(* Predicate for Partial Trees with Different Leaves *)
Definition distinct_pbleaves (t : pbtree) : Prop :=
  forall t0 t1 t2 : pbtree,
  inpb (pbnode t1 t2) t -> inpb t0 t1 -> inpb t0 t2 -> False.

Theorem distinct_pbleaves_pbleaf : forall a : A, distinct_pbleaves (pbleaf a).