proposition: Lemma app_inv_eq_l: forall (A:Type) (x:list A) y z, x ++ y = x ++ z -> y = z.
proof: Proof. intros. induction x. - simpl in *. assumption. - inversion H; subst; clear H. apply IHx. assumption. Qed.
imports: Coq.Arith.Plus Coq.Arith.PeanoNat Coq.Lists.List