v \ FV (stepPat step')" - hence "v \ foldl (\ fv step'. fv - FV (stepPat step')) V done" - by (induct "done" arbitrary: V) auto + and "\step'\set done. MVar v \ FV_rolestep step'" + hence "v \ foldl (\ fv step'. fv - sourced_vars step') V done" + by (induct "done" arbitrary: V) (auto intro!: sourced_imp_FV) } - hence "MVar n \ foldl (\ fv step'. fv - FV (stepPat step')) (FV (stepPat step)) done" - using 1 by auto - thus ?case using 1 + hence "n \ foldl (\ fv step'. fv - sourced_vars step') (sourced_vars step) done" + using 1 by auto + moreover { + interpret thread: reachable_thread P t r s i "done" "(step # todo)" skipped + using 1 by unfold_locales auto + fix st' + assume "st' \ set done" and "\ noteStep st'" + hence "(i, st') \ steps t" by (auto intro: thread.not_note_done_in_steps) + } + ultimately show ?case using 1 apply(subgoal_tac "True") apply(clarsimp) - apply(rule recv_case) + apply(rule source_case) by(assumption | simp add: remove_hints)+ qed @@ -875,12 +971,13 @@ hint ''case_name'' ''fake'' ) \ (\ R \ P. \ i. roleMap r i = Some R \ - (\ step \ set R. + (\ step \ set R. (sendStep step \ noteStep step) \ (\ m. Some m = inst s i (stepPat step) \ decrChain [] t {St (i, step)} m m') \ prefixClose s t R step i \ (\ v \ FV (stepPat step). \ n. v = MVar n \ - s (MVar n, i) \ typing (R, n) i (t,r,s)) \ + s (MVar n, i) \ typing (R, n) i (t,r,s) \ + hint ''case_name_subst'' n) \ hint ''decrChainFrom'' (i, R, step) \ hint ''case_name'' ''decrypt'' ) diff --git a/data/isabelle/src/ESPLogic/espl_definitions.ML b/data/isabelle/src/ESPLogic/espl_definitions.ML --- a/data/isabelle/src/ESPLogic/espl_definitions.ML +++ b/data/isabelle/src/ESPLogic/espl_definitions.ML @@ -21,7 +21,7 @@ (* Additional Utilities *) val unnamed_caseN: string - datatype steptyp = Recv | Send | Note of term + datatype steptyp = Recv | Send | Note of term | Match of bool * term val mk_rolestep: steptyp * term * term -> term val dest_rolestep: term -> steptyp * term * term val dest_role: term -> (steptyp * term * term) list @@ -76,15 +76,21 @@ ******************************************************************************) -datatype steptyp = Recv | Send | Note of term; +datatype steptyp = Recv | Send | Note of term | Match of bool * term; fun mk_rolestep (Send, lbl, msg) = @{const Send} $ lbl $ msg | mk_rolestep (Recv, lbl, msg) = @{const Recv} $ lbl $ msg | mk_rolestep (Note nTy, lbl, msg) = @{const Note} $ lbl $ nTy $ msg + | mk_rolestep (Match (true, mv), lbl, msg) = @{const Match} $ lbl $ @{const True} $ mv $ msg + | mk_rolestep (Match (false, mv), lbl, msg) = @{const Match} $ lbl $ @{const False} $ mv $ msg fun dest_rolestep (Const (@{const_name Send},_) $ lbl $ msg) = (Send, lbl, msg) | dest_rolestep (Const (@{const_name Recv},_) $ lbl $ msg) = (Recv, lbl, msg) | dest_rolestep (Const (@{const_name Note},_) $ lbl $ nTy $ msg) = (Note nTy, lbl, msg) + | dest_rolestep (Const (@{const_name Match},_) $ lbl $ Const (@{const_name True},_) $ mv $ msg) = + (Match (true, mv), lbl, msg) + | dest_rolestep (Const (@{const_name Match},_) $ lbl $ Const (@{const_name False},_) $ mv $ msg) = + (Match (false, mv), lbl, msg) | dest_rolestep t = raise TERM ("dest_rolestep", [t]) val dest_role = map dest_rolestep o HOLogic.dest_list @@ -178,14 +184,25 @@ val ss_full = lthy addsimps [step_def, msg_def] |> simpset_of; val sendStep_t = @{const sendStep} $ step_const; + val recvStep_t = @{const recvStep} $ step_const; + val matchStep_t = @{const matchStep} $ step_const; + val matchEqStep_t = @{const matchEqStep} $ step_const; + val notMatchStep_t = @{const notMatchStep} $ step_const; val noteStep_t = @{const noteStep} $ step_const; val stepPat_t = @{const stepPat} $ step_const; + val matchVar_t = @{const matchVar} $ step_const; val noteType_t = @{const noteType} $ step_const; + val sourced_vars_t = @{const sourced_vars} $ step_const; + val used_vars_t = @{const used_vars} $ step_const; + val FV_rolestep_t = @{const FV_rolestep} $ step_const; + val FAV_rolestep_t = @{const FAV_rolestep} $ step_const; + val inst_t = @{term "inst s i"} $ msg_const; - val FV_t = @{term "FV"} $ msg_const; - val FMV_t = @{term "FMV"} $ msg_const; - val FAV_t = @{term "FAV"} $ msg_const; + val any_inst_t = @{term "any_inst s i"} $ msg_const; + val FV_t = @{const FV} $ msg_const; + val FMV_t = @{const FMV} $ msg_const; + val FAV_t = @{const FAV} $ msg_const; in lthy (* unfold theorems *) @@ -193,13 +210,23 @@ (* step expansions *) |> #2 o notes_expansion ss_step [ (mk_binding "sendStep_conv", [([sendStep_t],[att_iff_add])]) + , (mk_binding "recvStep_conv", [([recvStep_t],[att_iff_add])]) + , (mk_binding "matchStep_conv", [([matchStep_t],[att_iff_add])]) + , (mk_binding "matchEqStep_conv", [([matchEqStep_t],[att_iff_add])]) + , (mk_binding "notMatchStep_conv", [([notMatchStep_t],[att_iff_add])]) , (mk_binding "noteStep_conv", [([noteStep_t],[att_iff_add])]) , (mk_binding "stepPat_conv", [([stepPat_t],[att_simp_add])]) + , (mk_binding "matchVar_conv", [([matchVar_t],[att_simp_add])]) , (mk_binding "noteType_conv", [([noteType_t],[att_simp_add])]) + , (mk_binding "sourced_vars_conv", [([sourced_vars_t],[att_simp_add])]) + , (mk_binding "used_vars_conv", [([used_vars_t],[att_simp_add])]) + , (mk_binding "FV_rolestep_conv", [([FV_rolestep_t],[att_simp_add])]) + , (mk_binding "FAV_rolestep_conv", [([FAV_rolestep_t],[att_simp_add])]) ] (* full expansions *) |> notes_expansion ss_full [ (mk_binding "inst_conv", [([inst_t], [att_simp_add])]) + , (mk_binding "any_inst_conv", [([any_inst_t], [att_simp_add])]) , (mk_binding "FV_conv", [([FV_t], [att_simp_add])]) , (mk_binding "FMV_conv", [([FMV_t], [att_simp_add])]) , (mk_binding "FAV_conv", [([FAV_t], [att_simp_add])]) @@ -260,13 +287,14 @@ val ss_role = ctxt addsimps [role_def, @{thm prefixClose_def}] |> simpset_of; val ss_full = ctxt addsimps ([role_def, @{thm prefixClose_def}] @ pat_defs @ step_defs @ - @{thms wf_role_def distinct_list_def wf_role_axioms_def}) |> simpset_of + @{thms wf_role_def distinct_list_def wf_role_axioms_def}) |> simpset_of; - fun simp_tactic {prems, context} = FIRSTGOAL (Simplifier.full_simp_tac (put_simpset ss_full context)); + fun simp_tactic {prems=_, context} = FIRSTGOAL (Simplifier.full_simp_tac (put_simpset ss_full context)); val distinct_steps_thms = prove_distinctness ctxt simp_tactic step_consts; - val ss_prefixClose = ctxt addsimps ([role_def, @{thm prefixClose_def}] @ distinct_steps_thms) |> simpset_of; + val ss_prefixClose = ctxt addsimps ([role_def, @{thm prefixClose_def}] @ distinct_steps_thms @ + @{thms exec_match_def}) |> simpset_of; val wf_goal = HOLogic.mk_Trueprop (@{const wf_role} $ role_const); @@ -489,7 +517,16 @@ #1 o dest_msg_eq; val fixed_msg = msg_name o #2 o dest_msg_eq; - val subst = try hd (ESPL_Utils.gather_props subst_var prems); + (* We only use substitutions which are enabled by the corresponding hint. + This excludes equalities introduced by the MatchEq rule from the name + computation. + *) + val naming_substs = map HOLogic.dest_string (Hints.gather_by_name "case_name_subst" prems); + fun is_naming_subst v1 = exists (fn v2 => v1 = v2) naming_substs; + + val subst = prems |> ESPL_Utils.gather_props subst_var + |> filter is_naming_subst + |> try hd; val fixed = try hd (ESPL_Utils.gather_props fixed_msg prems); in if is_none subst andalso is_none fixed then @@ -761,7 +798,7 @@ val mono_typ_th = (@{const monoTyp} $ typ_const) |> HOLogic.mk_Trueprop |> Thm.cterm_of (Proof_Context.theory_of ctxt) - |> (fn ct => Goal.prove_internal [] ct + |> (fn ct => Goal.prove_internal ctxt [] ct (K autom_tac) ); in diff --git a/data/isabelle/src/ESPLogic/espl_methods.ML b/data/isabelle/src/ESPLogic/espl_methods.ML --- a/data/isabelle/src/ESPLogic/espl_methods.ML +++ b/data/isabelle/src/ESPLogic/espl_methods.ML @@ -24,7 +24,7 @@ ((bool * term) * thm option) * (Context.generic * Token.T list) (* "prefix_close" proof state transformation *) - val prefix_close_thms: Proof.context -> thm list -> thm list + val prefix_close_thms: string -> Proof.context -> thm list -> thm list val prefix_close_cmd: Proof.state -> Proof.state val note_prefix_closed_cmd: Proof.state -> Proof.state @@ -84,7 +84,8 @@ end; (* The tactic underlying the "sources" proof method *) -fun sources_tac ctxt minimal msg_t opt_raw_rule facts = +fun sources_tac _ _ _ _ [] = (fn _ => fn _ => Seq.empty) (* fail when no facts are chained in *) + | sources_tac ctxt minimal msg_t opt_raw_rule facts = let val thy = Proof_Context.theory_of ctxt; val cert = Thm.cterm_of thy; @@ -108,7 +109,7 @@ val predOrd_elim_ths = @{thms in_knows_predOrd1 in_knows_predOrd2} val knows_thm = - Goal.prove_internal [] knows_ct + Goal.prove_internal ctxt [] knows_ct (fn facts' => ALLGOALS (Method.insert_tac (facts' @ facts)) THEN (ALLGOALS (assume_tac ORELSE' eresolve_tac predOrd_elim_ths) @@ -178,11 +179,11 @@ (* NOTE: this works only correctly in the context of a reachable_state locale as the theorem ext_prefixClose is dependent on this locale. *) -fun prefix_close_thms ctxt facts = +fun prefix_close_thms qualifier ctxt facts = let - val prefixClose_th = Proof_Context.get_thm ctxt "ext_prefixClose"; + val prefixClose_th = Proof_Context.get_thm ctxt (Long_Name.qualify qualifier "ext_prefixClose"); fun close step roleMap = [step, roleMap] MRS prefixClose_th; - val expand = Simplifier.simplify ctxt; + val expand = Simplifier.simplify (ctxt addsimps @{thms exec_match_def}); val distinct_prop = distinct (Thm.eq_thm); (* fun new_fact th = forall (not_equal (Thm.prop_of th) o Thm.prop_of) facts; *) @@ -204,7 +205,7 @@ fun note_prefix_closed_cmd state = let val ctxt = Proof.context_of state; val facts = Proof.the_facts state; - val facts' = facts @ prefix_close_thms ctxt facts + val facts' = facts @ prefix_close_thms "" ctxt facts in Proof.set_facts facts' state end (* A proof state transformation implementing prefix closing of @@ -215,14 +216,14 @@ val using = state |> Proof.goal |> (fn {context = ctxt, facts=using, goal=_} => - prefix_close_thms ctxt using) + prefix_close_thms "" ctxt using) in Proof.using [[(using,[])]] state end; (* registering the prefix_close command *) val _ = Outer_Syntax.command @{command_spec "prefix_close"} "prefix close facts being used" - (Scan.succeed (Toplevel.print o (Toplevel.proof prefix_close_cmd))); + (Scan.succeed (Toplevel.proof prefix_close_cmd)); (****************************************************************************** @@ -265,7 +266,7 @@ *) fun completeness_cases_attrib ctxt th = let - val ss = Context.proof_of ctxt addsimps @{thms finite_setdiff_compute}; + val ss = Context.proof_of ctxt addsimps @{thms finite_setdiff_compute exec_match_def}; fun add_case_info th = th |> Rule_Cases.add_consumes 0 |> Rule_Cases.name (completeness_case_names th) diff --git a/data/isabelle/src/ESPLogic/espl_utils.ML b/data/isabelle/src/ESPLogic/espl_utils.ML --- a/data/isabelle/src/ESPLogic/espl_utils.ML +++ b/data/isabelle/src/ESPLogic/espl_utils.ML @@ -150,7 +150,7 @@ inst is a positional instantiation. *) fun add_simple_locale b loc_name inst thy = - Expression.add_locale I b (Binding.empty) + Expression.add_locale b (Binding.empty) ( [ ( Locale.intern thy loc_name , ( ("",false) , Expression.Positional inst diff --git a/data/isabelle/src/isar-keywords.el b/data/isabelle/src/isar-keywords.el deleted file mode 100644 --- a/data/isabelle/src/isar-keywords.el +++ /dev/null @@ -1,704 +0,0 @@ -;; -;; Keyword classification tables for Isabelle/Isar. -;; 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 *** -;; - -(defconst isar-keywords-major - '("\\." - "\\.\\." - "Isabelle\\.command" - "ML" - "ML_command" - "ML_file" - "ML_prf" - "ML_val" - "ProofGeneral\\.inform_file_processed" - "ProofGeneral\\.inform_file_retracted" - "ProofGeneral\\.kill_proof" - "ProofGeneral\\.pr" - "ProofGeneral\\.process_pgip" - "ProofGeneral\\.restart" - "ProofGeneral\\.undo" - "abbreviation" - "also" - "apply" - "apply_end" - "arities" - "assume" - "atom_decl" - "attribute_setup" - "ax_specification" - "axiomatization" - "axioms" - "back" - "bnf_def" - "boogie_end" - "boogie_open" - "boogie_status" - "boogie_vc" - "bundle" - "by" - "cannot_undo" - "case" - "cd" - "chapter" - "class" - "class_deps" - "classes" - "classrel" - "codata" - "code_abort" - "code_class" - "code_const" - "code_datatype" - "code_deps" - "code_include" - "code_instance" - "code_modulename" - "code_monad" - "code_pred" - "code_reflect" - "code_reserved" - "code_thms" - "code_type" - "coinductive" - "coinductive_set" - "commit" - "consts" - "context" - "corollary" - "cpodef" - "data" - "datatype" - "declaration" - "declare" - "def" - "default_sort" - "defer" - "defer_recdef" - "definition" - "defs" - "disable_pr" - "display_drafts" - "domain" - "domain_isomorphism" - "domaindef" - "done" - "enable_pr" - "end" - "enriched_type" - "equivariance" - "exit" - "export_code" - "extract" - "extract_type" - "finally" - "find_consts" - "find_theorems" - "find_unused_assms" - "fix" - "fixrec" - "from" - "full_prf" - "fun" - "function" - "guess" - "have" - "header" - "help" - "hence" - "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" - "interpret" - "interpretation" - "judgment" - "kill" - "kill_thy" - "lemma" - "lemmas" - "let" - "lift_definition" - "linear_undo" - "local_setup" - "locale" - "locale_deps" - "method_setup" - "moreover" - "next" - "nitpick" - "nitpick_params" - "no_notation" - "no_syntax" - "no_translations" - "no_type_notation" - "nominal_datatype" - "nominal_inductive" - "nominal_inductive2" - "nominal_primrec" - "nonterminal" - "notation" - "note" - "note_cyclic" - "note_prefix_closed" - "note_unified" - "notepad" - "obtain" - "oops" - "oracle" - "overloading" - "parse_ast_translation" - "parse_translation" - "partial_function" - "pcpodef" - "pr" - "prefer" - "prefix_close" - "presume" - "pretty_setmargin" - "prf" - "primrec" - "print_abbrevs" - "print_antiquotations" - "print_ast_translation" - "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" - "print_syntax" - "print_theorems" - "print_theory" - "print_trans_rules" - "print_translation" - "proof" - "prop" - "protocol" - "pwd" - "qed" - "quickcheck" - "quickcheck_generator" - "quickcheck_params" - "quit" - "quotient_definition" - "quotient_type" - "realizability" - "realizers" - "recdef" - "recdef_tc" - "record" - "refute" - "refute_params" - "remove_thy" - "rep_datatype" - "role" - "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" - "sublocale" - "subsect" - "subsection" - "subsubsect" - "subsubsection" - "syntax" - "syntax_declaration" - "term" - "termination" - "text" - "text_raw" - "then" - "theorem" - "theorems" - "theory" - "thm" - "thm_deps" - "thus" - "thy_deps" - "translations" - "try" - "try0" - "txt" - "txt_raw" - "typ" - "type_invariant" - "type_notation" - "type_synonym" - "typed_print_translation" - "typedecl" - "typedef" - "ultimately" - "undo" - "undos_proof" - "unfolding" - "unused_thms" - "use" - "use_thy" - "using" - "value" - "values" - "welcome" - "with" - "wrap_data" - "write" - "{" - "}")) - -(defconst isar-keywords-minor - '("advanced" - "and" - "assumes" - "attach" - "avoids" - "begin" - "binder" - "checking" - "congs" - "constrains" - "datatypes" - "defaults" - "defines" - "file" - "fixes" - "for" - "functions" - "hints" - "identifier" - "if" - "imports" - "in" - "includes" - "infix" - "infixl" - "infixr" - "is" - "keywords" - "lazy" - "module_name" - "monos" - "morphisms" - "no_dests" - "notes" - "obtains" - "open" - "output" - "overloaded" - "permissive" - "pervasive" - "rep_compat" - "shows" - "structure" - "unchecked" - "unsafe" - "uses" - "where")) - -(defconst isar-keywords-control - '("Isabelle\\.command" - "ProofGeneral\\.inform_file_processed" - "ProofGeneral\\.inform_file_retracted" - "ProofGeneral\\.kill_proof" - "ProofGeneral\\.process_pgip" - "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" - "use_thy")) - -(defconst isar-keywords-diag - '("ML_command" - "ML_val" - "ProofGeneral\\.pr" - "boogie_status" - "class_deps" - "code_deps" - "code_thms" - "display_drafts" - "export_code" - "find_consts" - "find_theorems" - "find_unused_assms" - "full_prf" - "header" - "help" - "locale_deps" - "nitpick" - "pr" - "pretty_setmargin" - "prf" - "print_abbrevs" - "print_antiquotations" - "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" - "print_syntax" - "print_theorems" - "print_theory" - "print_trans_rules" - "prop" - "pwd" - "quickcheck" - "refute" - "sledgehammer" - "smt_status" - "solve_direct" - "spark_status" - "term" - "thm" - "thm_deps" - "thy_deps" - "try" - "try0" - "typ" - "unused_thms" - "value" - "values" - "welcome")) - -(defconst isar-keywords-theory-begin - '("theory")) - -(defconst isar-keywords-theory-switch - '()) - -(defconst isar-keywords-theory-end - '("end")) - -(defconst isar-keywords-theory-heading - '("chapter" - "section" - "subsection" - "subsubsection")) - -(defconst isar-keywords-theory-decl - '("ML" - "ML_file" - "abbreviation" - "arities" - "atom_decl" - "attribute_setup" - "axiomatization" - "axioms" - "boogie_end" - "boogie_open" - "bundle" - "class" - "classes" - "classrel" - "codata" - "code_abort" - "code_class" - "code_const" - "code_datatype" - "code_include" - "code_instance" - "code_modulename" - "code_monad" - "code_reflect" - "code_reserved" - "code_type" - "coinductive" - "coinductive_set" - "consts" - "context" - "data" - "datatype" - "declaration" - "declare" - "default_sort" - "defer_recdef" - "definition" - "defs" - "domain" - "domain_isomorphism" - "domaindef" - "equivariance" - "extract" - "extract_type" - "fixrec" - "fun" - "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_setup" - "locale" - "method_setup" - "nitpick_params" - "no_notation" - "no_syntax" - "no_translations" - "no_type_notation" - "nominal_datatype" - "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" - "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" - "use")) - -(defconst isar-keywords-theory-script - '("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" - "wrap_data")) - -(defconst isar-keywords-qed - '("\\." - "\\.