------------------------------------------------------------------------
-- The Agda standard library
--
-- Decidable setoid membership over lists
------------------------------------------------------------------------

{-# OPTIONS --without-K --safe #-}

open import Relation.Binary.Bundles using (DecSetoid)

module Data.List.Membership.DecSetoid {a ℓ} (DS : DecSetoid a ℓ) where

open import Data.List.Relation.Unary.Any using (any?)
open import Relation.Binary.Definitions using (Decidable)
open import Relation.Nullary.Decidable using (¬?)

open DecSetoid DS using (_≈?_; setoid)

------------------------------------------------------------------------
-- Re-export contents of propositional membership

open import Data.List.Membership.Setoid setoid public

------------------------------------------------------------------------
-- Other operations

infix  _∈?_ _∉?_

_∈?_ : Decidable _∈_
x ∈? xs = any? (x ≈?_) xs

_∉?_ : Decidable _∉_
x ∉? xs = ¬? (x ∈? xs)