intros.
elim H;intro q;intro.
elim H0;intro q';intro.
rewrite H2 in H1.
exists (q' * q).
rewrite H1.
auto with arith.
Qed.

(** the relation of divisibility is antisymmetric *)
Lemma divides_antisym : forall (a b:nat),(divides a b)->(divides b a)->a=b.
unfold divides.