lean2/tests/lean/scope.lean

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Scope
Variable A : Type
Variable B : Type
Variable f : A -> A -> A
Definition g (x y : A) : A := f y x
Variable h : A -> B
Variable hinv : B -> A
Axiom Inv (x : A) : hinv (h x) = x
Axiom H1 (x y : A) : f x y = f y x
Theorem f_eq_g : f = g := Abst (fun x, (Abst (fun y,
let L1 : f x y = f y x := H1 x y,
L2 : f y x = g x y := Refl (g x y)
in Trans L1 L2)))
Theorem Inj (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.
EndScope
Show Environment 3.
Eval g Int Int::sub 10 20