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+Require Import EquivDec Equivalence List Program.
+Require Import Relation_Definitions.
+Import ListNotations.
+Generalizable All Variables.
+
+Fixpoint removeV `{eqDecV : @EqDec V eqV equivV}`(x : V) (l : list V) : list V
+:=
+ match l with
+ | nil => nil
+ | y::tl => if (equiv_dec x y) then removeV x tl else y::(removeV x tl)
+ end.
+
+Lemma remove_le {V:Type}{eqV:relation V}{equivV:@Equivalence V eqV}{eqDecV :
+@EqDec V eqV equivV} (xs : list V) (x : V) :
+ length (removeV x xs) < length (x :: xs).
+ Proof. Admitted.
+
+(* Function version *)
+Set Printing Universes.
+
+Require Import Recdef.
+
+Function nubV {V:Type}{eqV:relation V}{equivV:@Equivalence V eqV}{eqDecV :
+@EqDec V eqV equivV} (l : list V) { measure length l} :=
+ match l with
+ | nil => nil
+ | x::xs => x :: @nubV V eqV equivV eqDecV (removeV x xs)
+ end.
+Proof. intros. apply remove_le. Qed.
+
+(* Program version *)
+
+Program Fixpoint nubV `{eqDecV : @EqDec V eqV equivV} (l : list V)
+ { measure (@length V l) lt } :=
+ match l with
+ | nil => nil
+ | x::xs => x :: @nubV V eqV equivV eqDecV (removeV x xs) _
+ end.