(* *********************************************************************)
(*                                                                     *)
(*              The Compcert verified compiler                         *)
(*                                                                     *)
(*          Xavier Leroy, INRIA Paris-Rocquencourt                     *)
(*                                                                     *)
(*  Copyright Institut National de Recherche en Informatique et en     *)
(*  Automatique.  All rights reserved.  This file is distributed       *)
(*  Automatique.  All rights reserved.  This file is distributed       *)
(*  under the terms of the GNU General Public License as published by  *)
(*  the Free Software Foundation, either version 2 of the License, or  *)
(*  (at your option) any later version.  This file is also distributed *)
(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
(*                                                                     *)
(* *********************************************************************)
(** Constructions of ordered types, for use with the [FSet] functors for finite sets and the [FMap] functors for finite maps. *)
(** The ordered type of positive numbers *)
Module OrderedPositive <: OrderedType.
Definition t := positive.
Definition eq (x y: t) := x = y.
Definition lt := Plt.

Lemma eq_trans : forall x y z : t, eq x y -> eq y z -> eq x z.
Definition lt (x y: t) :=
A.lt (fst x) (fst y) \/
(A.eq (fst x) (fst y) /\ B.lt (snd x) (snd y)).