38 lines
1.1 KiB
Text
38 lines
1.1 KiB
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: take a look at the Coq tricks
|
||
import hott.path hott.equiv
|
||
open path
|
||
|
||
set_option pp.universes true
|
||
|
||
-- Funext
|
||
-- ------
|
||
|
||
-- Define function extensionality as a type class
|
||
inductive funext.{l} [class] : Type.{l+3} :=
|
||
mk : (Π {A : Type.{l+1}} {P : A → Type.{l+2}} (f g : Π x, P x), IsEquiv (@apD10 A P f g))
|
||
→ funext.{l}
|
||
|
||
namespace funext
|
||
|
||
context
|
||
universe l
|
||
parameters [F : funext.{l}] {A : Type.{l+1}} {P : A → Type.{l+2}} (f g : Π x, P x)
|
||
|
||
protected definition apply [instance] : IsEquiv (@apD10 A P f g) :=
|
||
rec_on F (λ H, sorry)
|
||
|
||
definition path_forall : f ∼ g → f ≈ g :=
|
||
@IsEquiv.inv _ _ (@apD10 A P f g) apply
|
||
|
||
end
|
||
|
||
definition path_forall2 [F : funext] {A B : Type} {P : A → B → Type}
|
||
(f g : Πx y, P x y) : (Πx y, f x y ≈ g x y) → f ≈ g :=
|
||
λ E, path_forall f g (λx, path_forall (f x) (g x) (E x))
|
||
|
||
end funext
|