intros;apply gcd_sym;apply gcd_one.
Qed.

(** we have that a/gcd(a,b) and b/gcd(a,b) are relatively prime *)
Lemma gcd_rel_prime : forall (d a b:nat)(H:(is_gcd d a b)),(d <> O)->(rel_prime (quo a d (gcd_div_l d a b H)) (quo b d (gcd_div_r d a b H))).
unfold rel_prime.