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fix(library/hott) fill both gaps (I don't know why it works that way), change name from funext.apply to funext.ap, since apply seems to be a tactic name?

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Jakob von Raumer 2014-11-20 01:08:23 -05:00 committed by Leonardo de Moura
parent fd47a162de
commit 2d9621892b
3 changed files with 7 additions and 8 deletions
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8
library/hott/axioms/funext.lean
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@ -14,7 +14,7 @@ set_option pp.universes true
-- Define function extensionality as a type class -- Define function extensionality as a type class
inductive funext.{l} [class] : Type.{l+3} := 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)) 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} → funext.{l}
namespace funext namespace funext
@ -23,11 +23,11 @@ namespace funext
universe l universe l
parameters [F : funext.{l}] {A : Type.{l+1}} {P : A → Type.{l+2}} (f g : Π x, P x) 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) := protected definition ap [instance] : IsEquiv (@apD10 A P f g) :=
rec_on F (λ H, sorry) rec_on F (λ (H : Π A P f g, _), !H)
definition path_forall : f ∼ g → f ≈ g := definition path_forall : f ∼ g → f ≈ g :=
@IsEquiv.inv _ _ (@apD10 A P f g) apply @IsEquiv.inv _ _ (@apD10 A P f g) ap
end end

5
library/hott/axioms/ua.lean
View file

@ -5,7 +5,6 @@
import hott.path hott.equiv import hott.path hott.equiv
open path Equiv open path Equiv
set_option pp.universes true
--Ensure that the types compared are in the same universe --Ensure that the types compared are in the same universe
section section
universe variable l universe variable l
@ -29,8 +28,8 @@ namespace ua_type
parameters [F : ua_type.{k}] {A B: Type.{k}} parameters [F : ua_type.{k}] {A B: Type.{k}}
-- Make the Equivalence given by the axiom an instance -- Make the Equivalence given by the axiom an instance
protected definition inst [instance] : IsEquiv (equiv_path A B) := protected definition inst [instance] : IsEquiv (equiv_path.{k} A B) :=
rec_on F (λ H, sorry) rec_on F (λ H, H A B)
-- This is the version of univalence axiom we will probably use most often -- This is the version of univalence axiom we will probably use most often
definition ua : A ≃ B → A ≈ B := definition ua : A ≃ B → A ≈ B :=

2
library/hott/funext_varieties.lean
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@ -28,7 +28,7 @@ definition weak_funext.{l} :=
definition funext_implies_naive_funext [F : funext] : naive_funext := definition funext_implies_naive_funext [F : funext] : naive_funext :=
(λ A P f g h, (λ A P f g h,
have Fefg: IsEquiv (@apD10 A P f g), have Fefg: IsEquiv (@apD10 A P f g),
from (@funext.apply F A P f g), from (@funext.ap F A P f g),
have eq1 : _, from (@IsEquiv.inv _ _ (@apD10 A P f g) Fefg h), have eq1 : _, from (@IsEquiv.inv _ _ (@apD10 A P f g) Fefg h),
eq1 eq1
) )