Module Type ZLcmProp
(Import A : ZAxiomsSig')
(Import B : ZMulOrderProp A)
(Import C : ZSgnAbsProp A B)
(Import D : ZDivProp A B C)
(Import E : ZQuotProp A B C)
(Import F : ZGcdProp A B C).
(** The two notions of division are equal on non-negative numbers *)
(** We can use the sign rule to have an relation between divisions. *)

Lemma quot_div : forall a b, b~=0 ->
a÷b == (sgn a)*(sgn b)*(abs a / abs b).