Module Type NLcmProp
(Import A : NAxiomsSig')
(Import B : NSubProp A)
(Import C : NDivProp A B)
(Import D : NGcdProp A B).
(** Divibility and modulo *)
(** Gcd of divided elements, for exact divisions *)
(** The following equality is crucial for Euclid algorithm *)

Lemma gcd_mod : forall a b, b~=0 -> gcd (a mod b) b == gcd b a.