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_factor : forall a b c, c~=0 -> (c|a) -> (c|b) ->
gcd (a/c) (b/c) == (gcd a b)/c.