Proof using.
intros a a1 l1; generalize a a1; elim l1; simpl in |- *; auto; clear a a1 l1.
intros a2; case a2; auto.
Qed.

(* Specifications: *)
(* Adding in leaf does not create nodes  *)
Theorem in_pbleaf_node :
forall a1 a2 a3 a4 l, ~ inpb (pbnode a1 a2) (pbadd a3 (pbleaf a4) l).