Module Type ZMaxMinProp (Import Z : ZAxiomsMiniSig').
Include ZMulOrderProp Z.
(** The following results are concrete instances of [max_monotone] and similar lemmas. *)
(** Succ *)
(** Pred *)
(** Add *)
(** Opp *)
(** Sub *)
(** Mul *)

Lemma mul_max_distr_nonpos_l : forall n m p, p <= 0 ->
max (p * n) (p * m) == p * min n m.