elim H; intros.
rewrite H0.
elim (plus_n_Sm (2 * q) 0).
elim (pred_Sn (2 * q + 0)).
elim (plus_n_O (2 * q)).
apply (even_intro (2 * q) q); auto with arith.
Qed.

Lemma plus_even_odd : forall a b : nat, even a -> odd b -> odd (a + b).
intros.