Module Type NLcmProp
(Import A : NAxiomsSig')
(Import B : NSubProp A)
(Import C : NDivProp A B)
(Import D : NGcdProp A B).
(** Divibility and modulo *)

Lemma divide_div_mul_exact : forall a b c, b~=0 -> (b|a) ->
(c*a)/b == c*(a/b).