elim H0; elim H; intros.
rewrite H2; rewrite H1; intros.
rewrite (plus_comm (2 * q0) 1).
rewrite (plus_assoc (2 * q + 1) 1 (2 * q0)).
rewrite (plus_assoc_reverse (2 * q) 1 1).
apply (plus_even_even (2 * q + (1 + 1)) (2 * q0)).
apply (plus_even_even (2 * q) (1 + 1)).
apply (even_intro (2 * q) q); auto with arith.
apply (even_intro (1 + 1) 1); auto with arith.
apply (even_intro (2 * q0) q0); auto with arith.
Qed.
(************************** mult, even and odd ***************************)

(* Specifications: *)
Lemma mult_even : forall a b : nat, even a -> even (a * b).
intros.