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remove duplicate of Pushout.elimProp #923

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Sep 2, 2022
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remove duplicate of Pushout.elimProp #923

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11 changes: 0 additions & 11 deletions Cubical/HITs/Pushout/Properties.agda
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Expand Up @@ -359,17 +359,6 @@ record 3x3-span : Type₁ where
3x3-lemma : A□○ ≡ A○□
3x3-lemma = isoToPath 3x3-Iso

PushoutToProp : {f : A → B} {g : A → C}
{D : Pushout f g → Type ℓ'''}
→ ((x : Pushout f g) → isProp (D x))
→ ((a : B) → D (inl a))
→ ((c : C) → D (inr c))
→ (x : Pushout f g) → D x
PushoutToProp isset baseB baseC (inl x) = baseB x
PushoutToProp isset baseB baseC (inr x) = baseC x
PushoutToProp {f = f} {g = g} isset baseB baseC (push a i) =
isOfHLevel→isOfHLevelDep 1 isset (baseB (f a)) (baseC (g a)) (push a) i

-- explicit characterisation of equivalences
-- Pushout f₁ g₁ ≃ Pushout f₂ g₂ avoiding
-- transports
Expand Down
4 changes: 2 additions & 2 deletions Cubical/Homotopy/HopfInvariant/HopfMap.agda
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Expand Up @@ -44,7 +44,7 @@ open import Cubical.Algebra.Group.MorphismProperties
open import Cubical.Algebra.Group.Instances.Int
open import Cubical.Algebra.Group.GroupPath

open import Cubical.HITs.Pushout
open import Cubical.HITs.Pushout as Pushout
open import Cubical.HITs.Join
open import Cubical.HITs.S1 renaming (_·_ to _*_)
open import Cubical.HITs.Sn
Expand Down Expand Up @@ -93,7 +93,7 @@ conCP² x y = sRec2 squash₂ (λ p q → ∣ p ∙ sym q ∣₂) (conCP²' x) (
→ A (inl base)
→ ((a : hopfS¹.TotalSpaceHopfPush) → A a)
indLem {A = A} p b =
PushoutToProp p
Pushout.elimProp _ p
(sphereElim 0 (λ _ → p _) b)
(sphereElim 0 (λ _ → p _) (subst A (push (base , base)) b))

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4 changes: 2 additions & 2 deletions Cubical/ZCohomology/Groups/CP2.agda
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Expand Up @@ -26,7 +26,7 @@ open import Cubical.Algebra.Group.Morphisms
open import Cubical.Algebra.Group.MorphismProperties
open import Cubical.Algebra.Group.Instances.Unit

open import Cubical.HITs.Pushout
open import Cubical.HITs.Pushout as Pushout
open import Cubical.HITs.S1
open import Cubical.HITs.Sn
open import Cubical.HITs.Susp
Expand Down Expand Up @@ -72,7 +72,7 @@ leftInv characFunSpaceCP² _ =
H⁰CP²≅ℤ : GroupIso (coHomGr 0 CP²) ℤGroup
H⁰CP²≅ℤ =
H⁰-connected (inr tt)
(PushoutToProp (λ _ → squash₁)
(Pushout.elimProp _ (λ _ → squash₁)
(sphereElim _ (λ _ → isOfHLevelSuc 1 squash₁)
∣ sym (push (north , base)) ∣₁)
λ _ → ∣ refl ∣₁)
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9 changes: 5 additions & 4 deletions Cubical/ZCohomology/Groups/Wedge.agda
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Expand Up @@ -25,7 +25,7 @@ open import Cubical.HITs.Susp
open import Cubical.HITs.S1
open import Cubical.HITs.Sn
open import Cubical.HITs.Wedge
open import Cubical.HITs.Pushout
open import Cubical.HITs.Pushout as Pushout

open import Cubical.Homotopy.Connected

Expand Down Expand Up @@ -246,6 +246,7 @@ module _ {ℓ ℓ'} (A : Pointed ℓ) (B : Pointed ℓ') where

wedgeConnected : ((x : typ A) → ∥ pt A ≡ x ∥₁) → ((x : typ B) → ∥ pt B ≡ x ∥₁) → (x : A ⋁ B) → ∥ inl (pt A) ≡ x ∥₁
wedgeConnected conA conB =
PushoutToProp (λ _ → isPropPropTrunc)
(λ a → PT.rec isPropPropTrunc (λ p → ∣ cong inl p ∣₁) (conA a))
λ b → PT.rec isPropPropTrunc (λ p → ∣ push tt ∙ cong inr p ∣₁) (conB b)
Pushout.elimProp _
(λ _ → isPropPropTrunc)
(λ a → PT.rec isPropPropTrunc (λ p → ∣ cong inl p ∣₁) (conA a))
(λ b → PT.rec isPropPropTrunc (λ p → ∣ push tt ∙ cong inr p ∣₁) (conB b))