    ------------------------------------------------------------------------
    -- The Agda standard library
    --
    -- Decidable vector equality over propositional equality
    ------------------------------------------------------------------------

    {-# OPTIONS --cubical-compatible --safe #-}

    open import Relation.Binary.Definitions using (DecidableEquality)

    module Data.Vec.Relation.Binary.Equality.DecPropositional
      {a} {A : Set a} (_≟_ : DecidableEquality A) where

    open import Data.Vec.Base using (Vec)
    open import Data.Vec.Properties using (≡-dec)
    import Data.Vec.Relation.Binary.Equality.Propositional as PEq
    import Data.Vec.Relation.Binary.Equality.DecSetoid as DSEq
    open import Relation.Binary.PropositionalEquality.Properties using (decSetoid)

    ------------------------------------------------------------------------
    -- Publicly re-export everything from decSetoid and propositional
    -- equality

    open PEq public
    open DSEq (decSetoid _≟_) public
      using (_≋?_; ≋-isDecEquivalence; ≋-decSetoid)

    ------------------------------------------------------------------------
    -- Additional proofs

    infix 4 _≡?_

    _≡?_ : ∀ {n} → DecidableEquality (Vec A n)
    _≡?_ = ≡-dec _≟_