(** * Bezout's coefficients *)
Inductive Bezout (a b d : Z) : Prop :=
Bezout_intro : forall u v : Z, (u * a + v * b)%Z = d -> Bezout a b d.
(** Existence of Bezout's coefficients for the [gcd] of [a] and [b] *)

Lemma gcd_bezout : forall a b d : Z, gcd a b d -> Bezout a b d.