Proof using.
intros l1; elim l1; simpl in |- *; auto.
intros a l H l2 a0 H0 [H1| H1] H2.
inversion H0; auto.
case H5; rewrite H1; auto with datatypes.
apply (H l2 a0); auto.
apply ulist_inv with (1 := H0); auto.
Qed.

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