\\." - "by" - "done" - "sorry")) - -(defconst isar-keywords-qed-block - '("qed")) - -(defconst isar-keywords-qed-global - '("oops")) - -(defconst isar-keywords-proof-heading - '("sect" - "subsect" - "subsubsect")) - -(defconst isar-keywords-proof-goal - '("have" - "hence" - "interpret")) - -(defconst isar-keywords-proof-block - '("next" - "proof")) - -(defconst isar-keywords-proof-open - '("{")) - -(defconst isar-keywords-proof-close - '("}")) - -(defconst isar-keywords-proof-chain - '("finally" - "from" - "then" - "ultimately" - "with")) - -(defconst isar-keywords-proof-decl - '("ML_prf" - "also" - "include" - "including" - "let" - "moreover" - "note" - "note_cyclic" - "note_prefix_closed" - "note_unified" - "txt" - "txt_raw" - "unfolding" - "using" - "write")) - -(defconst isar-keywords-proof-asm - '("assume" - "case" - "def" - "fix" - "presume")) - -(defconst isar-keywords-proof-asm-goal - '("guess" - "obtain" - "show" - "thus")) - -(defconst isar-keywords-proof-script - '("apply" - "apply_end" - "back" - "defer" - "prefer")) - -(provide 'isar-keywords) diff --git a/dist/build/scyther-proof/scyther-proof-tmp/Scyther/Theory/Lexer.hs b/dist/build/scyther-proof/scyther-proof-tmp/Scyther/Theory/Lexer.hs new file mode 100644 --- /dev/null +++ b/dist/build/scyther-proof/scyther-proof-tmp/Scyther/Theory/Lexer.hs @@ -0,0 +1,623 @@ +{-# LANGUAGE CPP,MagicHash #-} +{-# LINE 1 "src/Scyther/Theory/Lexer.x" #-} + +-- Ignore the slew of warnings from definitions generated by Alex. +-- NOTE: you should disable this line when working on this module to make sure +-- that you don't miss important warnings. +{-# OPTIONS_GHC -fno-warn-missing-signatures -fno-warn-unused-binds #-} +{-# OPTIONS_GHC -fno-warn-unused-matches -fno-warn-name-shadowing #-} +{-# OPTIONS_GHC -fno-warn-unused-imports #-} + +module Scyther.Theory.Lexer where + +import Control.Applicative +import Control.Monad +import Data.Word (Word8) +import qualified Codec.Binary.UTF8.String as UTF8 + +#if __GLASGOW_HASKELL__ >= 603 +#include "ghcconfig.h" +#elif defined(__GLASGOW_HASKELL__) +#include "config.h" +#endif +#if __GLASGOW_HASKELL__ >= 503 +import Data.Array +import Data.Char (ord) +import Data.Array.Base (unsafeAt) +#else +import Array +import Char (ord) +#endif +#if __GLASGOW_HASKELL__ >= 503 +import GHC.Exts +#else +import GlaExts +#endif +alex_base :: AlexAddr +alex_base = AlexA# 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+ +alex_table :: AlexAddr +alex_table = AlexA# 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+ +alex_check :: AlexAddr +alex_check = AlexA# 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+ +alex_deflt :: AlexAddr +alex_deflt = AlexA# "\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\x10\x00\x10\x00\x12\x00\x12\x00\x14\x00\x14\x00\xff\xff\x1e\x00\x1e\x00\x24\x00\x24\x00\x27\x00\x27\x00\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\x3b\x00\x3b\x00\x3b\x00\xff\xff\xff\xff\xff\xff\x33\x00\x33\x00\x33\x00\x29\x00\x29\x00\x29\x00\xff\xff\x29\x00\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff"# + +alex_accept = listArray (0::Int,121) [AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccSkip,AlexAccSkip,AlexAcc (alex_action_2),AlexAcc (alex_action_3),AlexAcc (alex_action_4),AlexAcc (alex_action_5),AlexAcc (alex_action_6),AlexAcc (alex_action_7),AlexAcc (alex_action_8),AlexAcc (alex_action_9),AlexAcc (alex_action_10),AlexAcc (alex_action_10),AlexAcc (alex_action_10),AlexAcc (alex_action_10),AlexAcc (alex_action_11),AlexAcc (alex_action_12),AlexAcc (alex_action_13),AlexAcc (alex_action_14),AlexAcc (alex_action_15),AlexAcc (alex_action_15),AlexAcc (alex_action_15),AlexAcc (alex_action_15),AlexAcc (alex_action_16),AlexAcc (alex_action_17),AlexAcc (alex_action_18),AlexAcc (alex_action_19),AlexAcc (alex_action_20),AlexAcc (alex_action_21),AlexAcc (alex_action_22),AlexAcc (alex_action_23),AlexAcc (alex_action_24),AlexAcc (alex_action_25),AlexAcc (alex_action_26),AlexAcc (alex_action_27),AlexAcc (alex_action_28),AlexAcc (alex_action_29),AlexAcc (alex_action_30),AlexAcc (alex_action_31),AlexAcc (alex_action_32),AlexAcc (alex_action_33),AlexAcc (alex_action_34),AlexAcc (alex_action_35),AlexAcc (alex_action_36),AlexAcc (alex_action_37),AlexAcc (alex_action_38),AlexAcc (alex_action_39),AlexAcc (alex_action_40),AlexAcc (alex_action_41),AlexAcc (alex_action_42),AlexAcc (alex_action_43),AlexAcc (alex_action_44),AlexAcc (alex_action_45),AlexAcc (alex_action_46),AlexAcc (alex_action_47),AlexAcc (alex_action_48),AlexAcc (alex_action_49),AlexAcc (alex_action_50),AlexAcc (alex_action_51),AlexAcc (alex_action_52),AlexAcc (alex_action_53),AlexAcc (alex_action_54),AlexAcc (alex_action_55),AlexAcc (alex_action_55),AlexAcc (alex_action_55),AlexAcc (alex_action_55),AlexAcc (alex_action_55),AlexAcc (alex_action_55),AlexAcc (alex_action_55),AlexAcc (alex_action_55),AlexAcc (alex_action_55),AlexAcc (alex_action_55),AlexAcc (alex_action_55),AlexAcc (alex_action_55),AlexAcc (alex_action_55),AlexAcc (alex_action_55),AlexAcc (alex_action_55),AlexAcc (alex_action_55),AlexAcc (alex_action_55),AlexAcc (alex_action_55),AlexAcc (alex_action_55),AlexAcc (alex_action_55),AlexAcc (alex_action_55)] +{-# LINE 93 "src/Scyther/Theory/Lexer.x" #-} + + +-- | Lex a keyword +keyword :: Keyword -> AlexAction Keyword +keyword kw input len = return kw + +-- | Wrap a string into a keyword +scanString :: (String -> Keyword) -> AlexAction Keyword +scanString kw (_,_,_,input) len = return $ kw (take len input) + +{- +-- | Scan a string until EOF is encountered. +alexScanTokens :: String -> Either String [Keyword] +alexScanTokens inp = runAlex inp gather + where + gather = do + t <- alexMonadScan + case trace (show t) t of + EOF -> return [EOF] + _ -> (t:) `liftM` gather + +-- | Scan a file. +scanFile f = do + inp <- readFile f + return $ alexScanTokens inp +-} + +-- | Formal text types. +data TextType = + TextBegin String + | TextContent String + | TextEnd + deriving( Eq, Ord, Show ) + +-- | Lexable Keywords +data Keyword = + IDENT String + | TEXT TextType + | SQUOTE + | DQUOTE + | RIGHTARROW + | LEFTARROW + | LONGRIGHTARROW + | LONGLEFTARROW + | COMMA + | DOT + | COLON + | QUESTIONMARK + | BANG + | AND + | MID + | DOLLAR + | AT + | SHARP + | LPAREN + | RPAREN + | LBRACKET + | RBRACKET + | LBRACE + | RBRACE + | SLASH + | BACKSLASH + | TILDE + | HAT + | STAR + | UNDERSCORE + | MINUS + | PLUS + | EQUAL + | LESS + | GREATER + | EOF + | FORALL + | EXISTS + | LAND + | LOR + | LNOT + | APPROX + -- dummy keyword to get rid of overlapping pattern matches + | DUMMY_KEYWORD + deriving( Eq ) + +instance Show Keyword where + show kw = case kw of + IDENT i -> identifier i + TEXT t -> txt t + SQUOTE -> symbol "'" + DQUOTE -> symbol "\"" + RIGHTARROW -> symbol "->" + LEFTARROW -> symbol "<-" + LONGRIGHTARROW -> symbol "-->" + LONGLEFTARROW -> symbol "<--" + COMMA -> symbol "," + DOT -> symbol "." + COLON -> symbol ":" + QUESTIONMARK -> symbol "?" + BANG -> symbol "!" + AND -> symbol "&" + MID -> symbol "|" + DOLLAR -> symbol "$" + AT -> symbol "@" + SHARP -> symbol "#" + LPAREN -> symbol "(" + RPAREN -> symbol ")" + LBRACKET -> symbol "[" + RBRACKET -> symbol "]" + LBRACE -> symbol "{" + RBRACE -> symbol "}" + SLASH -> symbol "/" + BACKSLASH -> symbol "\\" + TILDE -> symbol "~" + HAT -> symbol "^" + STAR -> symbol "*" + UNDERSCORE -> symbol "_" + MINUS -> symbol "-" + PLUS -> symbol "+" + EQUAL -> symbol "=" + LESS -> symbol "<" + GREATER -> symbol ">" + EOF -> "end of file" + FORALL -> symbol "∀" + EXISTS -> symbol "∃" + LAND -> symbol "∧" + LOR -> symbol "∨" + LNOT -> symbol "¬" + APPROX -> symbol "≈" + DUMMY_KEYWORD -> "DUMMY_KEYWORD (this should not occur!)" + where + identifier i = "identifier `" ++ i ++ "'" + txt (TextBegin t) = "start of `" ++ t ++ "'" + txt (TextContent t) = "text `" ++ t ++ "'" + txt (TextEnd) = "start of text" + symbol s = "symbol `" ++ s ++ "'" + keyword s = "keyword `" ++ s ++ "'" + +-- ----------------------------------------------------------------------------- +-- Alex wrapper code. +-- +-- This code is in the PUBLIC DOMAIN; you may copy it freely and use +-- it for any purpose whatsoever. + +-- ----------------------------------------------------------------------------- +-- The input type + +type AlexInput = (AlexPosn, -- current position, + Char, -- previous char + [Word8], -- remaining bytes of current char + String) -- current input string + +alexInputPrevChar :: AlexInput -> Char +alexInputPrevChar (p,c,bs,s) = c + +alexGetByte :: AlexInput -> Maybe (Word8,AlexInput) +alexGetByte (p,c,(b:bs),s) = Just (b,(p,c,bs,s)) +alexGetByte (p,c,[],[]) = Nothing +alexGetByte (p,_,[],(c:s)) = let p' = alexMove p c + (b:bs) = UTF8.encodeChar c + in p' `seq` Just (b, (p', c, bs, s)) + +-- ----------------------------------------------------------------------------- +-- Token positions + +-- `Posn' records the location of a token in the input text. It has three +-- fields: the address (number of chacaters preceding the token), line number +-- and column of a token within the file. `start_pos' gives the position of the +-- start of the file and `eof_pos' a standard encoding for the end of file. +-- `move_pos' calculates the new position after traversing a given character, +-- assuming the usual eight character tab stops. + +data AlexPosn = AlexPn !Int !Int !Int + deriving (Eq) + +instance Show AlexPosn where + show (AlexPn _ l c) = "line "++show l++" column "++show c + +alexStartPos :: AlexPosn +alexStartPos = AlexPn 0 1 1 + +alexMove :: AlexPosn -> Char -> AlexPosn +alexMove (AlexPn a l c) '\t' = AlexPn (a+1) l (((c+7) `div` 8)*8+1) +alexMove (AlexPn a l c) '\n' = AlexPn (a+1) (l+1) 1 +alexMove (AlexPn a l c) _ = AlexPn (a+1) l (c+1) + + +-- ----------------------------------------------------------------------------- +-- Default monad + + +data AlexState = AlexState { + alex_pos :: !AlexPosn, -- position at current input location + alex_inp :: String, -- the current input + alex_chr :: !Char, -- the character before the input + alex_scd :: !Int, -- the current startcode + alex_ocd :: !Int, -- the old startcode before the comment started + alex_cmt :: [String] -- stack of begin comment identifiers + } + +-- Compile with -funbox-strict-fields for best results! + +runAlex :: String -> Alex a -> Either String a +runAlex input (Alex f) + = case f (AlexState {alex_pos = alexStartPos, + alex_inp = input, + alex_chr = '\n', + alex_scd = 0, + alex_ocd = 0, + alex_cmt = [] + }) of + Left msg -> Left msg + Right ( _, a ) -> Right a + +newtype Alex a = Alex { unAlex :: AlexState -> Either String (AlexState, a) } + +instance Functor Alex where + fmap = liftM + +instance Applicative Alex where + pure = return + (<*>) = ap + +instance Monad Alex where + m >>= k = Alex $ \s -> case unAlex m s of + Left msg -> Left msg + Right (s',a) -> unAlex (k a) s' + return a = Alex $ \s -> Right (s,a) + +alexGetPos :: Alex AlexPosn +alexGetPos = Alex $ \s@AlexState{alex_pos=pos} -> Right (s, pos) + +alexGetInput :: Alex AlexInput +alexGetInput + = Alex $ \s@AlexState{alex_pos=pos,alex_chr=c,alex_inp=inp} -> + Right (s, (pos,c,[],inp)) + +alexSetInput :: AlexInput -> Alex () +alexSetInput (pos,c,_,inp) + = Alex $ \s -> case s{alex_pos=pos,alex_chr=c,alex_inp=inp} of + s@(AlexState{}) -> Right (s, ()) + +alexError :: String -> Alex a +alexError message = Alex $ \s -> Left $ message ++ " in " ++ show (alex_pos s) + +alexGetStartCode :: Alex Int +alexGetStartCode = Alex $ \s@AlexState{alex_scd=sc} -> Right (s, sc) + +alexSetStartCode :: Int -> Alex () +alexSetStartCode sc = Alex $ \s -> Right (s{alex_scd=sc}, ()) + +alexGetOldStartCode :: Alex Int +alexGetOldStartCode = Alex $ \s@AlexState{alex_ocd=sc} -> Right (s, sc) + +alexSetOldStartCode :: Int -> Alex () +alexSetOldStartCode sc = Alex $ \s -> Right (s{alex_ocd=sc}, ()) + +alexGetComments :: Alex [String] +alexGetComments = Alex $ \s -> Right (s, alex_cmt s) + +alexSetComments :: [String] -> Alex () +alexSetComments cmt = Alex $ \s -> Right (s{alex_cmt=cmt}, ()) + +alexMonadScan = do + inp <- alexGetInput + sc <- alexGetStartCode + case alexScan inp sc of + AlexEOF -> alexEOF + AlexError inp' -> alexError "lexical error" + AlexSkip inp' len -> do + alexSetInput inp' + alexMonadScan + AlexToken inp' len action -> do + alexSetInput inp' + action inp len + +-- ----------------------------------------------------------------------------- +-- Useful token actions + +type AlexAction result = AlexInput -> Int -> Alex result + +-- just ignore this token and scan another one +skip :: AlexAction Keyword +skip input len = alexMonadScan + +-- ignore this token, but set the start code to a new value +begin :: Int -> AlexAction Keyword +begin code input len = do alexSetStartCode code; alexMonadScan + +-- | Begin a text starting of the given type. +beginText :: String -> Int -> AlexAction Keyword +beginText ty code _ _ = do + alexSetStartCode code + return $ TEXT $ TextBegin ty + +-- | End a text. +endText :: Int -> AlexAction Keyword +endText code _ _ = do + alexSetStartCode code + return $ TEXT TextEnd + +-- | Begin a comment starting with the given sign. +beginComment :: String -> Int -> AlexAction Keyword +beginComment cmtBegin code input len = do + cmts <- alexGetComments + alexSetComments $ cmtBegin : cmts + if null cmts + then alexGetStartCode >>= alexSetOldStartCode + else return () + alexSetStartCode code + alexMonadScan + +-- | End a comment that started with the given begin comment sign. +endComment :: String -> AlexAction Keyword +endComment cmtBegin input len = do + cmts <- alexGetComments + case cmts of + [] -> alexError $ "comment ended but no beginning '"++cmtBegin++"' marked." + (cmt:cmts') -> do + if cmt == cmtBegin + then do + alexSetComments cmts' + if null cmts' + then alexGetOldStartCode >>= alexSetStartCode + else return () + else return () + alexMonadScan + +-- perform an action for this token, and set the start code to a new value +-- andBegin :: AlexAction result -> Int -> AlexAction result +(action `andBegin` code) input len = do alexSetStartCode code; action input len + +alexEOF :: Alex Keyword +alexEOF = return EOF + + + + + +comment,text :: Int +comment = 1 +text = 2 +alex_action_2 = beginComment "(*" comment +alex_action_3 = beginComment "(*" comment +alex_action_4 = beginComment "(*" comment +alex_action_5 = endComment "(*" +alex_action_6 = beginComment "/*" comment +alex_action_7 = beginComment "/*" comment +alex_action_8 = beginComment "/*" comment +alex_action_9 = endComment "/*" +alex_action_10 = skip +alex_action_11 = beginText "text" text +alex_action_12 = beginText "section" text +alex_action_13 = beginText "subsection" text +alex_action_14 = endText 0 +alex_action_15 = scanString (TEXT . TextContent) +alex_action_16 = keyword FORALL +alex_action_17 = keyword EXISTS +alex_action_18 = keyword LAND +alex_action_19 = keyword LOR +alex_action_20 = keyword LNOT +alex_action_21 = keyword APPROX +alex_action_22 = keyword COMMA +alex_action_23 = keyword LPAREN +alex_action_24 = keyword RPAREN +alex_action_25 = keyword LBRACKET +alex_action_26 = keyword RBRACKET +alex_action_27 = keyword LBRACE +alex_action_28 = keyword RBRACE +alex_action_29 = keyword SLASH +alex_action_30 = keyword BACKSLASH +alex_action_31 = keyword SQUOTE +alex_action_32 = keyword DQUOTE +alex_action_33 = keyword TILDE +alex_action_34 = keyword HAT +alex_action_35 = keyword EQUAL +alex_action_36 = keyword COLON +alex_action_37 = keyword DOLLAR +alex_action_38 = keyword AT +alex_action_39 = keyword SHARP +alex_action_40 = keyword STAR +alex_action_41 = keyword LESS +alex_action_42 = keyword GREATER +alex_action_43 = keyword QUESTIONMARK +alex_action_44 = keyword BANG +alex_action_45 = keyword AND +alex_action_46 = keyword MID +alex_action_47 = keyword DOT +alex_action_48 = keyword UNDERSCORE +alex_action_49 = keyword MINUS +alex_action_50 = keyword PLUS +alex_action_51 = keyword RIGHTARROW +alex_action_52 = keyword LEFTARROW +alex_action_53 = keyword LONGRIGHTARROW +alex_action_54 = keyword LONGLEFTARROW +alex_action_55 = scanString IDENT +{-# LINE 1 "templates/GenericTemplate.hs" #-} +-- ----------------------------------------------------------------------------- +-- ALEX TEMPLATE +-- +-- This code is in the PUBLIC DOMAIN; you may copy it freely and use +-- it for any purpose whatsoever. + +-- ----------------------------------------------------------------------------- +-- INTERNALS and main scanner engine + + + + + + + +-- Do not remove this comment. Required to fix CPP parsing when using GCC and a clang-compiled alex. +#if __GLASGOW_HASKELL__ > 706 +#define GTE(n,m) (tagToEnum# (n >=# m)) +#define EQ(n,m) (tagToEnum# (n ==# m)) +#else +#define GTE(n,m) (n >=# m) +#define EQ(n,m) (n ==# m) +#endif + + + +data AlexAddr = AlexA# Addr# +-- Do not remove this comment. Required to fix CPP parsing when using GCC and a clang-compiled alex. +#if __GLASGOW_HASKELL__ < 503 +uncheckedShiftL# = shiftL# +#endif + +{-# INLINE alexIndexInt16OffAddr #-} +alexIndexInt16OffAddr (AlexA# arr) off = +#ifdef WORDS_BIGENDIAN + narrow16Int# i + where + i = word2Int# ((high `uncheckedShiftL#` 8#) `or#` low) + high = int2Word# (ord# (indexCharOffAddr# arr (off' +# 1#))) + low = int2Word# (ord# (indexCharOffAddr# arr off')) + off' = off *# 2# +#else + indexInt16OffAddr# arr off +#endif + + + + + +{-# INLINE alexIndexInt32OffAddr #-} +alexIndexInt32OffAddr (AlexA# arr) off = +#ifdef WORDS_BIGENDIAN + narrow32Int# i + where + i = word2Int# ((b3 `uncheckedShiftL#` 24#) `or#` + (b2 `uncheckedShiftL#` 16#) `or#` + (b1 `uncheckedShiftL#` 8#) `or#` b0) + b3 = int2Word# (ord# (indexCharOffAddr# arr (off' +# 3#))) + b2 = int2Word# (ord# (indexCharOffAddr# arr (off' +# 2#))) + b1 = int2Word# (ord# (indexCharOffAddr# arr (off' +# 1#))) + b0 = int2Word# (ord# (indexCharOffAddr# arr off')) + off' = off *# 4# +#else + indexInt32OffAddr# arr off +#endif + + + + + + +#if __GLASGOW_HASKELL__ < 503 +quickIndex arr i = arr ! i +#else +-- GHC >= 503, unsafeAt is available from Data.Array.Base. +quickIndex = unsafeAt +#endif + + + + +-- ----------------------------------------------------------------------------- +-- Main lexing routines + +data AlexReturn a + = AlexEOF + | AlexError !AlexInput + | AlexSkip !AlexInput !Int + | AlexToken !AlexInput !Int a + +-- alexScan :: AlexInput -> StartCode -> AlexReturn a +alexScan input (I# (sc)) + = alexScanUser undefined input (I# (sc)) + +alexScanUser user input (I# (sc)) + = case alex_scan_tkn user input 0# input sc AlexNone of + (AlexNone, input') -> + case alexGetByte input of + Nothing -> + + + + AlexEOF + Just _ -> + + + + AlexError input' + + (AlexLastSkip input'' len, _) -> + + + + AlexSkip input'' len + + (AlexLastAcc k input''' len, _) -> + + + + AlexToken input''' len k + + +-- Push the input through the DFA, remembering the most recent accepting +-- state it encountered. + +alex_scan_tkn user orig_input len input s last_acc = + input `seq` -- strict in the input + let + new_acc = (check_accs (alex_accept `quickIndex` (I# (s)))) + in + new_acc `seq` + case alexGetByte input of + Nothing -> (new_acc, input) + Just (c, new_input) -> + + + + case fromIntegral c of { (I# (ord_c)) -> + let + base = alexIndexInt32OffAddr alex_base s + offset = (base +# ord_c) + check = alexIndexInt16OffAddr alex_check offset + + new_s = if GTE(offset,0#) && EQ(check,ord_c) + then alexIndexInt16OffAddr alex_table offset + else alexIndexInt16OffAddr alex_deflt s + in + case new_s of + -1# -> (new_acc, input) + -- on an error, we want to keep the input *before* the + -- character that failed, not after. + _ -> alex_scan_tkn user orig_input (if c < 0x80 || c >= 0xC0 then (len +# 1#) else len) + -- note that the length is increased ONLY if this is the 1st byte in a char encoding) + new_input new_s new_acc + } + where + check_accs (AlexAccNone) = last_acc + check_accs (AlexAcc a ) = AlexLastAcc a input (I# (len)) + check_accs (AlexAccSkip) = AlexLastSkip input (I# (len)) + + +data AlexLastAcc a + = AlexNone + | AlexLastAcc a !AlexInput !Int + | AlexLastSkip !AlexInput !Int + +instance Functor AlexLastAcc where + fmap f AlexNone = AlexNone + fmap f (AlexLastAcc x y z) = AlexLastAcc (f x) y z + fmap f (AlexLastSkip x y) = AlexLastSkip x y + +data AlexAcc a user + = AlexAccNone + | AlexAcc a + | AlexAccSkip + + +-- used by wrappers +iUnbox (I# (i)) = i + diff --git a/scyther-proof.cabal b/scyther-proof.cabal --- a/scyther-proof.cabal +++ b/scyther-proof.cabal @@ -1,6 +1,6 @@ build-type: Simple name: scyther-proof -version: 0.8.0.0 +version: 0.10.0.0 license: GPL license-file: LICENSE category: Security, Theorem Provers @@ -86,7 +86,6 @@ isabelle/Makefile isabelle/README isabelle/ROOT - isabelle/src/isar-keywords.el isabelle/src/*.thy isabelle/src/ESPLogic/*.thy isabelle/src/ESPLogic/*.ML @@ -96,7 +95,7 @@ extra-source-files: .ghci interactive-only-src/Paths_scyther_proof.hs - src/Scyther/Theory/Lexer.x_src_only + src/Scyther/Theory/Lexer.x README.md CHANGES @@ -108,8 +107,8 @@ executable scyther-proof build-depends: base == 4.