(** * 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] *)

(* Specifications: *)
Lemma gcd_bezout : forall a b d : Z, gcd a b d -> Bezout a b d.
(** gcd of [ca] and [cb] is [c gcd(a,b)]. *)
Lemma gcd_mult : forall a b c d : Z, gcd a b d -> gcd (c * a) (c * b) (c * d).