25 lines
870 B
Text
25 lines
870 B
Text
-- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
|
||
-- Released under Apache 2.0 license as described in the file LICENSE.
|
||
-- Author: Jeremy Avigad, Jakob von Raumer
|
||
-- Ported from Coq HoTT
|
||
|
||
-- TODO: move this to an "axioms" folder
|
||
-- TODO: take a look at the Coq tricks
|
||
import .path .equiv
|
||
open path
|
||
|
||
-- Funext
|
||
-- ------
|
||
|
||
axiom funext {A : Type} {P : A → Type} (f g : Π x : A, P x) : IsEquiv (@apD10 A P f g)
|
||
|
||
theorem funext_instance [instance] {A : Type} {P : A → Type} (f g : Π x : A, P x) :
|
||
IsEquiv (@apD10 A P f g) :=
|
||
@funext A P f g
|
||
|
||
definition path_forall {A : Type} {P : A → Type} (f g : Π x : A, P x) : f ∼ g → f ≈ g :=
|
||
IsEquiv.inv !apD10
|
||
|
||
definition path_forall2 {A B : Type} {P : A → B → Type} (f g : Π x y, P x y) :
|
||
(Πx y, f x y ≈ g x y) → f ≈ g :=
|
||
λE, path_forall f g (λx, path_forall (f x) (g x) (E x))
|