(** * Relative primality *)
Definition rel_prime (a b:Z) : Prop := Zis_gcd a b 1.
(** Bezout's theorem: [a] and [b] are relatively prime if and only if there exist [u] and [v] such that [ua+vb = 1]. *)

Lemma bezout_rel_prime : forall a b:Z, Bezout a b 1 -> rel_prime a b.