(** a and b are relatively prime if gcd(a,b)=1 *)
Definition rel_prime (a b:nat) := (is_gcd 1 a b).

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))).