elim H0; elim H.
intros k1 evena k2 odda.
apply (le_Sn_n 1).
apply (less_div 1 (k1 - k2) 2); auto with arith.
rewrite mult_comm.
replace (2 * (k1 - k2)) with (2 * k1 - 2 * k2).
elim evena.
rewrite odda.
auto with arith.
elim mult_comm.
replace (2 * k1) with (k1 * 2).
2: apply mult_comm.
replace (2 * k2) with (k2 * 2).
2: apply mult_comm.
(* Rewrite (mult_minus_distr k1 k2 (S(S O))). *)
elim (mult_comm 2 k1); elim (mult_comm 2 k2).
apply sym_equal; auto with arith.
Qed.

Lemma odd_even : forall a : nat, odd a -> ~ even a.
unfold not in |- *; intros.