(** 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.

(** Bezout on natural numbers commutes *)
Theorem bezout_comm : forall a b g,
b ~= 0 -> Bezout a b g -> Bezout b a g.