intros l1; elim l1; simpl in |- *; auto.
intros a l H l2 H0; inversion H0; apply ulist_cons; auto.
Contradict H3; auto with datatypes.
apply H with l2; auto.
Qed.

(* Inversion theorem the appended list *)
Theorem ulist_app_inv_r : forall l1 l2 : list A, ulist (l1 ++ l2) -> ulist l2.
Proof using.