2014-08-12 00:35:25 +00:00
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-- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
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-- Released under Apache 2.0 license as described in the file LICENSE.
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-- Author: Jeremy Avigad
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-- Ported from Coq HoTT
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-- TODO: move this to an "axioms" folder
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-- TODO: take a look at the Coq tricks
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import .path .equiv
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2014-09-09 20:20:04 +00:00
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open path
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2014-08-12 00:35:25 +00:00
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-- Funext
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-- ------
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axiom funext {A : Type} {P : A → Type} (f g : Π x : A, P x) : IsEquiv (@apD10 A P f g)
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definition path_forall {A : Type} {P : A → Type} (f g : Π x : A, P x) : f ∼ g → f ≈ g :=
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(funext f g)⁻¹
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definition path_forall2 {A B : Type} {P : A → B → Type} (f g : Π x y, P x y) :
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(Πx y, f x y ≈ g x y) → f ≈ g :=
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λE, path_forall f g (λx, path_forall (f x) (g x) (E x))
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