------------------------------------------------------------------------
-- The Agda standard library
--
-- Lists made up entirely of unique elements (setoid equality)
------------------------------------------------------------------------
 
{-# OPTIONS --cubical-compatible --safe #-}
 
open import Relation.Binary.Bundles using (DecSetoid)
import Data.List.Relation.Unary.AllPairs as AllPairs
open import Relation.Unary using (Decidable)
open import Relation.Nullary.Decidable using (¬?)
 
module Data.List.Relation.Unary.Unique.DecSetoid
  {a ℓ} (DS : DecSetoid a ℓ) where
 
open DecSetoid DS renaming (setoid to S)
 
------------------------------------------------------------------------
-- Re-export setoid definition
 
open import Data.List.Relation.Unary.Unique.Setoid S public
 
------------------------------------------------------------------------
-- Additional properties
 
unique? : Decidable Unique
unique? = AllPairs.allPairs? (λ x y → ¬? (x ≟ y))