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