------------------------------------------------------------------------
-- The Agda standard library
--
-- Properties of lists made up entirely of decidably unique elements
------------------------------------------------------------------------
 
{-# OPTIONS --cubical-compatible --safe #-}
 
open import Data.List.Base using ([]; _∷_; deduplicate)
import Data.List.Relation.Unary.Unique.DecSetoid as Unique
open import Data.List.Relation.Unary.All.Properties using (all-filter)
open import Data.List.Relation.Unary.Unique.Setoid.Properties
open import Level
open import Relation.Binary.Bundles using (DecSetoid)
 
module Data.List.Relation.Unary.Unique.DecSetoid.Properties where
 
private
  variable
    a ℓ : Level
 
------------------------------------------------------------------------
-- deduplicate
 
module _ (DS : DecSetoid a ℓ) where
 
  open DecSetoid DS renaming (setoid to S)
  open Unique DS
 
  deduplicate-! : ∀ xs → Unique (deduplicate _≟_ xs)
  deduplicate-! []       = []
  deduplicate-! (x ∷ xs) = all-filter _ (deduplicate _≟_ xs) ∷ filter⁺ S _ (deduplicate-! xs)