Module Type NZOrderProp
(Import NZ : NZOrdSig')(Import NZBase : NZBaseProp NZ).
Instance le_wd : Proper (eq==>eq==>iff) le.
Ltac le_elim H := rewrite lt_eq_cases in H; destruct H as [H | H].
(** Trichotomy *)
Notation lt_eq_gt_cases := lt_trichotomy (only parsing).
(** Asymmetry and transitivity. *)
Notation lt_ngt := lt_asymm (only parsing).

Theorem lt_trans : forall n m p, n < m -> m < p -> n < p.