intros a1 l1; elim l1; simpl in |- *; auto.
intros b; case b; simpl in |- *; auto.
intros l H t1; (case t1; simpl in |- *; auto).
intros l H t1; (case t1; simpl in |- *; auto).
Qed.
Hint Resolve inpb_pbadd : core.

(* Specifications: *)
(* Subtrees in an added tree either contains the added leaf or was a subtree of the initial tree *)
Theorem inpb_pbadd_ex :
forall a1 l1 t1 t,
inpb t (pbadd a1 t1 l1) -> inpb (pbleaf a1) t \/ inpb t t1.