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 *)

Theorem lt_trichotomy : forall n m,  n < m \/ n == m \/ m < n.