------------------------------------------------------------------------
-- The Agda standard library
--
-- Membership predicate for fresh lists
------------------------------------------------------------------------

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

open import Relation.Binary.Core using (Rel)
open import Relation.Binary.Bundles using (Setoid)

module Data.List.Fresh.Membership.Setoid {c } (S : Setoid c ) where

open import Level using (Level; _⊔_)
open import Data.List.Fresh
open import Data.List.Fresh.Relation.Unary.Any as Any using (Any)
open import Relation.Nullary

open Setoid S renaming (Carrier to A)

infix 4 _∈_ _∉_

private
  variable
    r : Level

_∈_ : {R : Rel A r}  A  List# A R  Set _
x  xs = Any (x ≈_) xs

_∉_ : {R : Rel A r}  A  List# A R  Set _
x  xs = ¬ (x  xs)