(**************************************************************************)
(*       ___                                                              *)
(*      ||M||                                                             *)
(*      ||A||       A project by Andrea Asperti                           *)
(*      ||T||                                                             *)
(*      ||I||       Developers:                                           *)
(*      ||T||         The HELM team.                                      *)
(*      ||A||         http://helm.cs.unibo.it                             *)
(*      \   /                                                             *)
(*       \ /        This file is distributed under the terms of the       *)
(*        v         GNU General Public License Version 2                  *)
(*                                                                        *)
(**************************************************************************)

(* This file was automatically generated: do not edit *********************)

include "Coq.ma".

(*#***********************************************************************)

(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)

(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)

(*   \VV/  **************************************************************)

(*    //   *      This file is distributed under the terms of the       *)

(*         *       GNU Lesser General Public License Version 2.1        *)

(*#***********************************************************************)

(*i $Id: ArithProp.v,v 1.11.2.1 2004/07/16 19:31:10 herbelin Exp $ i*)

include "Reals/Rbase.ma".

include "Reals/Rbasic_fun.ma".

include "Arith/Even.ma".

include "Arith/Div2.ma".

(* UNEXPORTED
Open Local Scope Z_scope.
*)

(* UNEXPORTED
Open Local Scope R_scope.
*)

inline procedural "cic:/Coq/Reals/ArithProp/minus_neq_O.con" as lemma.

inline procedural "cic:/Coq/Reals/ArithProp/le_minusni_n.con" as lemma.

inline procedural "cic:/Coq/Reals/ArithProp/lt_minus_O_lt.con" as lemma.

inline procedural "cic:/Coq/Reals/ArithProp/even_odd_cor.con" as lemma.

(* 2m <= 2n => m<=n *)

inline procedural "cic:/Coq/Reals/ArithProp/le_double.con" as lemma.

(* Here, we have the euclidian division *)

(* This lemma is used in the proof of sin_eq_0 : (sin x)=0<->x=kPI *)

inline procedural "cic:/Coq/Reals/ArithProp/euclidian_division.con" as lemma.

inline procedural "cic:/Coq/Reals/ArithProp/tech8.con" as lemma.