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Remove the duplicate of eq-pair
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src/category-theory/functor-curry.lagda.md

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@@ -15,7 +15,7 @@ open import category-theory.precategory-of-functors
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open import category-theory.products-of-precategories
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open import foundation.action-on-identifications-functions
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open import foundation.cartesian-product-types
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open import foundation.equality-cartesian-product-types
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open import foundation.dependent-pair-types
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open import foundation.identity-types
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open import foundation.universe-levels
@@ -132,7 +132,7 @@ module CurryFunctor
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= hom-functor-Precategory CD E F (comp-hom-Precategory CD
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(f , id-hom-Precategory D)
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(id-hom-Precategory C , g))
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by ap (hom-functor-Precategory CD E F) (identity-product
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by ap (hom-functor-Precategory CD E F) (eq-pair
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(left-unit-law-comp-hom-Precategory C f
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∙ inv (right-unit-law-comp-hom-Precategory C f))
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(right-unit-law-comp-hom-Precategory D g

src/foundation/cartesian-product-types.lagda.md

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@@ -31,24 +31,6 @@ tr-product :
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tr-product B C refl u = refl
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```
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### Identities of products
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```agda
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identity-product :
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{l1 l2 : Level}
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{A : UU l1} {B : UU l2}
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{a a' : A} {b b' : B}
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→ a = a' → b = b' → (a , b) = (a' , b')
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identity-product refl refl = refl
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identity-product' :
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{l1 l2 : Level}
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{A : UU l1} {B : UU l2}
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{ab ab' : A × B}
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→ pr1 ab = pr1 ab' → pr2 ab = pr2 ab' → ab = ab'
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identity-product' refl refl = refl
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```
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### Subuniverses closed under cartesian product types
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```agda

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