------------------------------------------------------------------------
-- The Agda standard library
--
-- The extensional sublist relation over setoid equality.
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
open import Relation.Binary
module Data.List.Relation.Binary.Subset.Setoid
{c ℓ} (S : Setoid c ℓ) where
open import Data.List.Base using (List)
open import Data.List.Membership.Setoid S using (_∈_)
open import Level using (_⊔_)
open import Relation.Nullary using (¬_)
open Setoid S renaming (Carrier to A)
------------------------------------------------------------------------
-- Definitions
infix 4 _⊆_ _⊈_
_⊆_ : Rel (List A) (c ⊔ ℓ)
xs ⊆ ys = ∀ {x} → x ∈ xs → x ∈ ys
_⊈_ : Rel (List A) (c ⊔ ℓ)
xs ⊈ ys = ¬ xs ⊆ ys