intros t; elim t; simpl in |- *; auto.
intros a; exists a; auto.
intros b (a, H) b0 H0; exists a; auto.
Qed.
(* Compute the number of nodes of a tree *)
Fixpoint number_of_nodes (b : btree) : nat :=
match b with
| leaf _ => 0
| node b1 b2 => S (number_of_nodes b1 + number_of_nodes b2)
end.

(* Specifications: *)
(* Belonging gives smaller trees *)
Theorem number_of_nodes_inb_le :
forall t1 t2, inb t1 t2 -> number_of_nodes t1 <= number_of_nodes t2.