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

Lemma bezout_aux2 : forall (x y u v:nat),(x<=y)->(is_gcd (v*(y-x)-u*x) x (y-x))->(is_gcd (v*y-(u+v)*x) x y).