* , - array >= 0.3 && < 0.5 , - containers >= 0.4.2 && < 0.5 , + array >= 0.3 && < 0.6 , + containers >= 0.4.2 && < 0.6 , safe >= 0.2 && < 0.4 , mtl >= 2.1 && < 3.0, @@ -117,15 +116,18 @@ cmdargs >= 0.10.7 , filepath >= 1.2 && < 1.4 , directory >= 1.0 && < 1.3 , - process == 1.1.* , - time >= 1.1 && < 1.3 , + process >= 1.1 && < 1.3 , + time >= 1.1 && < 1.5 , parsec == 3.1.* , pretty >= 1.0 && < 1.2 , - tagsoup == 0.12.* , + tagsoup >= 0.12 && < 0.14 , json == 0.5.* , - uniplate == 1.6.* + uniplate == 1.6.* , + utf8-string >= 0.3.7 + build-tools: + alex >= 3.0 && < 3.2 if flag(threaded) ghc-options: -threaded diff --git a/src/Control/Monad/BoundedDFS.hs b/src/Control/Monad/BoundedDFS.hs --- a/src/Control/Monad/BoundedDFS.hs +++ b/src/Control/Monad/BoundedDFS.hs @@ -23,6 +23,7 @@ ) where +import Control.Applicative import Control.Monad import Control.Monad.State import Control.Monad.Reader @@ -41,11 +42,15 @@ -- | An unbounded depth-first search monad for searches formulated using -- MonadPlus. newtype UnboundedDFS c a = UnboundedDFS { runUnboundedDFS :: Maybe a } - deriving( Monad ) + deriving( Functor, Applicative, Monad ) instance MonadCost c (UnboundedDFS c) where updateCost _ = return () +instance Alternative (UnboundedDFS c) where + empty = mzero + (<|>) = mplus + instance MonadPlus (UnboundedDFS c) where mzero = UnboundedDFS $ mzero (UnboundedDFS m1) `mplus` (UnboundedDFS m2) = UnboundedDFS $ m1 `mplus` m2 @@ -55,7 +60,7 @@ -- All choices are handled committing and there is no differentiation between -- failure due to cost overrun and other failures. newtype BoundedDFS c a = BoundedDFS { unBoundedDFS :: ReaderT (c -> Bool) (StateT c Maybe) a } - deriving( Monad ) + deriving( Functor, Applicative, Monad ) instance MonadCost c (BoundedDFS c) where updateCost f = BoundedDFS $ do @@ -65,6 +70,10 @@ guard (cond b') put b' +instance Alternative (BoundedDFS c) where + empty = mzero + (<|>) = mplus + instance MonadPlus (BoundedDFS c) where mzero = BoundedDFS mzero m `mplus` _ = m @@ -86,7 +95,7 @@ BranchAndBound { unBranchAndBound :: ReaderT (c -> Bool) (StateT c Maybe) a } - deriving( Monad ) + deriving( Functor, Applicative, Monad ) -- | Run a branch and bound search. runBranchAndBound :: Cost c => BranchAndBound c a -> c -> Maybe (a, c) @@ -156,5 +165,8 @@ `mplus` -- m1 didn't do it, try m2 unBranchAndBound m2) - + +instance Cost c => Alternative (BranchAndBound c) where + empty = mzero + (<|>) = mplus diff --git a/src/Main.hs b/src/Main.hs --- a/src/Main.hs +++ b/src/Main.hs @@ -151,8 +151,8 @@ , " The '--html' flag requires the 'dot' tool from GraphViz available at:" , " " ++ "http://www.graphviz.org/" , " " - , " The '--isabelle' flag requires the 'Isabelle2013-2' release of Isabelle/HOL:" - , " " ++ "http://isabelle.in.tum.de/website-Isabelle2013-2/" + , " The '--isabelle' flag requires the 'Isabelle2014' release of Isabelle/HOL:" + , " " ++ "http://isabelle.in.tum.de/website-Isabelle2014/" , "" , " Check the '" ++ readmePath ++ "' file for instructions on how to load the generated theory files in Isabelle's interactive mode." ] @@ -734,8 +734,8 @@ putStrLn "" where check _ err - | "Graphviz" `isInfixOf` err = Right $ init err ++ ". OK." - | otherwise = Left $ unlines $ + | "graphviz" `isInfixOf` map toLower err = Right $ init err ++ ". OK." + | otherwise = Left $ unlines $ [ "WARNING:" , "" , " The dot tool seems not to be provided by Graphviz." @@ -752,40 +752,16 @@ ensureIsabelleESPL isabelle = do putStrLn $ "checking suitability of Isabelle tool: '" ++ isabelle ++ "'" _ <- testProcess checkVersion " version: " isabelle ["version"] "" - success <- testProcess checkLogics " installed logics: " isabelle ["findlogics"] "" - unless success buildESPL putStrLn "" where checkVersion out _ - | "Isabelle2013-2" `isInfixOf` out = Right $ init out ++ ". OK." + | "Isabelle2014" `isInfixOf` out = Right $ init out ++ ". OK." | otherwise = Left $ unlines $ [ "WARNING:" , "" - , " " ++ programName ++ " requires Isabelle2013-2." + , " " ++ programName ++ " requires Isabelle2014." , " Proof checking is likely not to work." - , " Please download Isabelle2013-2 from:" - , " http://isabelle.in.tum.de/website-Isabelle2013-2/" + , " Please download Isabelle2014 from:" + , " http://isabelle.in.tum.de/website-Isabelle2014/" ] - - checkLogics out _ - | "ESPL" `isInfixOf` out = Right $ init out ++ ". OK." - | otherwise = Left $ init out ++ ". WARNING: ESPL logic not installed." - - - buildESPL = do - putStrLn "---" - putStrLn "Attempting to build ESPL logic (this may take several minutes):" - theoryDir <- esplTheoryDir - let isamake args = - runProcess isabelle ("build" : "-d" : theoryDir : args) (Just theoryDir) Nothing Nothing Nothing Nothing - >>= waitForProcess - exitCode <- isamake ["-b", "ESPL"] - case exitCode of - ExitSuccess -> putStrLn "Sucess! :-)\n---" - ExitFailure code -> putStrLn $ unlines - [ " Logic building failed with code: " ++ show code - , " Proof checking is likely not to work." - , " To investigate the problem try manually loading/building the theories in" - , " '" ++ theoryDir ++ "'" - ] diff --git a/src/Scyther/Equalities.hs b/src/Scyther/Equalities.hs --- a/src/Scyther/Equalities.hs +++ b/src/Scyther/Equalities.hs @@ -9,6 +9,7 @@ , MVarEq , MsgEq , AnyEq(..) + , Inequality(..) , arbmEqToMsgEq , mvarEqToMsgEq @@ -31,6 +32,9 @@ , getPostEqs , toAnyEqs , anyEqTIDs + , anyEqAMIDs + , inequalityTIDs + , inequalityAMIDs -- ** Substitution , substTID @@ -40,12 +44,14 @@ , substAMID , substMsg , substAnyEq + , substInequality -- ** Additional Queries , threadRole , maxMappedTID , maxMappedArbMsgId , reflexive + , falseIneq , null -- * Mapping Logical Variables @@ -60,10 +66,12 @@ -- * Pretty Printing , sptAnyEq + , sptInequality ) where import Prelude hiding (null) +import qualified Data.List as L import qualified Data.Map as M import qualified Data.UnionFind as U import Data.Data @@ -124,12 +132,16 @@ TIDEq !TIDEq | TIDRoleEq !TIDRoleEq | RoleEq !RoleEq - | ArbMsgEq !ArbMsgEq + | ArbMsgEq !ArbMsgEq | AVarEq !AVarEq | MVarEq !MVarEq | MsgEq !MsgEq deriving( Eq, Ord, Show, Data, Typeable ) +-- | An inequality. Bound logical variables are universally quantified. +newtype Inequality = Inequality { getInequality :: AnyEq } + deriving( Eq, Ord, Show, Data, Typeable ) + -- | A conjunction of equality facts. -- -- Invariants for a value @eqs = Equalities tideqs roleeqs avareqs mvareqs arbmeqs@: @@ -275,7 +287,11 @@ MVarEq eq -> MsgEq $ substMVarEq eqs eq MsgEq eq -> MsgEq $ substMsgEq eqs eq +-- | Substitute both sides of an inequality. +substInequality :: Equalities -> Inequality -> Inequality +substInequality eqs = Inequality . substAnyEq eqs . getInequality + -- Checking for reflexivity --------------------------- @@ -298,6 +314,7 @@ MVarEq eq -> reflexive . MsgEq $ mvarEqToMsgEq eq MsgEq eq -> uncurry (==) eq + -- Deconstruction ----------------- @@ -352,7 +369,26 @@ MVarEq (v, m) -> return (mvarTID v) `mplus` msgTIDs m MsgEq (m1, m2) -> msgTIDs m1 `mplus` msgTIDs m2 +-- | The logical message variables occuring in an equality. +anyEqAMIDs :: AnyEq -> [ArbMsgId] +anyEqAMIDs eq = case eq of + TIDEq _ -> mzero + TIDRoleEq _ -> mzero + RoleEq _ -> mzero + ArbMsgEq (a, m) -> a : msgAMIDs m + AVarEq _ -> mzero + MVarEq (_, m) -> msgAMIDs m + MsgEq (m1, m2) -> msgAMIDs m1 `mplus` msgAMIDs m2 +-- | The threads occurring in an inequality. +inequalityTIDs :: Inequality -> [TID] +inequalityTIDs = anyEqTIDs . getInequality + +-- | The logical message variables occuring in an inequality. +inequalityAMIDs :: Inequality -> [ArbMsgId] +inequalityAMIDs = anyEqAMIDs . getInequality + + -- Unification -------------- @@ -574,12 +610,34 @@ maxMappedArbMsgId :: Equalities -> Maybe ArbMsgId maxMappedArbMsgId = fmap (fst . fst) . M.maxViewWithKey . arbmEqs - -- | Retrieve the role of a thread. threadRole :: TID -> Equalities -> Maybe Role threadRole tid eqs = M.lookup (substTID eqs tid) $ roleEqs eqs +-- | Test whether the equalities impose constraints on bound variables only. +onlyLocalConstraints :: Equalities -> Bool +onlyLocalConstraints eqs = + M.null (tidEqs eqs) && + M.null (roleEqs eqs) && + M.null (avarEqs eqs) && + all isBoundVarMsg (map snd $ M.toList $ mvarEqs eqs) && + all isBoundVarEq (M.toList $ arbmEqs eqs) && + L.null (U.toList (postEqs eqs)) + where + isBoundVar (BoundVarId _) = True + isBoundVar _ = False + isBoundVarMsg (MArbMsg v) = isBoundVar v + isBoundVarMsg _ = False + + isBoundVarEq (lhs, rhs) = isBoundVar lhs || isBoundVarMsg rhs + +-- | Check if an inequality is trivially false, i.e., there exists an +-- substitution of bound logical variables which makes it reflexive. +falseIneq :: Inequality -> Bool +falseIneq ineq = maybe False onlyLocalConstraints $ solve [getInequality ineq] empty + + ------------------------------------------------------------------------------- -- Abusing equalities to represent mappings of logical variables ------------------------------------------------------------------------------- @@ -641,42 +699,73 @@ -- Helper functions for pretty printing --------------------------------------- -ppEq :: (a -> Doc) -> (b -> Doc) -> (a, b) -> Doc -ppEq pp1 pp2 (x1, x2) = pp1 x1 <-> char '=' <-> pp2 x2 +ppEq :: Doc -> (a -> Doc) -> (b -> Doc) -> (a, b) -> Doc +ppEq sym pp1 pp2 (x1, x2) = pp1 x1 <-> sym <-> pp2 x2 -ppEq' :: (a -> Doc) -> (a, a) -> Doc -ppEq' pp = ppEq pp pp +ppEq' :: Doc -> (a -> Doc) -> (a, a) -> Doc +ppEq' sym pp = ppEq sym pp pp +filterBoundVars :: [ArbMsgId] -> [ArbMsgId] +filterBoundVars = filter p + where + p (BoundVarId _) = True + p (FreeVarId _) = False + -- Isar ------- +ppIsarEq :: Doc -> IsarConf -> AnyEq -> Doc +ppIsarEq sym conf eq0 = case eq0 of + TIDEq eq -> ppEq' sym ppIsar eq + RoleEq eq -> ppEq' sym (text . roleName) eq + TIDRoleEq (tid, role) -> + text "roleMap r" <-> ppIsar tid <-> sym <-> text ("Some " ++ roleName role) + ArbMsgEq eq -> ppEq sym ppIsar ppIsar eq + AVarEq eq -> ppEq' sym ppIsar eq + MVarEq eq -> ppEq sym ppIsar ppIsar eq + MsgEq eq -> ppEq' sym ppIsar eq + where + ppIsar :: Isar a => a -> Doc + ppIsar = isar conf + instance Isar AnyEq where - isar conf eq0 = case eq0 of - TIDEq eq -> ppEq' ppIsar eq - RoleEq eq -> ppEq' (text . roleName) eq - TIDRoleEq (tid, role) -> - text "roleMap r" <-> ppIsar tid <-> text ("= Some " ++ roleName role) - ArbMsgEq eq -> ppEq ppIsar ppIsar eq - AVarEq eq -> ppEq' ppIsar eq - MVarEq eq -> ppEq ppIsar ppIsar eq - MsgEq eq -> ppEq' ppIsar eq + isar = ppIsarEq (char '=') + +instance Isar Inequality where + isar conf eq = if L.null boundVars + then ineq + else parens $ quantifiers <-> ineq where - ppIsar :: Isar a => a -> Doc - ppIsar = isar conf + boundVars = map (isar conf) $ filterBoundVars $ inequalityAMIDs eq + ineq = ppIsarEq (isaNotEq conf) conf (getInequality eq) + quantifiers = foldl (<->) (isaForall conf) boundVars <> char '.' + -- SP Theory ------------ +ppSPTEq :: Doc -> AnyEq -> Doc +ppSPTEq sym eq0 = case eq0 of + TIDEq eq -> ppEq' sym sptTID eq + RoleEq eq -> ppEq' sym (text . roleName) eq + TIDRoleEq (tid, role) -> + text "role(" <-> sptTID tid <-> char ')' <-> sym <-> text (roleName role) + ArbMsgEq eq -> ppEq sym sptArbMsgId sptMessage eq + AVarEq eq -> ppEq' sym sptAVar eq + MVarEq eq -> ppEq sym sptMVar sptMessage eq + MsgEq eq -> ppEq' sym sptMessage eq + sptAnyEq :: AnyEq -> Doc -sptAnyEq eq0 = case eq0 of - TIDEq eq -> ppEq' sptTID eq - RoleEq eq -> ppEq' (text . roleName) eq - TIDRoleEq (tid, role) -> - text "role(" <-> sptTID tid <-> text (") = " ++ roleName role) - ArbMsgEq eq -> ppEq sptArbMsgId sptMessage eq - AVarEq eq -> ppEq' sptAVar eq - MVarEq eq -> ppEq sptMVar sptMessage eq - MsgEq eq -> ppEq' sptMessage eq +sptAnyEq = ppSPTEq (char '=') + +sptInequality :: Inequality -> Doc +sptInequality eq = if L.null boundVars + then ineq + else parens $ quantifiers <-> ineq + where + boundVars = map sptArbMsgId $ filterBoundVars $ inequalityAMIDs eq + ineq = ppSPTEq (text "!=") (getInequality eq) + quantifiers = foldl (<->) (char '!') boundVars <> char '.' {- diff --git a/src/Scyther/Facts.hs b/src/Scyther/Facts.hs --- a/src/Scyther/Facts.hs +++ b/src/Scyther/Facts.hs @@ -87,7 +87,7 @@ import qualified Scyther.Typing as T import Scyther.Typing hiding (substTypeAnn) import qualified Scyther.Equalities as E -import Scyther.Equalities hiding (solve, substTID, threadRole, substMVar, substAVar, substMsg, substAnyEq, substAMID, empty, null) +import Scyther.Equalities hiding (solve, substTID, threadRole, substMVar, substAVar, substMsg, substAnyEq, substInequality, substAMID, empty, null) import Scyther.Event hiding (substEv, substEvOrd) import qualified Scyther.Event as E import Scyther.Formula hiding (substAtom) @@ -126,6 +126,7 @@ , compromised :: S.Set Message -- ^ Statements about agents being compromised. , uncompromised :: S.Set Message -- ^ Statements about agents being uncompromised. , equalities :: E.Equalities -- ^ All equalities that must hold. + , inequalities :: S.Set Inequality -- ^ All inequalities that must hold. , tidQuantifiers :: S.Set TID -- ^ All thread IDs occurring in the facts. , amQuantifiers :: S.Set ArbMsgId -- ^ All arbitrary-message IDs ocurring in the facts. , optTyping :: Maybe Typing -- ^ The typing if there is any that the @@ -135,6 +136,8 @@ , covered :: S.Set Message -- ^ The messages that have already been used in a -- case distinction. + , failedEqs :: S.Set AnyEq -- ^ All equalities which could not be solved. + -- A non-empty set implies false. , protocol :: Protocol -- ^ The protocol that the current state -- is a reachable state of. } @@ -154,7 +157,9 @@ S.null (compromised facts) && S.null (uncompromised facts) && S.null (typeAnns facts) && - E.null (equalities facts) + E.null (equalities facts) && + S.null (inequalities facts) && + S.null (failedEqs facts) ------------------------------------------------------------------------------ -- Construction @@ -162,7 +167,8 @@ -- | Empty set of facts; logically equivalent to true. empty :: Protocol -> Facts -empty = Facts S.empty S.empty S.empty S.empty E.empty S.empty S.empty Nothing S.empty S.empty +empty = Facts + S.empty S.empty S.empty S.empty E.empty S.empty S.empty S.empty Nothing S.empty S.empty S.empty -- | Set the protocol. -- @@ -267,7 +273,8 @@ -- | Check if a agent id is quantified in these facts arbMsgIdQuantified :: Facts -> ArbMsgId -> CertResult -arbMsgIdQuantified facts aid = +arbMsgIdQuantified _facts (BoundVarId _) = certSuccess +arbMsgIdQuantified facts aid@(FreeVarId _) = certErrorIf (aid `S.notMember` amQuantifiers facts) $ "unquantified aid: " ++ show aid @@ -314,11 +321,16 @@ E.MVarEq (mv, m) -> mvarQuantified facts mv >< msgQuantified facts m E.MsgEq (m1, m2) -> msgQuantified facts m1 >< msgQuantified facts m2 +-- | Check if an inequality contains only quantified logical variables. +ineqQuantified :: Facts -> E.Inequality -> CertResult +ineqQuantified facts = anyEqQuantified facts . getInequality + -- | Check if an atom contains only quantified logical variables. atomQuantified :: Facts -> Atom -> CertResult atomQuantified facts atom = case atom of ABool _ -> certSuccess AEq eq -> anyEqQuantified facts eq + AIneq eq -> ineqQuantified facts eq AEv ev -> evQuantified facts ev AEvOrd ord -> evOrdQuantified facts ord ACompr m -> msgQuantified facts m @@ -365,6 +377,10 @@ certAnyEq :: Facts -> E.AnyEq -> Cert E.AnyEq certAnyEq = certify anyEqQuantified substAnyEq +-- | Certify an inequality. +certInequality :: Facts -> Inequality -> Cert Inequality +certInequality = certify ineqQuantified substInequality + -- | Certify an atom: All logical variables are quantified under the given -- facts and all values are invariant under the equalities associated with the -- facts. @@ -413,6 +429,10 @@ substAnyEq :: Facts -> E.AnyEq -> E.AnyEq substAnyEq = liftSubst E.substAnyEq +-- | Substitute an inequality. +substInequality :: Facts -> Inequality -> Inequality +substInequality = liftSubst E.substInequality + -- | Substitute an atom. substAtom :: Facts -> Atom -> Atom substAtom = liftSubst F.substAtom @@ -458,10 +478,12 @@ , compromised = S.map (E.substMsg eqs) (compromised facts) , uncompromised = S.map (E.substMsg eqs) (uncompromised facts) , equalities = eqs + , inequalities = S.map (E.substInequality eqs) (inequalities facts) , tidQuantifiers = tidQuantifiers facts , amQuantifiers = amQuantifiers facts , typeAnns = S.map (T.substTypeAnn eqs) (typeAnns facts) , covered = S.map (E.substMsg eqs) (covered facts) + , failedEqs = S.map (E.substAnyEq eqs) (failedEqs facts) } @@ -521,6 +543,16 @@ insertTypeAnn tya prems = prems { typeAnns = S.insert (certified tya) (typeAnns prems) } +-- | Insert an inequality. +insertInequality :: Cert Inequality -> Facts -> Facts +insertInequality ineq facts = + facts { inequalities = S.insert (certified ineq) (inequalities facts) } + +-- | Insert a failed equation. +insertFailedEq :: Cert E.AnyEq -> Facts -> Facts +insertFailedEq eq facts = + facts { failedEqs = S.insert (certified eq) (failedEqs facts) } + -- | Build the conjunction of the atoms and the facts; a result of 'Nothing' -- means that the conjunction is logically equivalent to False. This will occur -- in case 'AFalse' is conjoined or an equality that cannot be unified. @@ -538,6 +570,7 @@ -- FIXME: repeated calls to solve may be a bit expensive due to duplicated -- work of 'removeTrivialFacts'. AEq eq -> return $ solve [Cert eq] facts + AIneq eq -> return . Just $ insertInequality (Cert eq) facts AEv ev -> return . Just $ insertEvNonTrivial (Cert ev) facts AEvOrd ord -> return . Just $ insertEvOrdNonTrivial (Cert ord) facts ACompr m -> return . Just $ compromise m facts @@ -573,16 +606,22 @@ insertLearnBefore to p m = insertEvOrdAndEvs (Cert (Learn m, to)) p -- | Insert an executed role step and all non-trivial facts implied by the --- Input rule. -insertStepInputClosed :: Cert (TID, RoleStep) -> Facts -> Facts -insertStepInputClosed s prems = case certified s of - (tid, step@(Recv _ pt)) -> - let m = substMsg prems (inst tid pt) in - insertEvOrdNonTrivial (Cert (Learn m, Step tid step)) prems - (tid, step@(Send _ _)) -> insertEv (Cert (Step tid step)) prems +-- Input, MatchEq, and NotMatch rules. +insertStepClosed :: Cert (TID, RoleStep) -> Facts -> Facts +insertStepClosed s prems = case certified s of + (tid, step@(Recv _ pt)) -> + let m = substMsg prems (inst tid pt) + in insertEvOrdNonTrivial (Cert (Learn m, Step tid step)) prems + (tid, step@(Match _ True v pt)) -> + let eq = certAnyEq prems $ MsgEq (instVar tid v, inst tid pt) + in insertEv (Cert (Step tid step)) . maybe (insertFailedEq eq prems) id $ solve [eq] prems + (tid, step@(Match _ False v pt)) -> + let ineq = certInequality prems . Inequality $ MsgEq (instVar tid v, inst tid pt) + in insertEv (Cert (Step tid step)) $ insertInequality ineq prems + (tid, step) -> insertEv (Cert (Step tid step)) prems -- | Insert an executed role step and all non-trivial facts implied by the --- Input and Role rules. +-- Input, MatchEq, NotMatch, and Role rules. insertStepPrefixClosed :: Cert (TID, RoleStep) -> Facts -> Facts insertStepPrefixClosed s = case certified s of (tid, step) -> execState $ do @@ -590,11 +629,11 @@ role <- gets (fromMaybe err . threadRole tid) let prefix = takeWhile (/= step) (roleSteps role) ++ [step] insertStepOrd = modify . insertEvOrdAndEvs . Cert . (Step tid *** Step tid) - mapM_ (modify . insertStepInputClosed . (Cert . ((,) tid))) prefix + mapM_ (modify . insertStepClosed . (Cert . ((,) tid))) prefix mapM_ insertStepOrd $ zip prefix (tail prefix) --- | Insert an event an all non-trivial facts implied by the Input and Role --- rules. +-- | Insert an event an