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 *)

Lemma gcd_div_gcd : forall a b g, g~=0 -> g == gcd a b ->
gcd (a/g) (b/g) == 1.