08ccd58eb6
definitions are unfolded during elaboration Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
30 lines
872 B
Text
30 lines
872 B
Text
-- 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
|