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

(* An inversion theorem for node *)
Theorem distinct_leaves_r :
forall t1 t2 : btree, distinct_leaves (node t1 t2) -> distinct_leaves t2.