lean2/tests/lean/scope.lean.expected.out
Leonardo de Moura 08718e33dc refactor(builtin): only load the kernel and natural numbers by default
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-12-30 13:35:37 -08:00

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Set: pp::colors
Set: pp::unicode
Imported 'int'
Assumed: A
Assumed: B
Assumed: f
Defined: g
Assumed: h
Assumed: hinv
Assumed: Inv
Assumed: H1
Proved: f_eq_g
Proved: Inj
Definition g (A : Type) (f : A → A → A) (x y : A) : A := f y x
Theorem f_eq_g (A : Type) (f : A → A → A) (H1 : Π x y : A, f x y = f y x) : f = g A f :=
Abst (λ x : A,
Abst (λ y : A,
let L1 : f x y = f y x := H1 x y, L2 : f y x = g A f x y := Refl (g A f x y) in Trans L1 L2))
Theorem Inj (A B : Type) (h : A → B) (hinv : B → A) (Inv : Π x : A, hinv (h x) = x) (x y : A) (H : h x = h y) : x =
y :=
let L1 : hinv (h x) = hinv (h y) := Congr2 hinv H,
L2 : hinv (h x) = x := Inv x,
L3 : hinv (h y) = y := Inv y,
L4 : x = hinv (h x) := Symm L2,
L5 : x = hinv (h y) := Trans L4 L1
in Trans L5 L3
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