(* 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: *)
Theorem number_of_nodes_inb_le : forall t1 t2, inb t1 t2 -> number_of_nodes t1 <= number_of_nodes t2.
Theorem inb_antisym : forall t1 t2 : btree, inb t1 t2 -> inb t2 t1 -> t1 = t2.