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

Lemma bezout_exists_prod : forall (x:nat*nat),{y:nat*nat | (is_gcd ((fst y)*(fst x)-(snd y)*(snd x)) (fst x) (snd x))}+{y:nat*nat | (is_gcd ((snd y)*(snd x)-(fst y)*(fst x)) (fst x) (snd x))}.