elim (gcd_minus ((u+v)*x-v*y) x y H);intros.
apply H2.
rewrite mult_plus_distr_r;rewrite <- minus_minus_lemma1;try (auto with arith);rewrite <- mult_minus_lemma2;trivial.
Qed.

(* Specifications: *)
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).
intros.