elim H0; elim H.
intros.
rewrite H2; rewrite H1.
elim (mult_plus_distr_left q q0 2).
apply (even_intro (2 * (q + q0)) (q + q0)).
auto with arith.
Qed.

(* Specifications: *)
Lemma S_odd_even : forall a : nat, odd a -> even (S a).
intros.