unfold rel_prime.
intros.
unfold is_gcd;unfold is_cd.
split.
split;apply one_min_div.
intros.
elim H;intros.
elim H1;intros.
case (H3 d' H4);intro.
rewrite H6;apply divides_refl.
rewrite H6 in H5;tauto.
Qed.

(** We show some lemmae about prime numbers *)
(** if p is prime then gcd(a,p)=1 or gcd(a,p)=p *)
Lemma prime_gcd : forall (d p a:nat),(is_prime p)->(is_gcd d a p)->(d=1)\/(d=p).
unfold is_prime.