------------------------------------------------------------------------
-- The Agda standard library
--
-- Pointwise equality over lists using propositional equality
------------------------------------------------------------------------
 
-- Note think carefully about using this module as pointwise
-- propositional equality can usually be replaced with propositional
-- equality.
 
{-# OPTIONS --cubical-compatible --safe #-}
 
open import Relation.Binary.Core using (_⇒_)
 
module Data.List.Relation.Binary.Equality.Propositional {a} {A : Set a} where
 
open import Data.List.Base
import Data.List.Relation.Binary.Equality.Setoid as SetoidEquality
open import Relation.Binary.PropositionalEquality.Core using (_≡_; refl; cong)
import Relation.Binary.PropositionalEquality.Properties as ≡
 
------------------------------------------------------------------------
-- Re-export everything from setoid equality
 
open SetoidEquality (≡.setoid A) public
 
------------------------------------------------------------------------
-- ≋ is propositional
 
≋⇒≡ : _≋_ ⇒ _≡_
≋⇒≡ []             = refl
≋⇒≡ (refl ∷ xs≈ys) = cong (_ ∷_) (≋⇒≡ xs≈ys)
 
≡⇒≋ : _≡_ ⇒ _≋_
≡⇒≋ refl = ≋-refl