intros.
elim H;intros.
apply H2.
elim H0;intros.
elim H3;trivial.
Qed.

(** if p is prime and gcd(a,p)<>1 then p | a *)
Lemma prime_rel_prime : forall (p a:nat),(is_prime p)->~(rel_prime a p)->(divides a p).
unfold rel_prime.