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

(* If list of all the leaves of the tree is unique then the tree has distinct leaves *)
Theorem all_leaves_unique :
forall t, ulist (all_leaves t) -> distinct_leaves t.