all non-trivial facts implied by the Input, MatchEq, +-- and Role rules. insertEvSaturated :: Cert Event -> Facts -> Facts insertEvSaturated ev = case certified ev of (Learn _ ) -> insertEvNonTrivial ev @@ -663,7 +702,10 @@ -- | The next free agent identifier nextArbMsgId :: Facts -> ArbMsgId -nextArbMsgId = maybe 0 (succ . fst) . S.maxView . amQuantifiers +nextArbMsgId = FreeVarId . maybe 0 (next . fst) . S.maxView . amQuantifiers + where + next (FreeVarId aid) = succ aid + next (BoundVarId bid) = error ("nextArbMsgId: amQuantifiers contains BoundVarId " ++ show bid) -- | Try to retrieve the typing; equal to 'mzero' if there is none. getTyping :: MonadPlus m => Facts -> m Typing @@ -675,9 +717,11 @@ -- premises. The checks are separated due to efficiency reasons. proveFalse :: Facts -> Bool proveFalse prems = + not (S.null (failedEqs prems)) || not (S.null (compromised prems `S.intersection` uncompromised prems)) || any noAgent (S.toList (compromised prems)) || - cyclic (eventOrd prems) + cyclic (eventOrd prems) || + any falseIneq (S.toList (inequalities prems)) where noAgent (MMVar _) = False noAgent (MAVar _) = False @@ -697,6 +741,9 @@ checkAtom atom = case atom of ABool b -> b AEq eq -> E.reflexive eq + -- NOTE (SM): inequalities typically contain variables. It is therefore + -- not much use to try hard to prove inequalities. + AIneq _eq -> False AEv (Learn m) -> all checkLearn (splitNonTrivial m) AEv ev -> ev `S.member` events facts AEvOrd (Learn m, e2) -> all (checkLearnBefore e2) (splitNonTrivial m) @@ -756,6 +803,7 @@ where prove mapping (FAtom atom) = proveAtom facts (F.substAtom (getMappingEqs mapping) atom) prove mapping (FConj f1 f2) = prove mapping f1 && prove mapping f2 + prove mapping (FDisj f1 f2) = prove mapping f1 || prove mapping f2 prove mapping (FExists v f) = any (\mk -> prove (mk mapping) f) (mkMappings v) -- the mappings assign witnesses to the existentially quantified variables. mkMappings (Left tid) = map (E.addTIDMapping tid) (S.toList $ tidQuantifiers facts) @@ -783,9 +831,12 @@ ----------------- -- | Represent the facts as a set of atoms. +-- +-- TODO: non-empty failedEqs imply False? toAtoms :: Facts -> [Atom] toAtoms facts = mconcat [ AEq <$> E.toAnyEqs (equalities facts) + , AIneq <$> S.toList (inequalities facts) , AUncompr <$> S.toList (uncompromised facts) , ACompr <$> S.toList (compromised facts) , AEv <$> S.toList (events facts) @@ -1072,21 +1123,23 @@ msum . map stepChains $ roleSteps role where stepChains :: RoleStep -> ChainRuleM () - stepChains (Recv _ _) = mzero + stepChains (Recv _ _) = mzero + stepChains (Match _ _ _ _) = mzero stepChains step@(Send _ pt) = do -- trace ("stepChains: " ++ roleName role ++"_"++getLabel l) (return ()) modifyFacts $ insertStepPrefixClosed (Cert (tid, step)) addCaseFragment $ stepLabel step - mapM_ annotateMVarType $ S.toList $ patFMV pt + subst <- getsFacts substMsg + mapM_ annotateMVarType . nub . msgFMV . subst $ inst tid pt msgChains [(Step tid step)] (inst tid pt) where -- annotating message variables with their type - annotateMVarType mv = - case M.lookup (mv, role) typ of - Nothing -> error $ "stepChains: no type provided for '"++show v++"'" - Just ty -> addExpandedTypeAnn (v, ty, tid) - where - v = MMVar (MVar (LocalId (mv, tid))) + annotateMVarType mv@(MVar (LocalId (v, tid'))) + | tid' == tid = case M.lookup (v, role) typ of + Nothing -> error $ "stepChains: no type provided for '"++show v++ + "' of role "++roleName role + Just ty -> addExpandedTypeAnn (MMVar mv, ty, tid) + | otherwise = return () -- case naming msgName (MConst i) = getId i @@ -1274,6 +1327,7 @@ ( ppSet (isar conf) (tidQuantifiers facts) ++ ppSet (isar conf) (amQuantifiers facts) , map (isar conf) reprEqs ++ + ppSet (isar conf) (inequalities facts) ++ ppSet (isaUncompr conf) (uncompromised facts) ++ ppSet (isaCompr conf) (compromised facts) ++ ppSet (isaEventOrd conf (Mapping eqs)) (eventOrd facts) ++ @@ -1296,6 +1350,7 @@ ( ppSet sptTID (tidQuantifiers facts) ++ ppSet sptArbMsgId (amQuantifiers facts) , map sptAnyEq reprEqs ++ + ppSet sptInequality (inequalities facts) ++ ppComprInfo "uncompromised" (uncompromised facts) ++ ppComprInfo "compromised" (compromised facts) ++ (map (sptEventOrd (Mapping eqs)) $ transitiveChains $ S.toList $ eventOrd facts) ++ diff --git a/src/Scyther/Formula.hs b/src/Scyther/Formula.hs --- a/src/Scyther/Formula.hs +++ b/src/Scyther/Formula.hs @@ -10,8 +10,8 @@ -- ** Queries , hasQuantifiers - , conjuncts , conjunctionToAtoms + , distributeOverDisj , isTypingFormula , destTypingFormula , atomTIDs @@ -51,6 +51,7 @@ data Atom = ABool Bool -- ^ 'False' and 'True' in Isabelle. | AEq AnyEq -- ^ An equality + | AIneq Inequality -- ^ An inequality | AEv Event -- ^ An event must have happened. | AEvOrd (Event, Event) -- ^ An event order. | ACompr Message -- ^ A compromised agent variable. @@ -65,6 +66,7 @@ data Formula = FAtom Atom | FConj Formula Formula + | FDisj Formula Formula | FExists (Either TID ArbMsgId) Formula deriving( Eq, Show, Ord, Data, Typeable ) @@ -87,6 +89,7 @@ where go (FAtom atom) = FAtom <$> ((substAtom . getMappingEqs) <$> ask <*> pure atom) go (FConj l r) = FConj <$> go l <*> go r + go (FDisj l r) = FDisj <$> go l <*> go r go (FExists (Left tid) inner) = do tids <- get case tids of @@ -108,11 +111,13 @@ atomTIDs (AUncompr m) = msgTIDs m atomTIDs (AHasType tya) = typeAnnTIDs tya atomTIDs (AEq eq) = anyEqTIDs eq +atomTIDs (AIneq eq) = inequalityTIDs eq -- | Compute the free thread variables of the given formula. formulaTIDs :: Formula -> [TID] formulaTIDs (FAtom atom) = atomTIDs atom formulaTIDs (FConj f1 f2) = formulaTIDs f1 ++ formulaTIDs f2 +formulaTIDs (FDisj f1 f2) = formulaTIDs f1 ++ formulaTIDs f2 formulaTIDs (FExists (Left tid) f) = filter (tid /=) $ formulaTIDs f formulaTIDs (FExists (Right _) f) = formulaTIDs f @@ -127,12 +132,13 @@ substAtom :: Equalities -> Atom -> Atom substAtom eqs atom = case atom of ABool _ -> atom - AEq eq -> AEq $ substAnyEq eqs eq - AEv ev -> AEv $ substEv eqs ev - AEvOrd ord -> AEvOrd $ substEvOrd eqs ord - ACompr m -> ACompr $ substMsg eqs m - AUncompr m -> AUncompr $ substMsg eqs m - AHasType tya -> AHasType $ substTypeAnn eqs tya + AEq eq -> AEq $ substAnyEq eqs eq + AIneq eq -> AIneq $ substInequality eqs eq + AEv ev -> AEv $ substEv eqs ev + AEvOrd ord -> AEvOrd $ substEvOrd eqs ord + ACompr m -> ACompr $ substMsg eqs m + AUncompr m -> AUncompr $ substMsg eqs m + AHasType tya -> AHasType $ substTypeAnn eqs tya ATyping _ -> atom AReachable _ -> atom @@ -142,7 +148,10 @@ -- | True iff the formula does contain an existential quantifier. hasQuantifiers :: Formula -> Bool -hasQuantifiers = isNothing . conjunctionToAtoms +hasQuantifiers (FAtom _) = False +hasQuantifiers (FConj f1 f2) = hasQuantifiers f1 || hasQuantifiers f2 +hasQuantifiers (FDisj f1 f2) = hasQuantifiers f1 || hasQuantifiers f2 +hasQuantifiers (FExists _ _) = True -- | Convert a formula consisting of conjunctions only to a list of atoms. Uses -- 'fail' for error reporting. @@ -151,13 +160,26 @@ conjunctionToAtoms (FConj f1 f2) = (++) `liftM` conjunctionToAtoms f1 `ap` conjunctionToAtoms f2 conjunctionToAtoms _ = - fail "conjunctionToAtoms: existential quantifier encountered." + fail "conjunctionToAtoms: existential quantifier or disjunction encountered." --- | Split all toplevel conjunctions. -conjuncts :: Formula -> [Formula] -conjuncts (FConj f1 f2) = conjuncts f1 ++ conjuncts f2 -conjuncts f = pure f +-- | Produce a logically equivalent formula by pushing conjunctions and +-- quantifiers inside, i.e., apply their respective distributive laws over +-- disjunction. Obvious danger of exponential explosion! +distributeOverDisj :: Formula -> Formula +distributeOverDisj = go + where + go (FConj f1 f2) = distribConj (go f1) (go f2) + go (FDisj f1 f2) = FDisj (go f1) (go f2) + go (FExists v f) = distribEx v (go f) + go f = f + distribConj f (FDisj f1 f2) = FDisj (distribConj f f1) (distribConj f f2) + distribConj (FDisj f1 f2) f = FDisj (distribConj f1 f) (distribConj f2 f) + distribConj f1 f2 = FConj f1 f2 + + distribEx v (FDisj f1 f2) = FDisj (distribEx v f1) (distribEx v f2) + distribEx v f = FExists v f + -- | Find the first conjoined thread to role equality for this thread, if there -- is any. findRole :: TID -> Formula -> Maybe Role @@ -168,11 +190,23 @@ | otherwise = mzero go (FAtom _) = mzero go (FConj f1 f2) = go f1 `mplus` go f2 + go (FDisj f1 f2) = do + r1 <- go f1 + r2 <- go f2 + guard (r1 == r2) + return r1 go (FExists v f) | Left tid == v = mzero | otherwise = go f +-- | Add all thread to role equalities which are (immediate) conjuncts of a +-- formula to a mapping. +addRoles :: Formula -> Mapping -> Mapping +addRoles (FAtom (AEq (TIDRoleEq (tid, role)))) = addTIDRoleMapping tid role +addRoles (FConj f1 f2) = addRoles f1 . addRoles f2 +addRoles _ = id + ------------------------------------------------------------------------------ -- Pretty Printing ------------------------------------------------------------------------------ @@ -199,6 +233,7 @@ ABool False -> text "False" ABool True -> text "True" AEq eq -> ppIsar eq + AIneq eq -> ppIsar eq AEv ev -> isaEvent conf mapping ev AEvOrd ord -> isaEventOrd conf mapping ord ACompr av -> isaCompr conf av @@ -220,6 +255,7 @@ ABool False -> text "False" ABool True -> text "True" AEq eq -> sptAnyEq eq + AIneq eq -> sptInequality eq AEv ev -> sptEvent mapping ev AEvOrd (e1,e2) -> sptEventOrd mapping [e1,e2] ACompr av -> sptCompr av @@ -237,28 +273,34 @@ ppIsar = isar conf pp m (FAtom atom) = isaAtom conf m atom - pp m (FConj f1 f2) = sep [pp m f1 <-> isaAnd conf, pp m f2] + pp m (FConj f1 f2) = sep [ppConjunct m f1 <-> isaAnd conf, ppConjunct m f2] + pp m (FDisj f1 f2) = + sep [ppDisjunct (addRoles f1 m) f1 <-> isaOr conf, ppDisjunct (addRoles f2 m) f2] pp m (FExists v f) = parens $ sep [ isaExists conf <-> (either ppIsar ppIsar v) <> char '.' - , nest 2 $ pp m' f + , nest 2 $ pp (addRoles f m) f ] - where - m' = case v of - Left tid -> maybe id (addTIDRoleMapping tid) (findRole tid f) m - Right _ -> m + ppConjunct m f@(FDisj _ _) = parens $ pp m f + ppConjunct m f = pp m f + ppDisjunct m f@(FConj _ _) = parens $ pp m f + ppDisjunct m f = pp m f + + -- | A formula in security protocol theory format. sptFormula :: Mapping -> Formula -> Doc sptFormula = pp where pp m (FAtom atom) = sptAtom m atom - pp m (FConj f1 f2) = sep [pp m f1 <-> char '&', pp m f2] + pp m (FConj f1 f2) = sep [ppConjunct m f1 <-> char '&', ppConjunct m f2] + pp m (FDisj f1 f2) = + sep [ppDisjunct (addRoles f1 m) f1 <-> char '|', ppDisjunct (addRoles f2 m) f2] pp m (FExists v f) = parens $ sep [ char '?' <-> (either sptTID sptArbMsgId v) <> char '.' - , nest 2 $ pp m' f + , nest 2 $ pp (addRoles f m) f ] - where - m' = case v of - Left tid -> maybe id (addTIDRoleMapping tid) (findRole tid f) m - Right _ -> m + ppConjunct m f@(FDisj _ _) = parens $ pp m f + ppConjunct m f = pp m f + ppDisjunct m f@(FConj _ _) = parens $ pp m f + ppDisjunct m f = pp m f diff --git a/src/Scyther/GoalFlow.hs b/src/Scyther/GoalFlow.hs --- a/src/Scyther/GoalFlow.hs +++ b/src/Scyther/GoalFlow.hs @@ -129,10 +129,10 @@ -} firstRecvs :: Role -> RoleStep -> S.Set Id -firstRecvs _ (Send _ _) = S.empty firstRecvs role recv@(Recv _ pt) = patFMV pt `S.difference` (S.unions . map (patFMV . stepPat) $ takeWhile (/= recv) (roleSteps role)) +firstRecvs _ _ = S.empty -- | The role steps of a protocol. protoSteps :: Protocol -> [(Role, RoleStep)] diff --git a/src/Scyther/Message.hs b/src/Scyther/Message.hs --- a/src/Scyther/Message.hs +++ b/src/Scyther/Message.hs @@ -12,6 +12,7 @@ , MVar(..) , ArbMsgId(..) , Message(..) + -- ** Queries , lidId , lidTID @@ -31,6 +32,7 @@ , mapAVar , mapMVar , inst + , instVar , normMsg , splitNonTrivial @@ -44,6 +46,7 @@ ) where import Control.Monad +import Control.Monad.State import Control.Applicative import Data.Data @@ -65,8 +68,7 @@ -- Messages ------------------------------------------------------------------------------ --- | A logical variable for a thread identifier. Note that these are the only --- free logical variables being used during proofs. Depending on their context +-- | A logical variable for a thread identifier. Depending on their context -- they are either universally or existentially quantified. newtype TID = TID { getTID :: Int } deriving( Eq, Ord, Enum, Num, Data, Typeable {-! NFData !-}) @@ -74,13 +76,16 @@ instance Show TID where show (TID tid) = '#':show tid --- | An agent name identifier -newtype ArbMsgId = ArbMsgId { arbMsgId :: Int } - deriving( Eq, Ord, Enum, Num, Data, Typeable ) +-- | A logical message variable. There are two namespaces: Free variables have +-- global scope. Bound variables are used for inequalities with implicit local +-- quantification. +data ArbMsgId = FreeVarId !Int + | BoundVarId !Int + deriving( Eq, Ord, Data, Typeable ) instance Show ArbMsgId where - show (ArbMsgId aid) = 'a':show aid - + show (FreeVarId aid) = 'a':show aid + show (BoundVarId bid) = 'b':show bid -- | A local identifier. newtype LocalId = LocalId { getLocalId :: (Id, TID) } @@ -152,7 +157,7 @@ msgTIDs (MFresh f) = pure . lidTID . getFresh $ f msgTIDs (MAVar v) = pure . avarTID $ v msgTIDs (MMVar v) = pure . mvarTID $ v -msgTIDs (MArbMsg _) = empty +msgTIDs (MArbMsg _) = empty msgTIDs (MHash m) = msgTIDs m msgTIDs (MTup m1 m2) = msgTIDs m1 `mappend` msgTIDs m2 msgTIDs (MEnc m1 m2) = msgTIDs m1 `mappend` msgTIDs m2 @@ -168,7 +173,7 @@ msgAMIDs (MFresh _) = empty msgAMIDs (MAVar _) = empty msgAMIDs (MMVar _) = empty -msgAMIDs (MArbMsg a) = pure a +msgAMIDs (MArbMsg a) = pure a msgAMIDs (MHash m) = msgAMIDs m msgAMIDs (MTup m1 m2) = msgAMIDs m1 `mappend` msgAMIDs m2 msgAMIDs (MEnc m1 m2) = msgAMIDs m1 `mappend` msgAMIDs m2 @@ -258,20 +263,32 @@ -- symbolically. The resulting message is guaranteed to be normalized w.r.t -- `normMsg`. inst :: TID -> Pattern -> Message -inst _ (PConst i) = MConst i -inst tid (PFresh i) = MFresh (Fresh (LocalId (i, tid))) -inst tid (PAVar i) = MAVar (AVar (LocalId (i, tid))) -inst tid (PMVar i) = MMVar (MVar (LocalId (i, tid))) -inst tid (PHash pt) = MHash (inst tid pt) -inst tid (PTup pt1 pt2) = MTup (inst tid pt1) (inst tid pt2) -inst tid (PEnc pt1 pt2) = MEnc (inst tid pt1) (inst tid pt2) -inst tid (PSign pt1 pt2) = MTup m1 (MEnc m1 (normMsg $ MInvKey (inst tid pt2))) - where m1 = inst tid pt1 -inst tid (PSymK pt1 pt2) = MSymK (inst tid pt1) (inst tid pt2) -inst tid (PShrK pt1 pt2) = MShrK (inst tid pt1) (inst tid pt2) -inst tid (PAsymPK pt) = MAsymPK (inst tid pt) -inst tid (PAsymSK pt) = MAsymSK (inst tid pt) +inst tid pattern = evalState (go pattern) 0 + where + go :: Pattern -> State Int Message + go (PConst i) = return $ MConst i + go (PFresh i) = return $ MFresh (Fresh (LocalId (i, tid))) + go (PAVar i) = return $ MAVar (AVar (LocalId (i, tid))) + go (PMVar i) = return $ MMVar (MVar (LocalId (i, tid))) + go (PHash pt) = MHash <$> go pt + go (PTup pt1 pt2) = MTup <$> go pt1 <*> go pt2 + go (PEnc pt1 pt2) = MEnc <$> go pt1 <*> go pt2 + go (PSign pt1 pt2) = do m1 <- go pt1 + m2 <- go pt2 + return $ MTup m1 (MEnc m1 (normMsg $ MInvKey m2)) + go (PSymK pt1 pt2) = MSymK <$> go pt1 <*> go pt2 + go (PShrK pt1 pt2) = MShrK <$> go pt1 <*> go pt2 + go (PAsymPK pt) = MAsymPK <$> go pt + go (PAsymSK pt) = MAsymSK <$> go pt + go (PAny) = do bid <- get + put (bid + 1) + return $ MArbMsg (BoundVarId bid) +-- | Instantiate a generic specification variable. +instVar :: TID -> VarId -> Message +instVar tid (SAVar i) = MAVar (AVar (LocalId (i, tid))) +instVar tid (SMVar i) = MMVar (MVar (LocalId (i, tid))) + -- | Normalize a message; i.e., apply key-inversion if possible and swap shared -- key arguments, if required. normMsg :: Message -> Message @@ -326,7 +343,8 @@ isar _ tid = text "tid" <> int (getTID tid) instance Isar ArbMsgId where - isar _ aid = text "a" <> int (arbMsgId aid) + isar _ (FreeVarId aid) = text "a" <> int aid + isar _ (BoundVarId bid) = text "b" <> int bid instance Isar LocalId where isar conf (LocalId (i, tid)) = isar conf i <-> isar conf tid @@ -376,7 +394,8 @@ sptTID = text . show sptArbMsgId :: ArbMsgId -> Doc -sptArbMsgId = (char 'a' <>) . int . arbMsgId +sptArbMsgId (FreeVarId aid) = char 'a' <> int aid +sptArbMsgId (BoundVarId bid) = char 'b' <> int bid sptLocalId :: LocalId -> Doc sptLocalId (LocalId (i, tid)) = sptId i <> sptTID tid diff --git a/src/Scyther/Protocol.hs b/src/Scyther/Protocol.hs --- a/src/Scyther/Protocol.hs +++ b/src/Scyther/Protocol.hs @@ -5,6 +5,7 @@ -- * Types Id(..) + , VarId(..) , Pattern(..) , Label(..) , RoleStep(..) @@ -14,6 +15,9 @@ -- * Queries + -- ** Generic variables + , variable + -- ** Patterns , patFMV , patFAV @@ -26,6 +30,8 @@ , stepLabel , stepFMV , stepFAV + , stepUsedMV + , stepBoundMV -- ** Roles , roleFMV @@ -46,6 +52,9 @@ , wfProto , sptProtoIllformedness +-- * Construction + , patMapFMV + -- * Output , isaRoleStep , sptId @@ -76,6 +85,12 @@ instance Show Id where show (Id i) = i +-- | Either an agent or message variable. Currently only used for 'Match' steps. +data VarId = + SAVar Id -- ^ An agent variable. + | SMVar Id -- ^ A message variable. + deriving( Eq, Ord, Show, Data, Typeable {-! NFData !-} ) + -- | A message pattern. data Pattern = PConst Id -- ^ A global constant. @@ -90,6 +105,7 @@ | PShrK Pattern Pattern -- ^ A long-term bi-directional symmetric key. | PAsymPK Pattern -- ^ A long-term public key. | PAsymSK Pattern -- ^ A long-term private key + | PAny -- ^ A wildcard (anonymous logical variable). deriving( Eq, Ord, Show, Data, Typeable {-! NFData !-} ) -- | A label of a role step. @@ -98,8 +114,9 @@ -- | A role step. data RoleStep = - Send Label Pattern -- ^ A send step. - | Recv Label Pattern -- ^ A receive step. + Send Label Pattern -- ^ A send step. + | Recv Label Pattern -- ^ A receive step. + | Match Label Bool VarId Pattern -- ^ A match or not-match step. deriving( Eq, Ord, Show, Data, Typeable {-! NFData !