Proof using.
intros t1 t2 H; red in |- *.
intros a t0 t3 H0 H1 H2.
apply (H a t0 t3); auto.
Qed.

(* Direct subtrees of a tree with distinct leaves have distinct leaves *)
Theorem distinct_pbleaves_r :
forall t1 t2 : pbtree,
distinct_pbleaves (pbnode t1 t2) -> distinct_pbleaves t2.