Proof using.
intros t; elim t; simpl in |- *; auto.
intros a a0 H; inversion H; auto.
intros p H a H0; inversion H0; auto.
intros p H a H0; inversion H0; auto.
intros b H b0 H0 a H1; apply in_or_app; inversion H1; auto.
Qed.

(* An element of the list of all leaves is a leaf of the tree *)
Theorem all_pbleaves_inpb :
forall t a, In a (all_pbleaves t) -> inpb (pbleaf a) t.