Proof using.
intros l1; elim l1; simpl in |- *; auto.
intros a l H l2 l3 H0; apply H; injection H0; auto.
Qed.

Theorem app_inv_tail :
forall l1 l2 l3 : list A, l2 ++ l1 = l3 ++ l1 -> l2 = l3.