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

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

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 using (List#)
open import Data.List.Fresh.Relation.Unary.Any as Any using (Any)
open import Relation.Binary.Core using (Rel; REL)
open import Relation.Nullary.Negation.Core using (¬_)

open Setoid S
  using (_≈_)
  renaming (Carrier to A)

private
  variable
    r : Level
    R : Rel A r


infix 4 _∈_ _∉_

_∈_ : REL A (List# A R) _
x  xs = Any (x ≈_) xs

_∉_ : REL A (List# A R) _
x  xs = ¬ (x  xs)