------------------------------------------------------------------------
-- The Agda standard library
--
-- Data.List.Any.Membership instantiated with propositional equality,
-- along with some additional definitions.
------------------------------------------------------------------------

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

module Data.List.Membership.Propositional {a} {A : Set a} where

open import Data.List.Relation.Unary.Any using (Any)
open import Relation.Binary.PropositionalEquality.Core using (_≡_; _≢_; resp; subst)
open import Relation.Binary.PropositionalEquality.Properties using (setoid)

import Data.List.Membership.Setoid as SetoidMembership

------------------------------------------------------------------------
-- Re-export contents of setoid membership

open SetoidMembership (setoid A) public hiding (lose)

------------------------------------------------------------------------
-- Different members

infix 4 _≢∈_

_≢∈_ :  {x y : A} {xs}  x  xs  y  xs  Set _
_≢∈_ x∈xs y∈xs =  x≡y  subst (_∈ _) x≡y x∈xs  y∈xs

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

lose :  {p} {P : A  Set p} {x xs}  x  xs  P x  Any P xs
lose = SetoidMembership.lose (setoid A) (resp _)