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fix(library/hott) fix funext.lean by making funext an instance

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Jakob von Raumer 2014-11-04 09:49:07 -05:00 committed by Leonardo de Moura
parent 6944c7d902
commit 0ed046ed80
1 changed files with 5 additions and 1 deletions
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6
library/hott/funext.lean
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@ -13,8 +13,12 @@ open path
axiom funext {A : Type} {P : A → Type} (f g : Π x : A, P x) : IsEquiv (@apD10 A P f g) 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 := definition path_forall {A : Type} {P : A → Type} (f g : Π x : A, P x) : f ∼ g → f ≈ g :=
@IsEquiv.inv _ _ _ (funext f g) IsEquiv.inv !apD10
definition path_forall2 {A B : Type} {P : A → B → Type} (f g : Π x y, P x y) : 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 := (Πx y, f x y ≈ g x y) → f ≈ g :=