-} ) -- | A role of a protocol. Its name has no operational meaning, but is carried @@ -131,15 +148,25 @@ lookupRoleStep :: String -> Role -> Maybe RoleStep lookupRoleStep lbl = find ((== lbl) . stepLabel) . roleSteps --- | Pattern of of a role step +-- | Case distinction for specification variables. +variable :: (Id -> a) -- ^ Function to apply for an agent variable. + -> (Id -> a) -- ^ Function to apply for a message variable. + -> VarId + -> a +variable agent _ (SAVar a) = agent a +variable _ msg (SMVar m) = msg m + +-- | Pattern of a role step. stepPat :: RoleStep -> Pattern -stepPat (Send _ pt) = pt -stepPat (Recv _ pt) = pt +stepPat (Send _ pt) = pt +stepPat (Recv _ pt) = pt +stepPat (Match _ _ _ pt) = pt -- | The string label of a role step. stepLabel :: RoleStep -> String -stepLabel (Send l _) = getLabel l -stepLabel (Recv l _) = getLabel l +stepLabel (Send l _) = getLabel l +stepLabel (Recv l _) = getLabel l +stepLabel (Match l _ _ _) = getLabel l -- | Pattern subterms. subpatterns :: Pattern -> S.Set Pattern @@ -181,11 +208,12 @@ -- | Frees message variables of a role step. stepFMV :: RoleStep -> S.Set Id -stepFMV = patFMV . stepPat +stepFMV (Match _ _ (SMVar v) pt) = v `S.insert` patFMV pt +stepFMV step = patFMV $ stepPat step -- | Free message variables of a role. roleFMV :: Role -> S.Set Id -roleFMV = S.unions . map (patFMV . stepPat) . roleSteps +roleFMV = S.unions . map stepFMV . roleSteps -- | Free agent variables of a pattern. patFAV :: Pattern -> S.Set Id @@ -200,21 +228,40 @@ patFAV (PAsymSK pt) = patFAV pt patFAV _ = S.empty - -- | Frees agent variables of a role step. stepFAV :: RoleStep -> S.Set Id -stepFAV = patFAV . stepPat +stepFAV (Match _ _ (SAVar a) pt) = a `S.insert` patFAV pt +stepFAV step = patFAV $ stepPat step -- | Free agent variables of a role. roleFAV :: Role -> S.Set Id -roleFAV = S.unions . map (patFAV . stepPat) . roleSteps +roleFAV = S.unions . map stepFAV . roleSteps +-- | Semantically used message variables of a role step. +stepUsedMV :: RoleStep -> S.Set Id +stepUsedMV (Send _ pt) = patFMV pt +stepUsedMV (Recv _ _) = S.empty +stepUsedMV (Match _ eq v pt) + | eq = matched + | otherwise = matched `S.union` patFMV pt + where + matched = case v of + SAVar _ -> S.empty + SMVar m -> S.singleton m + +-- | Message variables of a role step which are bound there at the latest. +stepBoundMV :: RoleStep -> S.Set Id +stepBoundMV (Recv _ pt) = patFMV pt +stepBoundMV (Match _ True _ pt) = patFMV pt +stepBoundMV _ = S.empty + + -- Well-formedness of protocols and roles ----------------------------------------- data ProtoIllformedness = NonUnique Role - | SendBeforeReceive Role RoleStep Id + | UseBeforeBind Role RoleStep Id | AccessibleLongTermKey Role RoleStep Pattern deriving( Eq, Ord, Show ) @@ -223,21 +270,19 @@ -- contain long-term-keys in accessible positions. wfRole :: Role -> [ProtoIllformedness] wfRole role = msum - [ do guard (unique $ roleSteps role) + [ do guard (not . unique $ roleSteps role) return $ NonUnique role - , recv_before_send S.empty (roleSteps role) + , use_before_bind S.empty (roleSteps role) , msum . map accessibleLongTermKeys $ roleSteps role ] where - recv_before_send _ [] = mzero - recv_before_send received (step@(Send _ pt) : rs) = - do v <- S.toList $ patFMV pt - guard (v `S.member` received) - return $ SendBeforeReceive role step v + use_before_bind _ [] = mzero + use_before_bind bound (step : rs) = + do v <- S.toList $ stepUsedMV step + guard (not (v `S.member` bound)) + return $ UseBeforeBind role step v `mplus` - recv_before_send received rs - recv_before_send received (Recv _ pt : rs) = - recv_before_send (patFMV pt `S.union` received) rs + use_before_bind (stepBoundMV step `S.union` bound) rs accessibleLongTermKeys step = do m <- S.toList . patternparts $ stepPat step @@ -256,10 +301,10 @@ sptProtoIllformedness pif = case pif of NonUnique role -> text $ "role '" ++ roleName role ++ "' contains duplicate steps." - SendBeforeReceive role step v -> + UseBeforeBind role step v -> text (roleName role) <> colon <-> sptRoleStep Nothing step <> colon <-> - text "message variable" <-> quotes (sptId v) <-> text "sent before received." + text "message variable" <-> quotes (sptId v) <-> text "used before bound." AccessibleLongTermKey role step _ -> text (roleName role) <> colon <-> sptRoleStep Nothing step <> colon <-> @@ -278,7 +323,7 @@ where steps = zip (roleSteps role) (repeat role) --- | The order of role steps in the protocol such that every send step is +-- | The order of role steps in the protocol such that every send step -- occurs before every receive step having the same label. labelOrd :: Protocol -> RoleStepOrder labelOrd proto = @@ -292,6 +337,26 @@ protoOrd proto = labelOrd proto ++ concatMap roleOrd (protoRoles proto) +-- Construction +--------------- + +-- | Apply a function to the free message variables of a pattern, replacing +-- them by a subpattern. +patMapFMV :: (Id -> Pattern) -> Pattern -> Pattern +patMapFMV f = go + where + go (PMVar i) = f i + go (PHash pt) = PHash (go pt) + go (PTup pt1 pt2) = PTup (go pt1) (go pt2) + go (PEnc pt1 pt2) = PEnc (go pt1) (go pt2) + go (PSign pt1 pt2) = PSign (go pt1) (go pt2) + go (PSymK pt1 pt2) = PSymK (go pt1) (go pt2) + go (PShrK pt1 pt2) = PShrK (go pt1) (go pt2) + go (PAsymPK pt) = PAsymPK (go pt) + go (PAsymSK pt) = PAsymSK (go pt) + go pt = pt + + ------------------------------------------------------------------------------ -- ISAR Output ------------------------------------------------------------------------------ @@ -312,16 +377,17 @@ case optRole of Just role | step `elem` roleSteps role -> -- abbreviate text $ roleName role ++ "_" ++ stepLabel step - _ -> - text name <-> isar conf (Label $ stepLabel step) <-> ppPat (stepPat step) - where - name = case step of Send _ _ -> "Send"; Recv _ _ -> "Recv" - ppPat pt@(PTup _ _) = isar conf pt - ppPat pt = nestShort' "(" ")" (isar conf pt) + _ -> isar conf step instance Isar Id where isar _ (Id i) = text $ "''"++i++"''" +instance Isar VarId where + isar conf = nestShort' "(" ")" . variable ppAgent ppMsg + where + ppAgent a = text "AVar" <-> isar conf a + ppMsg m = text "MVar" <-> isar conf m + instance Isar Label where isar _ (Label l) = text $ "''"++l++"''" @@ -342,6 +408,7 @@ (PAsymPK a) -> text "PAsymPK" <-> ppTup a (PAsymSK (PAVar a)) -> text "sSK" <-> isar conf a (PAsymSK a) -> text "PAsymSK" <-> ppTup a + (PAny) -> text "PAny" where -- pretty print a tuple as right associate list ppTup pt@(PTup _ _) = nestShort n left right (fsep $ punctuate comma $ map (isar conf) $ split pt) @@ -360,7 +427,16 @@ instance Isar RoleStep where - isar conf = isaRoleStep conf Nothing + isar conf step = case step of + Send _ _ -> text "Send" <-> label <-> pattern + Recv _ _ -> text "Recv" <-> label <-> pattern + Match _ True v _ -> text "MatchEq" <-> label <-> isar conf v <-> pattern + Match _ False v _ -> text "NotMatch" <-> label <-> isar conf v <-> pattern + where + label = isar conf (Label $ stepLabel step) + pattern = ppPat (stepPat step) + ppPat pt@(PTup _ _) = isar conf pt + ppPat pt = nestShort' "(" ")" (isar conf pt) instance Isar Role where isar conf (Role name steps) = @@ -407,6 +483,7 @@ (PShrK a b) -> fcat [text "k[", sptPattern a, comma, sptPattern b, text "]"] (PAsymPK a) -> text "pk" <> ppBetween 1 "(" ")" a (PAsymSK a) -> text "sk" <> ppBetween 1 "(" ")" a + (PAny) -> char '_' where -- pretty print a tuple as right associate list ppBetween n lead finish pt@(PTup _ _) = @@ -423,12 +500,20 @@ case optRole of Just role | step `elem` roleSteps role -> -- abbreviate text $ roleName role ++ "_" ++ stepLabel step - _ -> - (text $ name ++ "_" ++ stepLabel step) <> ppPat (stepPat step) + _ -> case step of + Send _ _ -> labeled "Send" <> pattern + Recv _ _ -> labeled "Recv" <> pattern + Match _ True v pt -> labeled "Match" <> matching "->" v pt + Match _ False v pt -> labeled "Match" <> matching "#" v pt where - name = case step of Send _ _ -> "Send"; Recv _ _ -> "Recv" - ppPat pt@(PTup _ _) = sptPattern pt - ppPat pt = nestShort' "(" ")" (sptPattern pt) + labeled name = text $ name ++ "_" ++ stepLabel step + matching sym v pt = nestShort' "(" ")" $ ppVar v <-> text sym <-> sptPattern pt + pattern = ppPat (stepPat step) + + ppVar (SAVar a) = sptId a + ppVar (SMVar v) = char '?' <> sptId v + ppPat pt@(PTup _ _) = sptPattern pt + ppPat pt = nestShort' "(" ")" (sptPattern pt) -- | Pretty print a role in SP theory format. sptRole :: Role -> Doc diff --git a/src/Scyther/Sequent.hs b/src/Scyther/Sequent.hs --- a/src/Scyther/Sequent.hs +++ b/src/Scyther/Sequent.hs @@ -102,31 +102,37 @@ proveRecvs S.empty (roleSteps role) where proveRecvs _ [] = [] - proveRecvs recv ( Send _ _ : steps) = proveRecvs recv steps + proveRecvs recv (Send _ _ : steps) = proveRecvs recv steps + proveRecvs recv (Match _ False _ _ : steps) = proveRecvs recv steps proveRecvs recv ((Recv _ (PMVar lid)) : steps) = -- don't prove single reiceves as they are handled directly by the tactic -- on the Isabelle side. proveRecvs (S.insert lid recv) steps proveRecvs recv (step@(Recv _ pt) : steps) = let mvars = patFMV pt - in (S.toList mvars >>= proveVar) `mplus` + in (S.toList mvars >>= proveVar recv step) `mplus` (proveRecvs (recv `S.union` mvars) steps) + -- TODO: Merge? Special cases? + proveRecvs recv (step@(Match _ True _ pt) : steps) = + let mvars = patFMV pt + in (S.toList mvars >>= proveVar recv step) `mplus` + (proveRecvs (recv `S.union` mvars) steps) + + proveVar recv step v + | v `S.member` recv = fail "proveVar: not first receive" + | otherwise = return (name, Sequent prem concl Standard) where - proveVar v - | v `S.member` recv = fail "proveVar: not first receive" - | otherwise = return (name, Sequent prem concl Standard) - where - name = roleName role ++ "_" ++ stepLabel step ++ "_" ++ getId v - (tid, prem0) = freshTID (sePrem se) - mv = MVar (LocalId (v, tid)) - premErr = error $ "wellTypedCases: could not add thread " ++ show tid ++ ". This should not happen." - prem1 = maybe premErr saturateFacts . join $ - conjoinAtoms [AEv (Step tid step), AEq (E.TIDRoleEq (tid, role))] prem0 - prem = fromMaybe (error "failed to set typing") $ setTyping typ prem1 - concl = FAtom $ case M.lookup (v, role) typ of - Just ty -> AHasType (MMVar mv, ty, tid) - Nothing -> error $ - "wellTypedCases: no type given for '"++show v++"' in role '"++roleName role++"'" + name = roleName role ++ "_" ++ stepLabel step ++ "_" ++ getId v + (tid, prem0) = freshTID (sePrem se) + mv = MVar (LocalId (v, tid)) + premErr = error $ "wellTypedCases: could not add thread " ++ show tid ++ ". This should not happen." + prem1 = maybe premErr saturateFacts . join $ + conjoinAtoms [AEv (Step tid step), AEq (E.TIDRoleEq (tid, role))] prem0 + prem = fromMaybe (error "failed to set typing") $ setTyping typ prem1 + concl = FAtom $ case M.lookup (v, role) typ of + Just ty -> AHasType (MMVar mv, ty, tid) + Nothing -> error $ + "wellTypedCases: no type given for '"++show v++"' in role '"++roleName role++"'" wellTypedCases _ = mzero diff --git a/src/Scyther/Theory.hs b/src/Scyther/Theory.hs --- a/src/Scyther/Theory.hs +++ b/src/Scyther/Theory.hs @@ -309,6 +309,9 @@ -- | True, if the sequents conclusion contains an existentially quantified -- thread. + -- + -- TODO: Does this describe authentication properties precisely if disjunction + -- is present? isExistsStructureProp :: Sequent -> Bool isExistsStructureProp = hasQuantifiers . seConcl diff --git a/src/Scyther/Theory/Dot.hs b/src/Scyther/Theory/Dot.hs --- a/src/Scyther/Theory/Dot.hs +++ b/src/Scyther/Theory/Dot.hs @@ -56,6 +56,7 @@ getColorWithDefault :: TID -> M.Map (Maybe TID) v -> v getColorWithDefault tid m = M.findWithDefault (m M.! Nothing) (Just tid) m + ----------------------------------------------------------------------------- -- DOT Graph Generation ----------------------------------------------------------------------------- @@ -65,6 +66,8 @@ type TIDMap = M.Map TID (Maybe Role) +-- If a thread identifier may correspond to different roles, only one role gets +-- mapped. extractTIDMap :: Sequent -> TIDMap extractTIDMap se = formulaMap (seConcl se) (M.fromList fromPrem) where @@ -76,6 +79,7 @@ (FExists (Left tid) prop) -> formulaMap prop . M.insert tid Nothing (FExists (Right _ ) prop) -> formulaMap prop (FConj lprop rprop) -> formulaMap lprop . formulaMap rprop + (FDisj lprop rprop) -> formulaMap lprop . formulaMap rprop (FAtom (AEq (E.TIDRoleEq (tid, role)))) -> M.insert tid (Just role) _ -> id @@ -334,10 +338,11 @@ tryNoteRole tid (Just role) env = env { threadMapping = E.addTIDRoleMapping tid role (threadMapping env) } --- | Produce the dot code of the formula. +-- | Produce the dot code of a formula without disjunctions. dotFormula :: Formula -> MyDot () dotFormula (FAtom atom) = dotAtom atom dotFormula (FConj f1 f2) = dotFormula f1 >> dotFormula f2 +dotFormula (FDisj _f1 _f2) = error "dotFormula: disjunction encountered." dotFormula (FExists (Left tid) inner) = do localThreadInfo tid (findRole tid inner) $ do dotFormula inner @@ -347,14 +352,31 @@ _ <- liftDot $ node [("label", "some agent " ++ show aid)] dotFormula inner --- | Produce the dot code for a formula that is a conclusion of a sequent. This --- takes care of handling the quantifiers stemming from the premises. -dotConclusion :: Formula -> MyDot () -dotConclusion formula = do +-- | Produce the dot code for a formula that is a single alternative of a +-- conclusion. This takes care of handling the quantifiers stemming from the +-- premises. +dotConclusionAlt :: Formula -> MyDot () +dotConclusionAlt formula = do resetThreadAtoms [] dotFormula formula dotThreads False +-- | Produce the dot code for a formula that is a conclusion of a sequent. +-- Quantifiers and conjunctions are first pushed inside. The resulting +-- alternatives are put into separate clusters. +dotConclusion :: Formula -> MyDot () +dotConclusion concl = case distributeOverDisj concl of + f@(FDisj _ _) -> clusterAlts f + f -> dotConclusionAlt f -- no extra cluster for single alternative + where + clusterAlts (FDisj f1 f2) = clusterAlts f1 >> clusterAlts f2 + clusterAlts f = do + s <- get + _ <- myCluster $ do + liftDot $ attribute ("label","alternative") + dotConclusionAlt f + put s + -- | Dot a sequent with two separate clusters for premise and conclusion. dotSequent :: Sequent -> MyDot () dotSequent se = do @@ -406,10 +428,10 @@ dotStep (role, step) = mkNode (render $ sptRoleStep Nothing step) (getRoleColor role) [] - dotSend _ (_, Recv _ _) = return () dotSend stepMap send@(_, Send l _) = sequence_ [ edge (findShowError send stepMap) (findShowError recv stepMap) [] | recv@(_, Recv l' _) <- steps, l == l' ] + dotSend _ _ = return () dotRole stepMap role = do roleId <- mkNode ("role "++roleName role) (getRoleColor $ roleName role) [("peripheries","2")] diff --git a/src/Scyther/Theory/Lexer.hs b/src/Scyther/Theory/Lexer.hs deleted file mode 100644 --- a/src/Scyther/Theory/Lexer.hs +++ /dev/null @@ -1,612 +0,0 @@ -{-# LANGUAGE BangPatterns, CPP, MagicHash #-} -{-# LINE 1 "Theory/Lexer.x" #-} - -{-# OPTIONS_GHC -fno-warn-name-shadowing -fno-warn-unused-matches -fno-warn-unused-binds -fno-warn-missing-signatures #-} -module Scyther.Theory.Lexer where - - -#if __GLASGOW_HASKELL__ >= 603 -#include "ghcconfig.h" -#elif defined(__GLASGOW_HASKELL__) -#include "config.h" -#endif -#if __GLASGOW_HASKELL__ >= 503 -import Data.Array -import Data.Char (ord) -import Data.Array.Base (unsafeAt) -#else -import Array -import Char (ord) -#endif -#if __GLASGOW_HASKELL__ >= 503 -import GHC.Exts -#else -import GlaExts -#endif -alex_base :: AlexAddr -alex_base = AlexA# 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- -alex_table :: AlexAddr -alex_table = AlexA# 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- -alex_check :: AlexAddr -alex_check = AlexA# 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0\xd9\x00\xda\x00\xdb\x00\xdc\x00\xdd\x00\xde\x00\xdf\x00\xe0\x00\xe1\x00\xe2\x00\xe3\x00\xe4\x00\xe5\x00\xe6\x00\xe7\x00\xe8\x00\xe9\x00\xea\x00\xeb\x00\xec\x00\xed\x00\xee\x00\xef\x00\xf0\x00\xf1\x00\xf2\x00\xf3\x00\xf4\x00\xf5\x00\xf6\x00\xff\xff\xf8\x00\xf9\x00\xfa\x00\xfb\x00\xfc\x00\xfd\x00\xfe\x00\xff\x00"# - -alex_deflt :: AlexAddr -alex_deflt = AlexA# "\x5d\x00\xff\xff\xff\xff\xff\xff\xff\xff\x06\x00\x06\x00\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff"# - -alex_accept = listArray (0::Int,95) [[],[],[],[],[(AlexAccSkip)],[(AlexAccSkip)],[(AlexAccSkip)],[],[(AlexAcc (alex_action_2))],[(AlexAcc (alex_action_23))],[(AlexAcc (alex_action_3))],[(AlexAcc (alex_action_10))],[(AlexAcc (alex_action_4))],[(AlexAcc (alex_action_15))],[(AlexAcc (alex_action_5))],[(AlexAcc (alex_action_10))],[(AlexAcc (alex_action_6))],[(AlexAcc (alex_action_7))],[(AlexAcc (alex_action_10))],[(AlexAcc (alex_action_8))],[(AlexAcc (alex_action_15))],[(AlexAcc (alex_action_9))],[(AlexAcc (alex_action_10))],[(AlexAcc (alex_action_11))],[(AlexAcc (alex_action_53))],[(AlexAcc (alex_action_53))],[(AlexAcc (alex_action_53))],[(AlexAcc (alex_action_53))],[],[(AlexAcc (alex_action_12))],[(AlexAcc (alex_action_53))],[(AlexAcc (alex_action_53))],[(AlexAcc (alex_action_53))],[(AlexAcc (alex_action_53))],[(AlexAcc (alex_action_53))],[(AlexAcc (alex_action_53))],[(AlexAcc (alex_action_53))],[],[(AlexAcc (alex_action_13))],[(AlexAcc (alex_action_53))],[(AlexAcc (alex_action_53))],[(AlexAcc (alex_action_53))],[(AlexAcc (alex_action_53))],[(AlexAcc (alex_action_53))],[(AlexAcc (alex_action_53))],[(AlexAcc (alex_action_53))],[(AlexAcc (alex_action_53))],[(AlexAcc (alex_action_53))],[],[(AlexAcc (alex_action_14))],[(AlexAcc (alex_action_15))],[(AlexAcc (alex_action_15))],[(AlexAcc (alex_action_16))],[(AlexAcc (alex_action_53))],[],[(AlexAcc (alex_action_17))],[(AlexAcc (alex_action_18))],[(AlexAcc (alex_action_19))],[(AlexAcc (alex_action_20))],[(AlexAcc (alex_action_53))],[(AlexAcc (alex_action_21))],[],[(AlexAcc (alex_action_22))],[(AlexAcc (alex_action_24))],[(AlexAcc (alex_action_25))],[(AlexAcc (alex_action_26))],[(AlexAcc (alex_action_27))],[(AlexAcc (alex_action_28))],[(AlexAcc (alex_action_29))],[(AlexAcc (alex_action_30))],[(AlexAcc (alex_action_31))],[(AlexAcc (alex_action_32))],[(AlexAcc (alex_action_33))],[(AlexAcc (alex_action_34))],[(AlexAcc (alex_action_35))],[(AlexAcc (alex_action_36))],[(AlexAcc (alex_action_37))],[(AlexAcc (alex_action_38))],[(AlexAcc (alex_action_39))],[(AlexAcc (alex_action_40))],[(AlexAcc (alex_action_41))],[(AlexAcc (alex_action_42))],[(AlexAcc (alex_action_43))],[(AlexAcc (alex_action_44))],[(AlexAcc (alex_action_45))],[(AlexAcc (alex_action_46))],[(AlexAcc (alex_action_47))],[(AlexAcc (alex_action_48))],[(AlexAcc (alex_action_49))],[(AlexAcc (alex_action_50))],[(AlexAcc (alex_action_51))],[],[(AlexAcc (alex_action_52))],[(AlexAcc (alex_action_53))],[(AlexAcc (alex_action_53))],[(AlexAcc (alex_action_53))]] -{-# LINE 81 "Theory/Lexer.x" #-} - - --- | Lex a keyword -keyword :: Keyword -> AlexAction Keyword -keyword kw input len = return kw - --- | Wrap a string into a keyword -scanString :: (String -> Keyword) -> AlexAction Keyword -scanString kw (_,_,input) len = return $ kw (take len input) - -{- --- | Scan a string until EOF is encountered. -alexScanTokens :: String -> Either String [Keyword] -alexScanTokens inp = runAlex inp gather - where - gather = do - t <- alexMonadScan - case trace (show t) t of - EOF -> return [EOF] - _ -> (t:) `liftM` gather - --- | Scan a file. -scanFile f = do - inp <- readFile f - return $ alexScanTokens inp --} - --- | Formal text types. -data TextType = - TextBegin String - | TextContent String - | TextEnd - deriving( Eq, Ord, Show ) - --- | Lexable Keywords -data Keyword = - IDENT String - | TEXT TextType - | SQUOTE - | DQUOTE - | RIGHTARROW - | LEFTARROW - | LONGRIGHTARROW - | LONGLEFTARROW - | COMMA - | DOT - | COLON - | QUESTIONMARK - | BANG - | AND - | MID - | DOLLAR - | AT - | SHARP - | LPAREN - | RPAREN - | LBRACKET - | RBRACKET - | LBRACE - | RBRACE - | TILDE - | HAT - | STAR - | UNDERSCORE - | MINUS - | PLUS - | EQUAL - | LESS - | GREATER - | EOF - | FORALL - | EXISTS - | LAND - | LOR - | LNOT - | APPROX - -- dummy keyword to get rid of overlapping pattern matches - | DUMMY_KEYWORD - deriving( Eq ) - -instance Show Keyword where - show kw = case kw of - IDENT i -> identifier i - TEXT t -> txt t - SQUOTE -> symbol "'" - DQUOTE -> symbol "\"" - RIGHTARROW -> symbol "->" - LEFTARROW -> symbol "<-" - LONGRIGHTARROW -> symbol "-->" - LONGLEFTARROW -> symbol "<--" - COMMA -> symbol "," - DOT -> symbol "." - COLON -> symbol ":" - QUESTIONMARK -> symbol "?" - BANG -> symbol "!" - AND -> symbol "&" - MID -> symbol "|" - DOLLAR -> symbol "$" - AT -> symbol "@" - SHARP -> symbol "#" - LPAREN -> symbol "(" - RPAREN -> symbol ")" - LBRACKET -> symbol "[" - RBRACKET -> symbol "]" - LBRACE -> symbol "{" - RBRACE -> symbol "}" - TILDE -> symbol "~" - HAT -> symbol "^" - STAR -> symbol "*" - UNDERSCORE -> symbol "_" - MINUS -> symbol "-" - PLUS -> symbol "+" - EQUAL -> symbol "=" - LESS -> symbol "<" - GREATER -> symbol ">" - EOF -> "end of file" - FORALL -> symbol "∀" - EXISTS -> symbol "∃" - LAND -> symbol "∧" - LOR -> symbol "∨" - LNOT -> symbol "¬" - APPROX -> symbol "≈" - DUMMY_KEYWORD -> "DUMMY_KEYWORD (this should not occur!)" - where - identifier i = "identifier `" ++ i ++ "'" - txt (TextBegin t) = "start of `" ++ t ++ "'" - txt (TextContent t) = "text `" ++ t ++ "'" - txt (TextEnd) = "start of text" - symbol s = "symbol `" ++ s ++ "'" - keyword s = "keyword `" ++ s ++ "'" - --- ----------------------------------------------------------------------------- --- Alex wrapper code. --- --- This code is in the PUBLIC DOMAIN; you may copy it freely and use --- it for any purpose whatsoever. - --- ----------------------------------------------------------------------------- --- The input type - - -type AlexInput = (AlexPosn, -- current position, - Char, -- previous char - String) -- current input string - -alexInputPrevChar :: AlexInput -> Char -alexInputPrevChar (p,c,s) = c - -alexGetChar :: AlexInput -> Maybe (Char,AlexInput) -alexGetChar (p,c,[]) = Nothing -alexGetChar (p,_,(c:s)) = let p' = alexMove p c in p' `seq` - Just (c, (p', c, s)) - - --- ----------------------------------------------------------------------------- --- Token positions - --- `Posn' records the location of a token in the input text. It has three --- fields: the address (number of chacaters preceding the token), line number --- and column of a token within the file. `start_pos' gives the position of the --- start of the file and `eof_pos' a standard encoding for the end of file. --- `move_pos' calculates the new position after traversing a given character, --- assuming the usual eight character tab stops. - -data AlexPosn = AlexPn !Int !Int !Int - deriving (Eq) - -instance Show AlexPosn where - show (AlexPn _ l c) = "line "++show l++" column "++show c - -alexStartPos :: AlexPosn -alexStartPos = AlexPn 0 1 1 - -alexMove :: AlexPosn -> Char -> AlexPosn -alexMove (AlexPn a l c) '\t' = AlexPn (a+1) l (((c+7) `div` 8)*8+1) -alexMove (AlexPn a l c) '\n' = AlexPn (a+1) (l+1) 1 -alexMove (AlexPn a l c) _ = AlexPn (a+1) l (c+1) - - --- ----------------------------------------------------------------------------- --- Default monad - - -data AlexState = AlexState { - alex_pos :: !AlexPosn, -- position at current input location - alex_inp :: String, -- the current input - alex_chr :: !Char, -- the character before the input - alex_scd :: !Int, -- the current startcode - alex_ocd :: !Int, -- the old startcode before the comment started - alex_cmt :: [String] -- stack of begin comment identifiers - } - --- Compile with -funbox-strict-fields for best results! - -runAlex :: String -> Alex a -> Either String a -runAlex input (Alex f) - = case f (AlexState {alex_pos = alexStartPos, - alex_inp = input, - alex_chr = '\n', - alex_scd = 0, - alex_ocd = 0, - alex_cmt = [] - }) of - Left msg -> Left msg - Right ( _, a ) -> Right a - -newtype Alex a = Alex { unAlex :: AlexState -> Either String (AlexState, a) } - -instance Monad Alex where - m >>= k = Alex $ \s -> case unAlex m s of - Left msg -> Left msg - Right (s',a) -> unAlex (k a) s' - return a = Alex $ \s -> Right (s,a) - -alexGetPos :: Alex AlexPosn -alexGetPos = Alex $ \s@AlexState{alex_pos=pos} -> Right (s, pos) - -alexGetInput :: Alex AlexInput -alexGetInput - = Alex $ \s@AlexState{alex_pos=pos,alex_chr=c,alex_inp=inp} -> - Right (s, (pos,c,inp)) - -alexSetInput :: AlexInput -> Alex () -alexSetInput (pos,c,inp) - = Alex $ \s -> case s{alex_pos=pos,alex_chr=c,alex_inp=inp} of - s@(AlexState{}) -> Right (s, ()) - -alexError :: String -> Alex a -alexError message = Alex $ \s -> Left $ message ++ " in " ++ show (alex_pos s) - -alexGetStartCode :: Alex Int -alexGetStartCode = Alex $ \s@AlexState{alex_scd=sc} -> Right (s, sc) - -alexSetStartCode :: Int -> Alex () -alexSetStartCode sc = Alex $ \s -> Right (s{alex_scd=sc}, ()) - -alexGetOldStartCode :: Alex Int -alexGetOldStartCode = Alex $ \s@AlexState{alex_ocd=sc} -> Right (s, sc) - -alexSetOldStartCode :: Int -> Alex () -alexSetOldStartCode sc = Alex $ \s -> Right (s{alex_ocd=sc}, ()) - -alexGetComments :: Alex [String] -alexGetComments = Alex $ \s -> Right (s, alex_cmt s) - -alexSetComments :: [String] -> Alex () -alexSetComments cmt = Alex $ \s -> Right (s{alex_cmt=cmt}, ()) - -alexMonadScan = do - inp <- alexGetInput - sc <- alexGetStartCode - case alexScan inp sc of - AlexEOF -> alexEOF - AlexError inp' -> alexError "lexical error" - AlexSkip inp' len -> do - alexSetInput inp' - alexMonadScan - AlexToken inp' len action -> do - alexSetInput inp' - action inp len - --- ----------------------------------------------------------------------------- --- Useful token actions - -type AlexAction result = AlexInput -> Int -> Alex result - --- just ignore this token and scan another one -skip :: AlexAction Keyword -skip input len = alexMonadScan - --- ignore this token, but set the start code to a new value -begin :: Int -> AlexAction Keyword -begin code input len = do alexSetStartCode code; alexMonadScan - --- | Begin a text starting of the given type. -beginText :: String -> Int -> AlexAction Keyword -beginText ty code _ _ = do - alexSetStartCode code - return $ TEXT $ TextBegin ty - --- | End a text. -endText :: Int -> AlexAction Keyword -endText code _ _ = do - alexSetStartCode code - return $ TEXT TextEnd - --- | Begin a comment starting with the given sign. -beginComment :: String -> Int -> AlexAction Keyword -beginComment cmtBegin code input len = do - cmts <- alexGetComments - alexSetComments $ cmtBegin : cmts - if null cmts - then alexGetStartCode >>= alexSetOldStartCode - else return () - alexSetStartCode code - alexMonadScan - --- | End a comment that started with the given begin comment sign. -endComment :: String -> AlexAction Keyword -endComment cmtBegin input len = do - cmts <- alexGetComments - case cmts of - [] -> alexError $ "comment ended but no beginning '"++cmtBegin++"' marked." - (cmt:cmts') -> do - if cmt == cmtBegin - then do - alexSetComments cmts' - if null cmts' - then alexGetOldStartCode >>= alexSetStartCode - else return () - else return () - alexMonadScan - --- perform an action for this token, and set the start code to a new value --- andBegin :: AlexAction result -> Int -> AlexAction result -(action `andBegin` code) input len = do alexSetStartCode code; action input len - -alexEOF :: Alex Keyword -alexEOF = return EOF - - - - - -comment,text :: Int -comment = 1 -text = 2 -alex_action_2 = beginComment "(*" comment -alex_action_3 = beginComment "(*" comment -alex_action_4 = beginComment "(*" comment -alex_action_5 = endComment "(*" -alex_action_6 = beginComment "/*" comment -alex_action_7 = beginComment "/*" comment -alex_action_8 = beginComment "/*" comment -alex_action_9 = endComment "/*" -alex_action_10 = skip -alex_action_11 = beginText "text" text -alex_action_12 = beginText "section" text -alex_action_13 = beginText "subsection" text -alex_action_14 = endText 0 -alex_action_15 = scanString (TEXT . TextContent) -alex_action_16 = keyword FORALL -alex_action_17 = keyword EXISTS -alex_action_18 = keyword LAND -alex_action_19 = keyword LOR -alex_action_20 = keyword LNOT -alex_action_21 = keyword APPROX -alex_action_22 = keyword COMMA -alex_action_23 = keyword LPAREN -alex_action_24 = keyword RPAREN -alex_action_25 = keyword LBRACKET -alex_action_26 = keyword RBRACKET -alex_action_27 = keyword LBRACE -alex_action_28 = keyword RBRACE -alex_action_29 = keyword SQUOTE -alex_action_30 = keyword DQUOTE -alex_action_31 = keyword TILDE -alex_action_32 = keyword HAT -alex_action_33 = keyword EQUAL -alex_action_34 = keyword COLON -alex_action_35 = keyword DOLLAR -alex_action_36 = keyword AT -alex_action_37 = keyword SHARP -alex_action_38 = keyword STAR -alex_action_39 = keyword LESS -alex_action_40 = keyword GREATER -alex_action_41 = keyword QUESTIONMARK -alex_action_42 = keyword BANG -alex_action_43 = keyword AND -alex_action_44 = keyword MID -alex_action_45 = keyword DOT -alex_action_46 = keyword UNDERSCORE -alex_action_47 = keyword MINUS -alex_action_48 = keyword PLUS -alex_action_49 = keyword RIGHTARROW -alex_action_50 = keyword LEFTARROW -alex_action_51 = keyword LONGRIGHTARROW -alex_action_52 = keyword LONGLEFTARROW -alex_action_53 = scanString IDENT -{-# LINE 1 "templates/GenericTemplate.hs" #-} -{-# LINE 1 "templates/GenericTemplate.hs" #-} -{-# LINE 1 "" #-} -{-# LINE 1 "" #-} -{-# LINE 1 "templates/GenericTemplate.hs" #-} --- ----------------------------------------------------------------------------- --- ALEX TEMPLATE --- --- This code is in the PUBLIC DOMAIN; you may copy it freely and use --- it for any purpose whatsoever. - --- ----------------------------------------------------------------------------- --- INTERNALS and main scanner engine - -{-# LINE 35 "templates/GenericTemplate.hs" #-} - -{-# LINE 45 "templates/GenericTemplate.hs" #-} - - -data AlexAddr = AlexA# Addr# - -#if __GLASGOW_HASKELL__ < 503 -uncheckedShiftL# = shiftL# -#endif - -{-# INLINE alexIndexInt16OffAddr #-} -alexIndexInt16OffAddr (AlexA# arr) off = -#ifdef WORDS_BIGENDIAN - narrow16Int# i - where - i = word2Int# ((high `uncheckedShiftL#` 8#) `or#` low) - high = int2Word# (ord# (indexCharOffAddr# arr (off' +# 1#))) - low = int2Word# (ord# (indexCharOffAddr# arr off')) - off' = off *# 2# -#else - indexInt16OffAddr# arr off -#endif - - - - - -{-# INLINE alexIndexInt32OffAddr #-} -alexIndexInt32OffAddr (AlexA# arr) off = -#ifdef WORDS_BIGENDIAN - narrow32Int# i - where - i = word2Int# ((b3 `uncheckedShiftL#` 24#) `or#` - (b2 `uncheckedShiftL#` 16#) `or#` - (b1 `uncheckedShiftL#` 8#) `or#` b0) - b3 = int2Word# (ord# (indexCharOffAddr# arr (off' +# 3#))) - b2 = int2Word# (ord# (indexCharOffAddr# arr (off' +# 2#))) - b1 = int2Word# (ord# (indexCharOffAddr# arr (off' +# 1#))) - b0 = int2Word# (ord# (indexCharOffAddr# arr off')) - off' = off *# 4# -#else - indexInt32OffAddr# arr off -#endif - - - - - -#if __GLASGOW_HASKELL__ < 503 -quickIndex arr i = arr ! i -#else --- GHC >= 503, unsafeAt is available from Data.Array.Base. -quickIndex = unsafeAt -#endif - - - - --- ----------------------------------------------------------------------------- --- Main lexing routines - -data AlexReturn a - = AlexEOF - | AlexError !AlexInput - | AlexSkip !AlexInput !Int - | AlexToken !AlexInput !Int a - --- alexScan :: AlexInput -> StartCode -> AlexReturn a -alexScan input (I# (sc)) - = alexScanUser undefined input (I# (sc)) - -alexScanUser user input (I# (sc)) - = case alex_scan_tkn user input 0# input sc AlexNone of - (AlexNone, input') -> - case alexGetChar input of - Nothing -> - - - - AlexEOF - Just _ -> - - - - AlexError input' - - (AlexLastSkip input len, _) -> - - - - AlexSkip input len - - (AlexLastAcc k input len, _) -> - - - - AlexToken input len k - - --- Push the input through the DFA, remembering the most recent accepting --- state it encountered. - -alex_scan_tkn user orig_input len input s last_acc = - input `seq` -- strict in the input - let - new_acc = check_accs (alex_accept `quickIndex` (I# (s))) - in - new_acc `seq` - case alexGetChar input of - Nothing -> (new_acc, input) - Just (c, new_input) -> - - - - let - base = alexIndexInt32OffAddr alex_base s - !(I# (ord_c)) = ord c - offset = (base +# ord_c) - check = alexIndexInt16OffAddr alex_check offset - - new_s = if (offset >=# 0#) && (check ==# ord_c) - then alexIndexInt16OffAddr alex_table offset - else alexIndexInt16OffAddr alex_deflt s - in - case new_s of - -1# -> (new_acc, input) - -- on an error, we want to keep the input *before* the - -- character that failed, not after. - _ -> alex_scan_tkn user orig_input (len +# 1#) - new_input new_s new_acc - - where - check_accs [] = last_acc - check_accs (AlexAcc a : _) = AlexLastAcc a input (I# (len)) - check_accs (AlexAccSkip : _) = AlexLastSkip input (I# (len)) - check_accs (AlexAccPred a pred : rest) - | pred user orig_input (I# (len)) input - = AlexLastAcc a input (I# (len)) - check_accs (AlexAccSkipPred pred : rest) - | pred user orig_input (I# (len)) input - = AlexLastSkip input (I# (len)) - check_accs (_ : rest) = check_accs rest - -data AlexLastAcc a - = AlexNone - | AlexLastAcc a !AlexInput !Int - | AlexLastSkip !AlexInput !Int - -data AlexAcc a user - = AlexAcc a - | AlexAccSkip - | AlexAccPred a (AlexAccPred user) - | AlexAccSkipPred (AlexAccPred user) - -type AlexAccPred user = user -> AlexInput -> Int -> AlexInput -> Bool - --- ----------------------------------------------------------------------------- --- Predicates on a rule - -alexAndPred p1 p2 user in1 len in2 - = p1 user in1 len in2 && p2 user in1 len in2 - ---alexPrevCharIsPred :: Char -> AlexAccPred _ -alexPrevCharIs c _ input _ _ = c == alexInputPrevChar input - ---alexPrevCharIsOneOfPred :: Array Char Bool -> AlexAccPred _ -alexPrevCharIsOneOf arr _ input _ _ = arr ! alexInputPrevChar input - ---alexRightContext :: Int -> AlexAccPred _ -alexRightContext (I# (sc)) user _ _ input = - case alex_scan_tkn user input 0# input sc AlexNone of - (AlexNone, _) -> False - _ -> True - -- TODO: there's no need to find the longest - -- match when checking the right context, just - -- the first match will do. - --- used by wrappers -iUnbox (I# (i)) = i diff --git a/src/Scyther/Theory/Lexer.x b/src/Scyther/Theory/Lexer.x new file mode 100644 --- /dev/null +++ b/src/Scyther/Theory/Lexer.x @@ -0,0 +1,430 @@ +{ +-- Ignore the slew of warnings from definitions generated by Alex. +-- NOTE: you should disable this line when working on this module to make sure +-- that you don't miss important warnings. +{-# OPTIONS_GHC -fno-warn-missing-signatures -fno-warn-unused-binds #-} +{-# OPTIONS_GHC -fno-warn-unused-matches -fno-warn-name-shadowing #-} +{-# OPTIONS_GHC -fno-warn-unused-imports #-} + +module Scyther.Theory.Lexer where + +import Control.Applicative +import Control.Monad +import Data.Word (Word8) +import qualified Codec.Binary.UTF8.String as UTF8 +} + +$digit = [0-9] +$letter = [a-zA-Z] +$others = [\192-\214\216-\246\248-\255] + +@integer = $digit+ +@identifierFirst = ($letter | $digit | $others) +@identifierAfter = ($letter | $digit | "_" | $others) +@identifier = @identifierFirst @identifierAfter* +@comment = $printable | $white +@text = $printable | $white +@lineComment = "//".* + +tokens :- + <0> $white+ ; + + <0> @lineComment ; + <0> "(*" { beginComment "(*" comment } + "(*" { beginComment "(*" comment } + "(*" { beginComment "(*" comment } + "*)" { endComment "(*" } + <0> "/*" { beginComment "/*" comment } + "/*" { beginComment "/*" comment } + "/*" { beginComment "/*" comment } + "*/" { endComment "/*" } + @comment { skip } + + <0> "text{*" { beginText "text" text } + <0> "section{*" { beginText "section" text } + <0> "subsection{*" { beginText "subsection" text } + "*}" { endText 0} + @text { scanString (TEXT . TextContent) } + + + <0> "∀" { keyword FORALL } + <0> "∃" { keyword EXISTS } + <0> "∧" { keyword LAND } + <0> "∨" { keyword LOR } + <0> "¬" { keyword LNOT } + <0> "≈" { keyword APPROX } + + <0> "," { keyword COMMA } + <0> "(" { keyword LPAREN } + <0> ")" { keyword RPAREN } + <0> "[" { keyword LBRACKET } + <0> "]" { keyword RBRACKET } + <0> "{" { keyword LBRACE } + <0> "}" { keyword RBRACE } + <0> "/" { keyword SLASH } + <0> "\\" { keyword BACKSLASH } + <0> "'" { keyword SQUOTE } + <0> \" { keyword DQUOTE } + <0> "~" { keyword TILDE } + <0> "^" { keyword HAT } + <0> "=" { keyword EQUAL } + <0> ":" { keyword COLON } + <0> "$" { keyword DOLLAR } + <0> "@" { keyword AT } + <0> "#" { keyword SHARP } + <0> "*" { keyword STAR } + <0> "<" { keyword LESS } + <0> ">" { keyword GREATER } + <0> "?" { keyword QUESTIONMARK } + <0> "!" { keyword BANG } + <0> "&" { keyword AND } + <0> "|" { keyword MID } + <0> "." { keyword DOT } + <0> "_" { keyword UNDERSCORE } + <0> "-" { keyword MINUS } + <0> "+" { keyword PLUS } + <0> "->" { keyword RIGHTARROW } + <0> "<-" { keyword LEFTARROW } + <0> "-->" { keyword LONGRIGHTARROW } + <0> "<--" { keyword LONGLEFTARROW } + <0> @identifier { scanString IDENT} + + +{ + +-- | Lex a keyword +keyword :: Keyword -> AlexAction Keyword +keyword kw input len = return kw + +-- | Wrap a string into a keyword +scanString :: (String -> Keyword) -> AlexAction Keyword +scanString kw (_,_,_,input) len = return $ kw (take len input) + +{- +-- | Scan a string until EOF is encountered. +alexScanTokens :: String -> Either String [Keyword] +alexScanTokens inp = runAlex inp gather + where + gather = do + t <- alexMonadScan + case trace (show t) t of + EOF -> return [EOF] + _ -> (t:) `liftM` gather + +-- | Scan a file. +scanFile f = do + inp <- readFile f + return $ alexScanTokens inp +-} + +-- | Formal text types. +data TextType = + TextBegin String + | TextContent String + | TextEnd + deriving( Eq, Ord, Show ) + +-- | Lexable Keywords +data Keyword = + IDENT String + | TEXT TextType + | SQUOTE + | DQUOTE + | RIGHTARROW + | LEFTARROW + | LONGRIGHTARROW + | LONGLEFTARROW + | COMMA + | DOT + | COLON + | QUESTIONMARK + | BANG + | AND + | MID + | DOLLAR + | AT + | SHARP + | LPAREN + | RPAREN + | LBRACKET + | RBRACKET + | LBRACE + | RBRACE + | SLASH + | BACKSLASH + | TILDE + | HAT + | STAR + | UNDERSCORE + | MINUS + | PLUS + | EQUAL + | LESS + | GREATER + | EOF + | FORALL + | EXISTS + | LAND + | LOR + | LNOT + | APPROX + -- dummy keyword to get rid of overlapping pattern matches + | DUMMY_KEYWORD + deriving( Eq ) + +instance Show Keyword where + show kw = case kw of + IDENT i -> identifier i + TEXT t -> txt t + SQUOTE -> symbol "'" + DQUOTE -> symbol "\"" + RIGHTARROW -> symbol "->" + LEFTARROW -> symbol "<-" + LONGRIGHTARROW -> symbol "-->" + LONGLEFTARROW -> symbol "<--" + COMMA -> symbol "," + DOT -> symbol "." + COLON -> symbol ":" + QUESTIONMARK -> symbol "?" + BANG -> symbol "!" + AND -> symbol "&" + MID -> symbol "|" + DOLLAR -> symbol "$" + AT -> symbol "@" + SHARP -> symbol "#" + LPAREN -> symbol "(" + RPAREN -> symbol ")" + LBRACKET -> symbol "[" + RBRACKET -> symbol "]" + LBRACE -> symbol "{" + RBRACE -> symbol "}" + SLASH -> symbol "/" + BACKSLASH -> symbol "\\" + TILDE -> symbol "~" + HAT -> symbol "^" + STAR -> symbol "*" + UNDERSCORE -> symbol "_" + MINUS -> symbol "-" + PLUS -> symbol "+" + EQUAL -> symbol "=" + LESS -> symbol "<" + GREATER -> symbol ">" + EOF -> "end of file" + FORALL -> symbol "∀" + EXISTS -> symbol "∃" + LAND -> symbol "∧" + LOR -> symbol "∨" + LNOT -> symbol "¬" + APPROX -> symbol "≈" + DUMMY_KEYWORD -> "DUMMY_KEYWORD (this should not occur!)" + where + identifier i = "identifier `" ++ i ++ "'" + txt (TextBegin t) = "start of `" ++ t ++ "'" + txt (TextContent t) = "text `" ++ t ++ "'" + txt (TextEnd) = "start of text" + symbol s = "symbol `" ++ s ++ "'" + keyword s = "keyword `" ++ s ++ "'" + +-- ----------------------------------------------------------------------------- +-- Alex wrapper code. +-- +-- This code is in the PUBLIC DOMAIN; you may copy it freely and use +-- it for any purpose whatsoever. + +-- ----------------------------------------------------------------------------- +-- The input type + +type AlexInput = (AlexPosn, -- current position, + Char, -- previous char + [Word8], -- remaining bytes of current char + String) -- current input string + +alexInputPrevChar :: AlexInput -> Char +alexInputPrevChar (p,c,bs,s) = c + +alexGetByte :: AlexInput -> Maybe (Word8,AlexInput) +alexGetByte (p,c,(b:bs),s) = Just (b,(p,c,bs,s)) +alexGetByte (p,c,[],[]) = Nothing +alexGetByte (p,_,[],(c:s)) = let p' = alexMove p c + (b:bs) = UTF8.encodeChar c + in p' `seq` Just (b, (p', c, bs, s)) + +-- ----------------------------------------------------------------------------- +-- Token positions + +-- `Posn' records the location of a token in the input text. It has three +-- fields: the address (number of chacaters preceding