{- This module converts between the path types and the inductively defined equality types. It provides the following for the inductively defined equality type _≡_. - Basic theory for _≡_ (J, ap, transport, ...) - A proof of function extensionality using _≡_ - A proof of univalence for _≡_ and equivalences using _≡_ - S¹ and propositional truncation with (path) constructors, eliminators and β rules all in terms of _≡_. -} {-# OPTIONS --safe #-} module Cubical.Data.Equality where open import Cubical.Data.Equality.Base public open import Cubical.Data.Equality.Conversion public open import Cubical.Data.Equality.FunctionExtensionality public open import Cubical.Data.Equality.Univalence public open import Cubical.Data.Equality.S1 public open import Cubical.Data.Equality.PropositionalTruncation public