{-# OPTIONS --erased-cubical --safe #-}
module Equality.Propositional.Cubical where
import Equality.Path as P
open import Equality.Propositional
open Equality.Propositional public using (refl; equivalence-relation⁺)
private
equality-with-paths′ :
∀ {a p} → P.Equality-with-paths a p equivalence-relation⁺
equality-with-paths′ =
P.Equality-with-J⇒Equality-with-paths equality-with-J
equality-with-paths :
∀ {a p} → P.Equality-with-paths a p equivalence-relation⁺
equality-with-paths .P.Equality-with-paths.equality-with-J = equality-with-paths′ .P.Equality-with-paths.equality-with-J
equality-with-paths {p = p} .P.Equality-with-paths.to-path = equality-with-paths′ {p = p} .P.Equality-with-paths.to-path
equality-with-paths {p = p} .P.Equality-with-paths.from-path = equality-with-paths′ {p = p} .P.Equality-with-paths.from-path
equality-with-paths {p = p} .P.Equality-with-paths.to-path∘from-path = equality-with-paths′ {p = p} .P.Equality-with-paths.to-path∘from-path
equality-with-paths {p = p} .P.Equality-with-paths.from-path∘to-path = equality-with-paths′ {p = p} .P.Equality-with-paths.from-path∘to-path
equality-with-paths {p = p} .P.Equality-with-paths.to-path-refl = equality-with-paths′ {p = p} .P.Equality-with-paths.to-path-refl
equality-with-paths {p = p} .P.Equality-with-paths.from-path-refl = equality-with-paths′ {p = p} .P.Equality-with-paths.from-path-refl
open P.Derived-definitions-and-properties equality-with-paths public
hiding (refl)
open import Equality.Path.Isomorphisms equality-with-paths public