intros t1 t2 t3 H H1; generalize t1 H; elim H1; clear H H1 t1 t2 t3; auto.
Qed.

(* Specifications: *)
(* A tree has at least one leaf  *)
Theorem inb_ex : forall t : btree, exists x : _, inb (leaf x) t.
Proof using.
(* A partial tree has always a leaf *)
Theorem inpb_ex : forall t : pbtree, exists x : _, inpb (pbleaf x) t.
Proof using.