the token), line number +-- and column of a token within the file. `start_pos' gives the position of the +-- start of the file and `eof_pos' a standard encoding for the end of file. +-- `move_pos' calculates the new position after traversing a given character, +-- assuming the usual eight character tab stops. + +data AlexPosn = AlexPn !Int !Int !Int + deriving (Eq) + +instance Show AlexPosn where + show (AlexPn _ l c) = "line "++show l++" column "++show c + +alexStartPos :: AlexPosn +alexStartPos = AlexPn 0 1 1 + +alexMove :: AlexPosn -> Char -> AlexPosn +alexMove (AlexPn a l c) '\t' = AlexPn (a+1) l (((c+7) `div` 8)*8+1) +alexMove (AlexPn a l c) '\n' = AlexPn (a+1) (l+1) 1 +alexMove (AlexPn a l c) _ = AlexPn (a+1) l (c+1) + + +-- ----------------------------------------------------------------------------- +-- Default monad + + +data AlexState = AlexState { + alex_pos :: !AlexPosn, -- position at current input location + alex_inp :: String, -- the current input + alex_chr :: !Char, -- the character before the input + alex_scd :: !Int, -- the current startcode + alex_ocd :: !Int, -- the old startcode before the comment started + alex_cmt :: [String] -- stack of begin comment identifiers + } + +-- Compile with -funbox-strict-fields for best results! + +runAlex :: String -> Alex a -> Either String a +runAlex input (Alex f) + = case f (AlexState {alex_pos = alexStartPos, + alex_inp = input, + alex_chr = '\n', + alex_scd = 0, + alex_ocd = 0, + alex_cmt = [] + }) of + Left msg -> Left msg + Right ( _, a ) -> Right a + +newtype Alex a = Alex { unAlex :: AlexState -> Either String (AlexState, a) } + +instance Functor Alex where + fmap = liftM + +instance Applicative Alex where + pure = return + (<*>) = ap + +instance Monad Alex where + m >>= k = Alex $ \s -> case unAlex m s of + Left msg -> Left msg + Right (s',a) -> unAlex (k a) s' + return a = Alex $ \s -> Right (s,a) + +alexGetPos :: Alex AlexPosn +alexGetPos = Alex $ \s@AlexState{alex_pos=pos} -> Right (s, pos) + +alexGetInput :: Alex AlexInput +alexGetInput + = Alex $ \s@AlexState{alex_pos=pos,alex_chr=c,alex_inp=inp} -> + Right (s, (pos,c,[],inp)) + +alexSetInput :: AlexInput -> Alex () +alexSetInput (pos,c,_,inp) + = Alex $ \s -> case s{alex_pos=pos,alex_chr=c,alex_inp=inp} of + s@(AlexState{}) -> Right (s, ()) + +alexError :: String -> Alex a +alexError message = Alex $ \s -> Left $ message ++ " in " ++ show (alex_pos s) + +alexGetStartCode :: Alex Int +alexGetStartCode = Alex $ \s@AlexState{alex_scd=sc} -> Right (s, sc) + +alexSetStartCode :: Int -> Alex () +alexSetStartCode sc = Alex $ \s -> Right (s{alex_scd=sc}, ()) + +alexGetOldStartCode :: Alex Int +alexGetOldStartCode = Alex $ \s@AlexState{alex_ocd=sc} -> Right (s, sc) + +alexSetOldStartCode :: Int -> Alex () +alexSetOldStartCode sc = Alex $ \s -> Right (s{alex_ocd=sc}, ()) + +alexGetComments :: Alex [String] +alexGetComments = Alex $ \s -> Right (s, alex_cmt s) + +alexSetComments :: [String] -> Alex () +alexSetComments cmt = Alex $ \s -> Right (s{alex_cmt=cmt}, ()) + +alexMonadScan = do + inp <- alexGetInput + sc <- alexGetStartCode + case alexScan inp sc of + AlexEOF -> alexEOF + AlexError inp' -> alexError "lexical error" + AlexSkip inp' len -> do + alexSetInput inp' + alexMonadScan + AlexToken inp' len action -> do + alexSetInput inp' + action inp len + +-- ----------------------------------------------------------------------------- +-- Useful token actions + +type AlexAction result = AlexInput -> Int -> Alex result + +-- just ignore this token and scan another one +skip :: AlexAction Keyword +skip input len = alexMonadScan + +-- ignore this token, but set the start code to a new value +begin :: Int -> AlexAction Keyword +begin code input len = do alexSetStartCode code; alexMonadScan + +-- | Begin a text starting of the given type. +beginText :: String -> Int -> AlexAction Keyword +beginText ty code _ _ = do + alexSetStartCode code + return $ TEXT $ TextBegin ty + +-- | End a text. +endText :: Int -> AlexAction Keyword +endText code _ _ = do + alexSetStartCode code + return $ TEXT TextEnd + +-- | Begin a comment starting with the given sign. +beginComment :: String -> Int -> AlexAction Keyword +beginComment cmtBegin code input len = do + cmts <- alexGetComments + alexSetComments $ cmtBegin : cmts + if null cmts + then alexGetStartCode >>= alexSetOldStartCode + else return () + alexSetStartCode code + alexMonadScan + +-- | End a comment that started with the given begin comment sign. +endComment :: String -> AlexAction Keyword +endComment cmtBegin input len = do + cmts <- alexGetComments + case cmts of + [] -> alexError $ "comment ended but no beginning '"++cmtBegin++"' marked." + (cmt:cmts') -> do + if cmt == cmtBegin + then do + alexSetComments cmts' + if null cmts' + then alexGetOldStartCode >>= alexSetStartCode + else return () + else return () + alexMonadScan + +-- perform an action for this token, and set the start code to a new value +-- andBegin :: AlexAction result -> Int -> AlexAction result +(action `andBegin` code) input len = do alexSetStartCode code; action input len + +alexEOF :: Alex Keyword +alexEOF = return EOF + + + +} + + + diff --git a/src/Scyther/Theory/Lexer.x_src_only b/src/Scyther/Theory/Lexer.x_src_only deleted file mode 100644 --- a/src/Scyther/Theory/Lexer.x_src_only +++ /dev/null @@ -1,416 +0,0 @@ -{ -{-# OPTIONS_GHC -fno-warn-name-shadowing -fno-warn-unused-matches -fno-warn-unused-binds -fno-warn-missing-signatures #-} -module Scyther.Theory.Lexer where - --- Note that this file is not compatible with alex-3.0 and therefore we use --- the autogenerated file in the distributed version. Use this file together --- with a 2.x version of alex in case you have to modify the lexer. - -} - -$digit = [0-9] -$letter = [a-zA-Z] -$others = [\192-\214\216-\246\248-\255] - -@integer = $digit+ -@identifierFirst = ($letter | $digit | $others) -@identifierAfter = ($letter | $digit | "_" | $others) -@identifier = @identifierFirst @identifierAfter* -@comment = $printable | $white -@text = $printable | $white -@lineComment = "//".* - -tokens :- - <0> $white+ ; - - <0> @lineComment ; - <0> "(*" { beginComment "(*" comment } - "(*" { beginComment "(*" comment } - "(*" { beginComment "(*" comment } - "*)" { endComment "(*" } - <0> "/*" { beginComment "/*" comment } - "/*" { beginComment "/*" comment } - "/*" { beginComment "/*" comment } - "*/" { endComment "/*" } - @comment { skip } - - <0> "text{*" { beginText "text" text } - <0> "section{*" { beginText "section" text } - <0> "subsection{*" { beginText "subsection" text } - "*}" { endText 0} - @text { scanString (TEXT . TextContent) } - - - <0> "∀" { keyword FORALL } - <0> "∃" { keyword EXISTS } - <0> "∧" { keyword LAND } - <0> "∨" { keyword LOR } - <0> "¬" { keyword LNOT } - <0> "≈" { keyword APPROX } - - <0> "," { keyword COMMA } - <0> "(" { keyword LPAREN } - <0> ")" { keyword RPAREN } - <0> "[" { keyword LBRACKET } - <0> "]" { keyword RBRACKET } - <0> "{" { keyword LBRACE } - <0> "}" { keyword RBRACE } - <0> "/" { keyword SLASH } - <0> "\\" { keyword BACKSLASH } - <0> "'" { keyword SQUOTE } - <0> \" { keyword DQUOTE } - <0> "~" { keyword TILDE } - <0> "^" { keyword HAT } - <0> "=" { keyword EQUAL } - <0> ":" { keyword COLON } - <0> "$" { keyword DOLLAR } - <0> "@" { keyword AT } - <0> "#" { keyword SHARP } - <0> "*" { keyword STAR } - <0> "<" { keyword LESS } - <0> ">" { keyword GREATER } - <0> "?" { keyword QUESTIONMARK } - <0> "!" { keyword BANG } - <0> "&" { keyword AND } - <0> "|" { keyword MID } - <0> "." { keyword DOT } - <0> "_" { keyword UNDERSCORE } - <0> "-" { keyword MINUS } - <0> "+" { keyword PLUS } - <0> "->" { keyword RIGHTARROW } - <0> "<-" { keyword LEFTARROW } - <0> "-->" { keyword LONGRIGHTARROW } - <0> "<--" { keyword LONGLEFTARROW } - <0> @identifier { scanString IDENT} - - -{ - --- | Lex a keyword -keyword :: Keyword -> AlexAction Keyword -keyword kw input len = return kw - --- | Wrap a string into a keyword -scanString :: (String -> Keyword) -> AlexAction Keyword -scanString kw (_,_,input) len = return $ kw (take len input) - -{- --- | Scan a string until EOF is encountered. -alexScanTokens :: String -> Either String [Keyword] -alexScanTokens inp = runAlex inp gather - where - gather = do - t <- alexMonadScan - case trace (show t) t of - EOF -> return [EOF] - _ -> (t:) `liftM` gather - --- | Scan a file. -scanFile f = do - inp <- readFile f - return $ alexScanTokens inp --} - --- | Formal text types. -data TextType = - TextBegin String - | TextContent String - | TextEnd - deriving( Eq, Ord, Show ) - --- | Lexable Keywords -data Keyword = - IDENT String - | TEXT TextType - | SQUOTE - | DQUOTE - | RIGHTARROW - | LEFTARROW - | LONGRIGHTARROW - | LONGLEFTARROW - | COMMA - | DOT - | COLON - | QUESTIONMARK - | BANG - | AND - | MID - | DOLLAR - | AT - | SHARP - | LPAREN - | RPAREN - | LBRACKET - | RBRACKET - | LBRACE - | RBRACE - | SLASH - | BACKSLASH - | TILDE - | HAT - | STAR - | UNDERSCORE - | MINUS - | PLUS - | EQUAL - | LESS - | GREATER - | EOF - | FORALL - | EXISTS - | LAND - | LOR - | LNOT - | APPROX - -- dummy keyword to get rid of overlapping pattern matches - | DUMMY_KEYWORD - deriving( Eq ) - -instance Show Keyword where - show kw = case kw of - IDENT i -> identifier i - TEXT t -> txt t - SQUOTE -> symbol "'" - DQUOTE -> symbol "\"" - RIGHTARROW -> symbol "->" - LEFTARROW -> symbol "<-" - LONGRIGHTARROW -> symbol "-->" - LONGLEFTARROW -> symbol "<--" - COMMA -> symbol "," - DOT -> symbol "." - COLON -> symbol ":" - QUESTIONMARK -> symbol "?" - BANG -> symbol "!" - AND -> symbol "&" - MID -> symbol "|" - DOLLAR -> symbol "$" - AT -> symbol "@" - SHARP -> symbol "#" - LPAREN -> symbol "(" - RPAREN -> symbol ")" - LBRACKET -> symbol "[" - RBRACKET -> symbol "]" - LBRACE -> symbol "{" - RBRACE -> symbol "}" - SLASH -> symbol "/" - BACKSLASH -> symbol "\\" - TILDE -> symbol "~" - HAT -> symbol "^" - STAR -> symbol "*" - UNDERSCORE -> symbol "_" - MINUS -> symbol "-" - PLUS -> symbol "+" - EQUAL -> symbol "=" - LESS -> symbol "<" - GREATER -> symbol ">" - EOF -> "end of file" - FORALL -> symbol "∀" - EXISTS -> symbol "∃" - LAND -> symbol "∧" - LOR -> symbol "∨" - LNOT -> symbol "¬" - APPROX -> symbol "≈" - DUMMY_KEYWORD -> "DUMMY_KEYWORD (this should not occur!)" - where - identifier i = "identifier `" ++ i ++ "'" - txt (TextBegin t) = "start of `" ++ t ++ "'" - txt (TextContent t) = "text `" ++ t ++ "'" - txt (TextEnd) = "start of text" - symbol s = "symbol `" ++ s ++ "'" - keyword s = "keyword `" ++ s ++ "'" - --- ----------------------------------------------------------------------------- --- Alex wrapper code. --- --- This code is in the PUBLIC DOMAIN; you may copy it freely and use --- it for any purpose whatsoever. - --- ----------------------------------------------------------------------------- --- The input type - - -type AlexInput = (AlexPosn, -- current position, - Char, -- previous char - String) -- current input string - -alexInputPrevChar :: AlexInput -> Char -alexInputPrevChar (p,c,s) = c - -alexGetChar :: AlexInput -> Maybe (Char,AlexInput) -alexGetChar (p,c,[]) = Nothing -alexGetChar (p,_,(c:s)) = let p' = alexMove p c in p' `seq` - Just (c, (p', c, s)) - - --- ----------------------------------------------------------------------------- --- Token positions - --- `Posn' records the location of a token in the input text. It has three --- fields: the address (number of chacaters preceding the token), line number --- and column of a token within the file. `start_pos' gives the position of the --- start of the file and `eof_pos' a standard encoding for the end of file. --- `move_pos' calculates the new position after traversing a given character, --- assuming the usual eight character tab stops. - -data AlexPosn = AlexPn !Int !Int !Int - deriving (Eq) - -instance Show AlexPosn where - show (AlexPn _ l c) = "line "++show l++" column "++show c - -alexStartPos :: AlexPosn -alexStartPos = AlexPn 0 1 1 - -alexMove :: AlexPosn -> Char -> AlexPosn -alexMove (AlexPn a l c) '\t' = AlexPn (a+1) l (((c+7) `div` 8)*8+1) -alexMove (AlexPn a l c) '\n' = AlexPn (a+1) (l+1) 1 -alexMove (AlexPn a l c) _ = AlexPn (a+1) l (c+1) - - --- ----------------------------------------------------------------------------- --- Default monad - - -data AlexState = AlexState { - alex_pos :: !AlexPosn, -- position at current input location - alex_inp :: String, -- the current input - alex_chr :: !Char, -- the character before the input - alex_scd :: !Int, -- the current startcode - alex_ocd :: !Int, -- the old startcode before the comment started - alex_cmt :: [String] -- stack of begin comment identifiers - } - --- Compile with -funbox-strict-fields for best results! - -runAlex :: String -> Alex a -> Either String a -runAlex input (Alex f) - = case f (AlexState {alex_pos = alexStartPos, - alex_inp = input, - alex_chr = '\n', - alex_scd = 0, - alex_ocd = 0, - alex_cmt = [] - }) of - Left msg -> Left msg - Right ( _, a ) -> Right a - -newtype Alex a = Alex { unAlex :: AlexState -> Either String (AlexState, a) } - -instance Monad Alex where - m >>= k = Alex $ \s -> case unAlex m s of - Left msg -> Left msg - Right (s',a) -> unAlex (k a) s' - return a = Alex $ \s -> Right (s,a) - -alexGetPos :: Alex AlexPosn -alexGetPos = Alex $ \s@AlexState{alex_pos=pos} -> Right (s, pos) - -alexGetInput :: Alex AlexInput -alexGetInput - = Alex $ \s@AlexState{alex_pos=pos,alex_chr=c,alex_inp=inp} -> - Right (s, (pos,c,inp)) - -alexSetInput :: AlexInput -> Alex () -alexSetInput (pos,c,inp) - = Alex $ \s -> case s{alex_pos=pos,alex_chr=c,alex_inp=inp} of - s@(AlexState{}) -> Right (s, ()) - -alexError :: String -> Alex a -alexError message = Alex $ \s -> Left $ message ++ " in " ++ show (alex_pos s) - -alexGetStartCode :: Alex Int -alexGetStartCode = Alex $ \s@AlexState{alex_scd=sc} -> Right (s, sc) - -alexSetStartCode :: Int -> Alex () -alexSetStartCode sc = Alex $ \s -> Right (s{alex_scd=sc}, ()) - -alexGetOldStartCode :: Alex Int -alexGetOldStartCode = Alex $ \s@AlexState{alex_ocd=sc} -> Right (s, sc) - -alexSetOldStartCode :: Int -> Alex () -alexSetOldStartCode sc = Alex $ \s -> Right (s{alex_ocd=sc}, ()) - -alexGetComments :: Alex [String] -alexGetComments = Alex $ \s -> Right (s, alex_cmt s) - -alexSetComments :: [String] -> Alex () -alexSetComments cmt = Alex $ \s -> Right (s{alex_cmt=cmt}, ()) - -alexMonadScan = do - inp <- alexGetInput - sc <- alexGetStartCode - case alexScan inp sc of - AlexEOF -> alexEOF - AlexError inp' -> alexError "lexical error" - AlexSkip inp' len -> do - alexSetInput inp' - alexMonadScan - AlexToken inp' len action -> do - alexSetInput inp' - action inp len - --- ----------------------------------------------------------------------------- --- Useful token actions - -type AlexAction result = AlexInput -> Int -> Alex result - --- just ignore this token and scan another one -skip :: AlexAction Keyword -skip input len = alexMonadScan - --- ignore this token, but set the start code to a new value -begin :: Int -> AlexAction Keyword -begin code input len = do alexSetStartCode code; alexMonadScan - --- | Begin a text starting of the given type. -beginText :: String -> Int -> AlexAction Keyword -beginText ty code _ _ = do - alexSetStartCode code - return $ TEXT $ TextBegin ty - --- | End a text. -endText :: Int -> AlexAction Keyword -endText code _ _ = do - alexSetStartCode code - return $ TEXT TextEnd - --- | Begin a comment starting with the given sign. -beginComment :: String -> Int -> AlexAction Keyword -beginComment cmtBegin code input len = do - cmts <- alexGetComments - alexSetComments $ cmtBegin : cmts - if null cmts - then alexGetStartCode >>= alexSetOldStartCode - else return () - alexSetStartCode code - alexMonadScan - --- | End a comment that started with the given begin comment sign. -endComment :: String -> AlexAction Keyword -endComment cmtBegin input len = do - cmts <- alexGetComments - case cmts of - [] -> alexError $ "comment ended but no beginning '"++cmtBegin++"' marked." - (cmt:cmts') -> do - if cmt == cmtBegin - then do - alexSetComments cmts' - if null cmts' - then alexGetOldStartCode >>= alexSetStartCode - else return () - else return () - alexMonadScan - --- perform an action for this token, and set the start code to a new value --- andBegin :: AlexAction result -> Int -> AlexAction result -(action `andBegin` code) input len = do alexSetStartCode code; action input len - -alexEOF :: Alex Keyword -alexEOF = return EOF - - - -} - - - diff --git a/src/Scyther/Theory/Parser.hs b/src/Scyther/Theory/Parser.hs --- a/src/Scyther/Theory/Parser.hs +++ b/src/Scyther/Theory/Parser.hs @@ -55,12 +55,13 @@ import Data.Char import Data.List +import Data.Either import qualified Data.Set as S import qualified Data.Map as M import Data.DAG.Simple import Data.Foldable (asum) -import Control.Arrow ( (***) ) +import Control.Arrow ( (***), first ) import Control.Monad hiding (sequence) import Control.Applicative hiding (empty, many, optional) @@ -70,7 +71,7 @@ import Text.Parsec.Pos import qualified Scyther.Equalities as E -import Scyther.Facts as F hiding (protocol) +import Scyther.Facts as F hiding (variable, protocol) import Scyther.Sequent import Scyther.Proof import Scyther.Theory @@ -282,7 +283,8 @@ -- TODO: Remove this ugly string hack. pattern :: Parser s Pattern pattern = asum - [ string "1" *> pure mkMultIdentityPat + [ string "1" *> pure mkMultIdentityPat + , kw UNDERSCORE *> pure PAny , PConst <$> singleQuoted ident , PMVar <$> (kw QUESTIONMARK *> ident) , PAVar <$> (kw DOLLAR *> ident) @@ -299,13 +301,16 @@ , PSign <$> genFunApp (kw LBRACE) (kw RBRACE) (string "sign") tuplepattern <*> pattern , PMVar <$> tempIdentifier ] - where - tempIdentifier = do i <- identifier - if isLetter (head i) - then return (Id (' ':i)) - else fail $ "invalid variable name '" ++ i ++ - "': variable names must start with a letter" +-- | Parse a specification variable. Untyped identifiers are handled as in +-- 'pattern'. +specVariable :: Parser s VarId +specVariable = asum + [ SMVar <$> (kw QUESTIONMARK *> ident) + , SAVar <$> (kw DOLLAR *> ident) + , SMVar <$> tempIdentifier + ] + -- | Parse multiple ^ applications as a left-associative list of exponentations -- hackily marked using hashes and constant identifiers. exppattern :: Parser s Pattern @@ -321,6 +326,15 @@ tuplepattern :: Parser s Pattern tuplepattern = chainr1 multpattern (PTup <$ kw COMMA) +-- | Parse a local identifier which is yet unresolved. The identifier is +-- prefixed by a space to mark it for later resolution. +tempIdentifier :: Parser s Id +tempIdentifier = do i <- identifier + if isLetter (head i) + then return (Id (' ':i)) + else fail $ "invalid variable name '" ++ i ++ + "': variable names must start with a letter" + -- | Drops the space prefix used for identifying identifiers that need to be -- resolved later. dropSpacePrefix :: Id -> Id @@ -338,23 +352,11 @@ -- | Resolve all identifiers in the pattern. resolveIds :: S.Set Id -> S.Set Id -> Pattern -> Pattern -resolveIds avars mvars = go +resolveIds avars mvars = patMapFMV resolve where - resolve = resolveId avars mvars - go pt@(PConst _) = pt - go pt@(PFresh _) = pt - go pt@(PAVar _) = pt - go pt@(PMVar i) = case getId i of - ' ':i' -> resolve (Id i') -- marked for resolution - _ -> pt - go (PHash pt) = PHash (go pt) - go (PTup pt1 pt2) = PTup (go pt1) (go pt2) - go (PEnc pt1 pt2) = PEnc (go pt1) (go pt2) - go (PSign pt1 pt2) = PSign (go pt1) (go pt2) - go (PSymK pt1 pt2) = PSymK (go pt1) (go pt2) - go (PShrK pt1 pt2) = PShrK (go pt1) (go pt2) - go (PAsymPK