subset.golden

MiniAgda by Andreas Abel and Karl Mehltretter
--- opening "subset.ma" ---
--- scope checking ---
--- type checking ---
type  Subset : ^(A : Set) -> ^(P : A -> Set) -> Set
term  Subset.put : .[A : Set] -> .[P : A -> Set] -> ^(get : A) -> .[y1 : P get] -> < Subset.put get y1 : Subset A P >
type  Nat : Set
term  Nat.zero : < Nat.zero : Nat >
term  Nat.succ : ^(y0 : Nat) -> < Nat.succ y0 : Nat >
type  Odd : ^ Nat -> Set
term  Odd.odd1 : < Odd.odd1 : Odd (Nat.succ Nat.zero) >
term  Odd.odd3 : < Odd.odd3 : Odd (Nat.succ (Nat.succ (Nat.succ Nat.zero))) >
term  Odd.oddSS : .[n : Nat] -> ^(y1 : Odd n) -> < Odd.oddSS n y1 : Odd (Nat.succ (Nat.succ n)) >
type  Eq : ^(A : Set) -> ^(a : A) -> ^ A -> Set
term  Eq.refl : .[A : Set] -> .[a : A] -> < Eq.refl : Eq A a a >
type  OddN : Set
type  OddN = Subset Nat Odd
term  one : Nat
term  one = Nat.succ Nat.zero
term  three : Nat
term  three = Nat.succ (Nat.succ one)
term  o3 : OddN
term  o3 = Subset.put three [Odd.odd3]
term  o3' : OddN
term  o3' = Subset.put three [Odd.oddSS [one] Odd.odd1]
term  p : Eq OddN o3 o3'
term  p = Eq.refl
--- evaluating ---
--- closing "subset.ma" ---