Notation Zgcd_inv_0_l := Z.gcd_eq_0_l (only parsing).Notation Zgcd_inv_0_r := Z.gcd_eq_0_r (only parsing).

(* Specifications: *)
Theorem Zgcd_div_swap0 : forall a b : Z, 0 < Z.gcd a b -> 0 < b -> (a / Z.gcd a b) * b = a * (b/Z.gcd a b).
Theorem Zgcd_div_swap : forall a b c : Z, 0 < Z.gcd a b -> 0 < b -> (c * a) / Z.gcd a b * b = c * a * (b/Z.gcd a b).
Lemma Zgcd_ass a b c : Z.gcd (Z.gcd a b) c = Z.gcd a (Z.gcd b c).