------------------------------------------------------------------------
-- The Agda standard library
--
-- Decidable setoid membership over lists
------------------------------------------------------------------------
{-# OPTIONS --cubical-compatible --safe #-}
open import Relation.Binary using (Decidable; DecSetoid)
open import Relation.Nullary.Negation using (¬?)
module Data.List.Membership.DecSetoid {a ℓ} (DS : DecSetoid a ℓ) where
open import Data.List.Relation.Unary.Any using (any?)
open DecSetoid DS
------------------------------------------------------------------------
-- Re-export contents of propositional membership
open import Data.List.Membership.Setoid (DecSetoid.setoid DS) public
------------------------------------------------------------------------
-- Other operations
infix 4 _∈?_ _∉?_
_∈?_ : Decidable _∈_
x ∈? xs = any? (x ≟_) xs
_∉?_ : Decidable _∉_
x ∉? xs = ¬? (x ∈? xs)