(** Relative primality *)

Definition rel_prime (a b : Z) : Prop := gcd a b 1.

(* Specifications: *)
Lemma rel_prime_bezout : forall a b : Z, rel_prime a b -> Bezout a b 1.
Lemma bezout_rel_prime : forall a b : Z, Bezout a b 1 -> rel_prime a b.
Theorem Gauss : forall a b c : Z, (a | b * c)%Z -> rel_prime a b -> (a | c)%Z.
Lemma rel_prime_mult : forall a b c : Z, rel_prime a b -> rel_prime a c -> rel_prime a (b * c).