2018-02-09 11:09:59 +00:00
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{-# OPTIONS --cubical #-}
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2018-01-30 21:41:18 +00:00
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-- Defines equality-principles for data-types from the standard library.
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module Cat.Equality where
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open import Level
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open import Cubical
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-- _[_≡_] = PathP
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module Equality where
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module Data where
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module Product where
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2018-01-31 13:39:54 +00:00
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open import Data.Product
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2018-01-30 21:41:18 +00:00
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module _ {ℓa ℓb : Level} {A : Set ℓa} {B : A → Set ℓb} {a b : Σ A B}
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(proj₁≡ : (λ _ → A) [ proj₁ a ≡ proj₁ b ])
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(proj₂≡ : (λ i → B (proj₁≡ i)) [ proj₂ a ≡ proj₂ b ]) where
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Σ≡ : a ≡ b
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proj₁ (Σ≡ i) = proj₁≡ i
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proj₂ (Σ≡ i) = proj₂≡ i
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