Proof using.
intros a b; generalize a; elim b; clear a b; simpl in |- *; auto.
intros a a0 H; inversion H; auto.
intros p H a H0; apply H; auto; inversion H0; auto.
intros p H a H0; apply H; auto; inversion H0; auto.
intros p H p0 H0 a H1; inversion H1; auto.
Qed.

(* Leaves do not change *)
Theorem to_btree_inpb :
forall a b, inb (leaf a) (to_btree b) -> inpb (pbleaf a) b.