(** On natural numbers, we should use a particular form for the Bezout identity, since we don't have full subtraction. *)
#[global]
Instance Bezout_wd : Proper (eq==>eq==>eq==>iff) Bezout.

(** For strictly positive numbers, we have Bezout in the two directions. *)
Lemma gcd_bezout_pos_pos : forall n, 0<n -> forall m, 0<m ->
Bezout n m (gcd n m) /\ Bezout m n (gcd n m).