unfold gcd.
generalize (gcd_exists a b).
intro;elim s;intro d;trivial.
Qed.
(** a and b are relatively prime if gcd(a,b)=1 *)
Definition rel_prime (a b:nat) := (is_gcd 1 a b).

(* Specifications: *)
(** if a and b are relatively prime then so are b and a *)
Lemma rel_prime_sym : forall (a b:nat),(rel_prime a b)->(rel_prime b a).
unfold rel_prime.