lean2/library/logic/axioms/funext.lean
Leonardo de Moura 08ccd58eb6 feat(frontends/lean): add 'reducible' modifier for controlling which
definitions are unfolded during elaboration

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-09-19 15:54:32 -07:00

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-- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Author: Leonardo de Moura
-- logic.axioms.funext
-- ===================
import logic.core.eq algebra.function
open function
-- Function extensionality
axiom funext : ∀ {A : Type} {B : A → Type} {f g : Π x, B x} (H : ∀ x, f x = g x), f = g
namespace function
section
parameters {A B C D: Type}
theorem compose_assoc (f : C → D) (g : B → C) (h : A → B) : (f ∘ g) ∘ h = f ∘ (g ∘ h) :=
funext (take x, rfl)
theorem compose_id_left (f : A → B) : id ∘ f = f :=
funext (take x, rfl)
theorem compose_id_right (f : A → B) : f ∘ id = f :=
funext (take x, rfl)
theorem compose_const_right (f : B → C) (b : B) : f ∘ (const A b) = const A (f b) :=
funext (take x, rfl)
end
end function