intros l1; elim l1; simpl in |- *; auto.
intros a l H l2 H0; inversion H0; auto.
Qed.
(* Uniqueness is decidable *)
Definition ulist_dec : forall l, {ulist l} + {~ ulist l}.
intros l; elim l; auto.
intros a l1 [H| H]; auto.
case (In_dec eqA_dec a l1); intros H2; auto.
right; red in |- *; intros H1; inversion H1; auto.
right; Contradict H; apply ulist_inv with (1 := H).
Defined.

(* Uniqueness is compatible with permutation *)
Theorem ulist_perm :
forall l1 l2 : list A, permutation l1 l2 -> ulist l1 -> ulist l2.