------------------------------------------------------------------------ -- 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