Proof using.
intros l; elim l; simpl in |- *; auto.
intros b; case b; simpl in |- *; auto.
Qed.

(* Adding a new leaf preserves the uniqueness of the list of all leaves *)
Theorem ulist_pbadd_prop2 :
forall a1 l1 t,
~ inpb (pbleaf a1) t ->
ulist (all_pbleaves t) -> ulist (all_pbleaves (pbadd a1 t l1)).