pt) = PAsymPK (go pt) - go (PAsymSK pt) = PAsymSK (go pt) + resolve i = case getId i of + ' ':i' -> resolveId avars mvars (Id i') + _ -> PMVar i -- | Resolve identifiers as identifiers of the given role. -- PRE: The role must use disjoint identifiers for fresh messages, agent @@ -362,7 +364,21 @@ resolveIdsLocalToRole :: Role -> Pattern -> Pattern resolveIdsLocalToRole role = resolveIds (roleFAV role) (roleFMV role) +-- | Resolve the type of a specification variable according to the set of +-- agent and message variables. +-- +-- TODO: Better error handling. +resolveVarId :: S.Set Id -> S.Set Id -> VarId -> VarId +resolveVarId avars mvars (SMVar i) = case getId i of + ' ':i' + | Id i' `S.member` avars -> SAVar (Id i') + | Id i' `S.member` mvars -> SMVar (Id i') + | otherwise -> error $ "resolveVarId: '" ++ i' ++ + "' resolves to neither agent nor message variable" + _ -> SMVar i +resolveVarId _ _ v = v + -- Messages ----------- @@ -463,59 +479,73 @@ -} --- | Parse a single transfer. -transfer :: Parser s [(Id, RoleStep)] -transfer = do +-- | Parse a single transfer with the given label. +transfer :: Label -> Parser s [(Id, RoleStep)] +transfer lbl = + do right <- kw RIGHTARROW *> ident <* kw COLON + pt <- tuplepattern + return [(right, Recv lbl pt)] + <|> + do right <- kw LEFTARROW *> ident <* kw COLON + ptr <- tuplepattern + (do left <- try $ ident <* kw LEFTARROW <* kw COLON + ptl <- tuplepattern + return [(left, Recv lbl ptl),(right, Send lbl ptr)] + <|> + return [(right, Send lbl ptr)] + ) + <|> + do left <- ident + (do kw RIGHTARROW + (do right <- ident <* kw COLON + pt <- tuplepattern + return [(left,Send lbl pt), (right, Recv lbl pt)] + <|> + do ptl <- kw COLON *> tuplepattern + (do right <- kw RIGHTARROW *> ident <* kw COLON + ptr <- tuplepattern + return [(left,Send lbl ptl), (right, Recv lbl ptr)] + <|> + do return [(left, Send lbl ptl)] + ) + ) + <|> + do kw LEFTARROW + (do pt <- kw COLON *> tuplepattern + return [(left, Recv lbl pt)] + <|> + do right <- ident <* kw COLON + pt <- tuplepattern + return [(left, Recv lbl pt), (right, Send lbl pt)] + ) + ) + +-- | Try to parse a local computation with the given label. +compute :: Label -> Parser s [(Id, RoleStep)] +compute lbl = do + actor <- try $ ident <* kw COLON + v <- specVariable + eq <- (kw RIGHTARROW *> pure True) <|> (kw SHARP *> pure False) + ptr <- tuplepattern + return [(actor, Match lbl eq v ptr)] + +-- | Parse a labeled part of a protocol specification, i.e., either a transfer +-- or a computation. +labeledSteps :: Parser s [(Id, RoleStep)] +labeledSteps = do lbl <- Label <$> identifier <* kw DOT - (do right <- kw RIGHTARROW *> ident <* kw COLON - pt <- tuplepattern - return [(right, Recv lbl pt)] - <|> - do right <- kw LEFTARROW *> ident <* kw COLON - ptr <- tuplepattern - (do left <- try $ ident <* kw LEFTARROW <* kw COLON - ptl <- tuplepattern - return [(left, Recv lbl ptl),(right, Send lbl ptr)] - <|> - return [(right, Send lbl ptr)] - ) - <|> - do left <- ident - (do kw RIGHTARROW - (do right <- ident <* kw COLON - pt <- tuplepattern - return [(left,Send lbl pt), (right, Recv lbl pt)] - <|> - do ptl <- kw COLON *> tuplepattern - (do right <- kw RIGHTARROW *> ident <* kw COLON - ptr <- tuplepattern - return [(left,Send lbl ptl), (right, Recv lbl ptr)] - <|> - do return [(left, Send lbl ptl)] - ) - ) - <|> - do kw LEFTARROW - (do pt <- kw COLON *> tuplepattern - return [(left, Recv lbl pt)] - <|> - do right <- ident <* kw COLON - pt <- tuplepattern - return [(left, Recv lbl pt), (right, Send lbl pt)] - ) - ) - ) + compute lbl <|> transfer lbl -- | Parse a protocol. protocol :: Parser s Protocol protocol = do name <- string "protocol" *> identifier - transfers <- concat <$> braced (many1 transfer) - -- convert parsed transfers into role scripts - let roleIds = S.fromList $ map fst transfers + allSteps <- concat <$> braced (many1 labeledSteps) + -- convert parsed steps into role scripts + let roleIds = S.fromList $ map fst allSteps roles = do actor <- S.toList roleIds - let steps = [ step | (i, step) <- transfers, i == actor ] + let steps = [ step | (i, step) <- allSteps, i == actor ] return $ Role (getId actor) (ensureFreshSteps actor (S.map addSpacePrefix roleIds) steps) return $ Protocol name roles @@ -526,18 +556,25 @@ ensureFreshSteps actor possibleAvars = go (S.singleton (addSpacePrefix actor)) S.empty S.empty where + -- TODO: Make sure that this does what one expects. go _ _ _ [] = [] - go avars mvars fresh (Send l pt : rs) = - let avars' = avars `S.union` (((patFMV pt `S.intersection` possibleAvars) - `S.difference` mvars) `S.difference` fresh) - fresh' = fresh `S.union` ((patFMV pt `S.difference` avars') `S.difference` mvars) - pt' = resolveIds (dropSpacePrefixes avars') (dropSpacePrefixes mvars) pt - in Send l pt' : go avars' mvars fresh' rs - go avars mvars fresh (Recv l pt : rs) = - let mvars' = mvars `S.union` ((patFMV pt `S.difference` avars) `S.difference` fresh) - pt' = resolveIds (dropSpacePrefixes avars) (dropSpacePrefixes mvars') pt - in Recv l pt' : go avars mvars' fresh rs + go avars mvars fresh (step : rs) = step' : go avars' mvars' fresh' rs + where + avars' = avars `S.union` (((stepUsedMV step `S.intersection` possibleAvars) + `S.difference` mvars) `S.difference` fresh) + mvars' = mvars `S.union` ((stepBoundMV step `S.difference` avars') + `S.difference` fresh) + fresh' = fresh `S.union` ((stepUsedMV step `S.difference` avars') + `S.difference` mvars') + pt' = resolveIds (dropSpacePrefixes avars') (dropSpacePrefixes mvars') + (stepPat step) + step' = case step of + Send l _ -> Send l pt' + Recv l _ -> Recv l pt' + Match l eq v _ -> Match l eq (resolveVarId (dropSpacePrefixes avars') + (dropSpacePrefixes mvars') v) pt' + ------------------------------------------------------------------------------ -- Parse Claims ------------------------------------------------------------------------------ @@ -588,10 +625,9 @@ n@(PFresh i) <- S.toList $ subpatterns pt guard (not (plainUse pt n) && firstUse n) return $ secrecySe (MFresh . Fresh) i - Recv _ pt -> do - v@(PMVar i) <- S.toList $ subpatterns pt - guard (not (plainUse pt v) && firstUse v) - return $ secrecySe (MMVar . MVar) i + Recv _ pt -> varSequents pt + Match _ True _ pt -> varSequents pt + Match _ False _ _ -> mzero where (tid, prem0) = freshTID (empty proto) (prefix, _) = break (step ==) $ roleSteps role @@ -599,6 +635,10 @@ plainUse pt = (`S.member` splitpatterns pt) avars = [ MAVar (AVar (LocalId (v,tid))) | (PAVar v) <- S.toList . S.unions . map (subpatterns.stepPat) $ roleSteps role ] + varSequents pt = do + v@(PMVar i) <- S.toList $ subpatterns pt + guard (not (plainUse pt v) && firstUse v) + return $ secrecySe (MMVar . MVar) i secrecySe constr i = ( (++("_"++roleName role++"_sec_"++getId i)) , Sequent prem (FAtom (ABool False)) Standard @@ -628,7 +668,8 @@ where steps = roleSteps role (tid, prem0) = freshTID (empty proto) - mkStepSequents (_, Recv _ _ ) = [] + mkStepSequents (_, Recv _ _) = [] + mkStepSequents (_, Match _ _ _ _) = [] mkStepSequents (prefix, step@(Send _ pt)) = do n@(PFresh i) <- S.toList $ splitpatterns pt guard (n `S.notMember` S.unions (map (subpatterns.stepPat) prefix)) @@ -858,17 +899,30 @@ falseConcl :: Parser s Formula falseConcl = doubleQuoted (string "False" *> pure (FAtom (ABool False))) +-- | Parse a conclusion formula consisting of raw facts. +-- +-- TODO: Handling of role equalities is incomplete. +factsFormula :: Protocol -> E.Mapping -> Parser s Formula +factsFormula proto mapping = doubleQuoted formula + where + formula = foldr1 FDisj `liftM` sepBy1 term (kw MID) + term = do + conjuncts <- sepBy1 factOrFormula (kw AND) + let (facts, subformulas) = first concat $ partitionEithers conjuncts + roleeqs <- extractRoleEqs proto facts + let mapping' = foldr (uncurry E.addTIDRoleMapping) mapping roleeqs + atoms <- (map (AEq . E.TIDRoleEq) roleeqs ++) `liftM` + sequence [ mkAtom mapping' | RawAtom mkAtom <- facts ] + return $ foldr1 FConj (map FAtom atoms ++ subformulas) + factOrFormula = (Left <$> try rawFacts) <|> (Right <$> parens formula) + -- | Parse a conclusion stating existence of some threads of a specific -- structure. existenceConcl :: Protocol -> E.Mapping -> Parser s Formula existenceConcl proto mapping = do tids <- map (Left . TID) <$> (threads <|> pure []) - facts <- concat <$> doubleQuoted (sepBy1 rawFacts (kw AND)) - roleeqs <- extractRoleEqs proto facts - let mapping' = foldr (uncurry E.addTIDRoleMapping) mapping roleeqs - atoms <- (map (AEq . E.TIDRoleEq) roleeqs ++) `liftM` - sequence [ mkAtom mapping' | RawAtom mkAtom <- facts ] - return $ foldr FExists (foldr1 FConj . map FAtom $ atoms) tids + inner <- factsFormula proto mapping + return $ foldr FExists inner tids where singleThread = pure <$> (strings ["a", "thread"] *> integer) multiThreads = strings ["threads"] *> sepBy1 integer (kw COMMA) @@ -892,9 +946,10 @@ prems0 <- foldM (flip quantifyTID) (F.empty proto) quantifiers optPrems <- conjoinAtoms atoms prems0 prems <- maybe (fail "contradictory premises") return optPrems + qualifier <- option Standard (string "injectively" *> pure Injective) string "imply" concl <- conclusion proto mapping - return $ Sequent prems concl Standard + return $ Sequent prems concl qualifier {- -- | Construct the premise modifier. The given set of role equalities is used diff --git a/src/Scyther/Theory/Pretty.hs b/src/Scyther/Theory/Pretty.hs --- a/src/Scyther/Theory/Pretty.hs +++ b/src/Scyther/Theory/Pretty.hs @@ -303,7 +303,7 @@ prettySoundness thy = case unsoundTheorems thy of [] -> emptyDoc ths -> vcat $ - map text ["", "(* NOTE that the proofs of the following theorems are UNSOUND:", ""] ++ + map text ["", "(* NOTE that the proofs of the following theorems are INVALID:", ""] ++ map ppThm ths ++ map text ["*)"] where @@ -342,8 +342,8 @@ -- | Convert a triviality reason to a string representing the corresponding -- Isabelle tactic. isaTactic :: TrivReason -> String -isaTactic TrivContradictoryPremises = "((clarsimp, order?) | order)" -isaTactic (TrivLongTermKeySecrecy _) = "(fastforce dest!: ltk_secrecy)" +isaTactic TrivContradictoryPremises = "((clarsimp, order?) | order | fast)" +isaTactic (TrivLongTermKeySecrecy _) = "(auto dest!: ltk_secrecy)" isaTactic TrivPremisesImplyConclusion = "(fastforce intro: event_predOrdI split: if_splits)" -- | Isabelle proof of long-term key secrecy. @@ -491,9 +491,9 @@ | 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, fastforce+)?" -- be conservative + | null tactics = kwQED <-> text "(safe?, simp_all?, insert facts, (fastforce+)?)" -- be conservative | otherwise = - kwQED <-> text "(insert facts, (" <> hsep (intersperse (text "|") tactics) <> text ")+)?" + kwQED <-> text "(safe?, simp_all?, insert facts, ((" <> hsep (intersperse (text "|") tactics) <> text ")+)?)" where tactics = map text . nub . map isaTactic . snd $ genericChainRuleSplitCases snd trivCases @@ -519,10 +519,11 @@ monoTyp = typName ++ ".monoTyp" prettyTypingCase typName name = - kwCase <-> text ("("++ name ++" t r s") <-> prettyTID 0 <> text") note facts = this" $-$ + kwCase <-> text ("("++ name ++" t r s") <-> prettyTID 0 <> text")" $-$ text ("then interpret state: "++ typingLocale typName ++" t r s") $-$ nest 2 (text "by unfold_locales auto") $-$ - text "show ?case using facts" + text ("note_prefix_closed (state) facts = " ++ name) $-$ + text "thus ?case" -- equality splitting prettySplitEqCase name = diff --git a/src/Scyther/Typing.hs b/src/Scyther/Typing.hs --- a/src/Scyther/Typing.hs +++ b/src/Scyther/Typing.hs @@ -66,7 +66,12 @@ normType (AsymSKT ty) = AsymSKT ty normType ty = ty +-- | Split all sums in a type term and return the basic types. +splitSums :: Type -> [Type] +splitSums (SumT ty1 ty2) = splitSums ty1 `mplus` splitSums ty2 +splitSums ty = pure ty + ------------------------------------------------------------------------------ -- Type annotations on messages ------------------------------------------------------------------------------ @@ -107,55 +112,96 @@ rolemap = M.fromList $ zip (protoRoles proto) [1..] steps = map (second (rolemap M.!)) . toposort $ protoOrd proto - typeStep eqs (Send _ _, _) = do - return eqs - typeStep eqs (recv@(Recv lR ptR), tidR) = + typeStep eqs (Send _ _, _) = return eqs + typeStep eqs step@(Match _ True v pt, tidM) = do + eqs' <- lift $ E.solve [E.MsgEq (instVar tidM v, inst tidM pt)] eqs + lty <- variable (const . return $ AgentT) (lookupType step) v + typeMatchVars step lty (E.getMVarEqs eqs') + return eqs' + typeStep eqs (Match _ _ _ _, _) = return eqs + typeStep eqs step@(Recv lR ptR, tidR) = case [ send | send@(Send lS _, _) <- steps, lS == lR ] of [] -> do -- no matching send: assume intruder knows all message variables -- in the received pattern that are not yet mapped. sequence_ $ do PMVar v <- S.toList $ subpatterns ptR - return (knownAtRecv v) + return (knownAtRecv step v) return eqs ((Send _ ptS, tidS):_) -> do eqs' <- lift $ E.solve [E.MsgEq (inst tidR ptR, inst tidS ptS)] eqs - mapM_ typeMVar (E.getMVarEqs eqs') + mapM_ (typeMVar step) (E.getMVarEqs eqs') -- variables not mapped yet are mapped to they known type. sequence_ $ do PMVar v <- S.toList $ subpatterns ptR - return (knownAtRecv v) + return (knownAtRecv step v) return eqs' _ -> error "mscTyping: the impossible happened" + + lookupType (_step, tid) v = gets (M.! (v, roleeqs M.! tid)) + + keepExisting _new old = old + + typeMVar (step, tid) (MVar (LocalId (v, vTid)), m) + | vTid == tid && PMVar v `S.member` splitpatterns (stepPat step) = + noteType (KnownT step) + | otherwise = + noteType $ maybe (KnownT step) (SumT (KnownT step)) (typeMsg m) where - typeMVar (MVar (LocalId (v, vTid)), m) - | vTid == tidR && PMVar v `S.member` splitpatterns ptR = - noteType (KnownT recv) - | otherwise = - noteType $ maybe (KnownT recv) (SumT (KnownT recv)) (typeMsg m) - where - noteType = modify . M.insertWith keepSimpler (v, roleeqs M.! vTid) - -- prefer non-sum-types and then the existing one - keepSimpler _ x@(KnownT _) = x - keepSimpler x@(KnownT _) _ = x - keepSimpler _ x = x + noteType = modify . M.insertWith keepSimpler (v, roleeqs M.! vTid) + -- prefer non-sum-types and then the existing one + keepSimpler _ x@(KnownT _) = x + keepSimpler x@(KnownT _) _ = x + keepSimpler _ x = x - knownAtRecv v = - modify (M.insertWith keepExisting (v, roleeqs M.! tidR) (KnownT recv)) - where - keepExisting _new old = old - - typeMsg (MFresh (Fresh fr)) = pure $ NonceT (roleeqs M.! lidTID fr) (lidId fr) - typeMsg (MConst c) = pure $ ConstT c - typeMsg (MAVar _) = pure $ AgentT - typeMsg (MMVar _) = Nothing - typeMsg (MHash m) = HashT <$> typeMsg m - typeMsg (MTup m1 m2) = TupT <$> typeMsg m1 <*> typeMsg m2 - typeMsg (MEnc m1 m2) = EncT <$> typeMsg m1 <*> typeMsg m2 - typeMsg (MSymK m1 m2) = SymKT <$> typeMsg m1 <*> typeMsg m2 - typeMsg (MAsymPK m) = AsymPKT <$> typeMsg m - typeMsg (MAsymSK m) = AsymSKT <$> typeMsg m - typeMsg (MArbMsg _) = error $ "mscTyping: agent variable encountered" - typeMsg (MInvKey _) = error $ "mscTyping: key inversion encountered" - typeMsg (MShrK _ _) = error $ "mscTyping: bi-directional shared key encountered" + knownAtRecv (step, tid) v = + modify (M.insertWith keepExisting (v, roleeqs M.! tid) (KnownT step)) + + -- Infer types of variables on RHS of a matching step. We use both the type + -- of the LHS variable and the types implied by the message equalities. + typeMatchVars (step, tid) lty meqs = mapM_ noteType vars + where + vars = [v | PMVar v <- S.toList $ subpatterns $ stepPat step] + noteType v = modify $ M.insertWith keepExisting (v, roleeqs M.! tid) (inferType v) + inferType v = case known ++ structuralTypesOf v of + [] -> error $ "mscTyping: Cannot infer type. Impossible match?" + tys -> foldr1 SumT tys + structuralTypesOf v = S.toList $ M.findWithDefault S.empty v structuralTypes + -- Due to deficiencies of the well-typedness proof strategy, use the + -- current match step in KnownT types. + known = case [ty | ty@(KnownT _) <- splitSums lty] of + [] -> [] + _ -> [KnownT step] + + structuralTypes = transfer lty (stepPat step) eqTypes + eqTypes = foldr eqType1 M.empty meqs + eqType1 (MVar (LocalId (v, vTid)), msg) + | vTid == tid = maybe id (M.insert v . S.singleton) (typeMsg msg) + | otherwise = id + + transfer (SumT ty1 ty2) pt = transfer ty1 pt . transfer ty2 pt + transfer (KnownT _) _ = id + transfer ty (PMVar v) = M.insertWith S.union v (S.singleton ty) + transfer (HashT ty) (PHash pt) = transfer ty pt + transfer (EncT ty1 ty2) (PEnc p1 p2) = transfer ty1 p1 . transfer ty2 p2 + transfer (TupT ty1 ty2) (PTup p1 p2) = transfer ty1 p1 . transfer ty2 p2 + transfer (SymKT ty1 ty2) (PSymK p1 p2) = transfer ty1 p1 . transfer ty2 p2 + transfer (AsymPKT ty) (PAsymPK pt) = transfer ty pt + transfer (AsymSKT ty) (PAsymSK pt) = transfer ty pt + transfer _ _ = id + + + typeMsg (MFresh (Fresh fr)) = pure $ NonceT (roleeqs M.! lidTID fr) (lidId fr) + typeMsg (MConst c) = pure $ ConstT c + typeMsg (MAVar _) = pure $ AgentT + typeMsg (MMVar _) = Nothing + typeMsg (MHash m) = HashT <$> typeMsg m + typeMsg (MTup m1 m2) = TupT <$> typeMsg m1 <*> typeMsg m2 + typeMsg (MEnc m1 m2) = EncT <$> typeMsg m1 <*> typeMsg m2 + typeMsg (MSymK m1 m2) = SymKT <$> typeMsg m1 <*> typeMsg m2 + typeMsg (MAsymPK m) = AsymPKT <$> typeMsg m + typeMsg (MAsymSK m) = AsymSKT <$> typeMsg m + typeMsg (MArbMsg _) = error $ "mscTyping: logical variable encountered" + typeMsg (MInvKey _) = error $ "mscTyping: key inversion encountered" + typeMsg (MShrK _ _) = error $ "mscTyping: bi-directional shared key encountered" ------------------------------------------------------------------------------ diff --git a/src/System/Isabelle.hs b/src/System/Isabelle.hs --- a/src/System/Isabelle.hs +++ b/src/System/Isabelle.hs @@ -2,7 +2,7 @@ -- -- Requirements: -- --- 1. A working installation of Isabelle2013-2 (http://isabelle.in.tum.de/) +-- 1. A working installation of Isabelle2014 (http://isabelle.in.tum.de/) -- 2. The \'isabelle\' command must be on the PATH. -- module System.Isabelle ( diff --git a/src/Text/Dot.hs b/src/Text/Dot.hs --- a/src/Text/Dot.hs +++ b/src/Text/Dot.hs @@ -51,7 +51,8 @@ ) where import Data.List (intersperse) -import Control.Monad (liftM) +import Control.Applicative +import Control.Monad (ap, liftM) data NodeId = NodeId String | UserNodeId Int @@ -69,6 +70,13 @@ | SubGraph NodeId [GraphElement] data Dot a = Dot { unDot :: Int -> ([GraphElement],Int,a) } + +instance Functor Dot where + fmap = liftM + +instance Applicative Dot where + pure = return + (<*>) = ap instance Monad Dot where return a = Dot $ \ uq -> ([],uq,a) diff --git a/src/Text/Isar.hs b/src/Text/Isar.hs --- a/src/Text/Isar.hs +++ b/src/Text/Isar.hs @@ -25,12 +25,14 @@ , isaForall , isaLambda , isaAnd + , isaOr , isaImplies , isaNotIn , isaIn , isaSubsetEq , isaAlpha , isaSublocale + , isaNotEq -- * Extensions of 'Text.PrettyPrint' , module Text.PrettyPrint.Class @@ -266,6 +268,12 @@ | isPlainStyle conf = text "&" | otherwise = symbol "\\" +-- | The logical or symbol: @|@ +isaOr :: Document d => IsarConf -> d +isaOr conf + | isPlainStyle conf = text "|" + | otherwise = symbol "\\" + -- | The logical and symbol: @-->@ isaImplies :: Document d => IsarConf -> d isaImplies conf @@ -283,6 +291,12 @@ isaSublocale conf | isPlainStyle conf = text "<" | otherwise = symbol "\\" + +-- | The not equal symbol: @~=@ +isaNotEq :: Document d => IsarConf -> d +isaNotEq conf + | isPlainStyle conf = text "~=" + | otherwise = symbol "\\" ------------------------------------------------------------------------------ -- Isabelle theory components