cat/src/Cat/Equality.agda

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{-# OPTIONS --cubical #-}
-- Defines equality-principles for data-types from the standard library.
module Cat.Equality where
open import Level
open import Cubical
-- _[_≡_] = PathP
module Equality where
module Data where
module Product where
open import Data.Product
module _ {a b : Level} {A : Set a} {B : A Set b} {a b : Σ A B}
(proj₁≡ : (λ _ A) [ proj₁ a proj₁ b ])
(proj₂≡ : (λ i B (proj₁≡ i)) [ proj₂ a proj₂ b ]) where
Σ≡ : a b
proj₁ (Σ≡ i) = proj₁≡ i
proj₂ (Σ≡ i) = proj₂≡ i