------------------------------------------------------------------------
-- The Agda standard library
--
-- Decidable semi-heterogeneous vector equality over setoids
------------------------------------------------------------------------

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

open import Relation.Binary.Bundles using (DecSetoid)
open import Relation.Binary.Structures using (IsDecEquivalence)

module Data.Vec.Relation.Binary.Equality.DecSetoid
  {a ℓ} (DS : DecSetoid a ℓ) where

open import Data.Nat.Base using (ℕ)
import Data.Vec.Relation.Binary.Equality.Setoid as Equality
import Data.Vec.Relation.Binary.Pointwise.Inductive as PW
open import Level using (_⊔_)
open import Relation.Binary.Definitions using (Decidable)

open DecSetoid DS

------------------------------------------------------------------------
-- Make all definitions from equality available

open Equality setoid public

------------------------------------------------------------------------
-- Additional properties

infix 4 _≋?_

_≋?_ : ∀ {m n} → Decidable (_≋_ {m} {n})
_≋?_ = PW.decidable _≟_

≋-isDecEquivalence : ∀ n → IsDecEquivalence (_≋_ {n})
≋-isDecEquivalence = PW.isDecEquivalence isDecEquivalence

≋-decSetoid : ℕ → DecSetoid a (a ⊔ ℓ)
≋-decSetoid = PW.decSetoid DS