(** * 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]. *)

(** If [a] is relatively prime to [b] and [c], then it is to [bc] *)
Lemma rel_prime_mult :
forall a b c:Z, rel_prime a b -> rel_prime a c -> rel_prime a (b * c).