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(*       ___                                                              *)
(*      ||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: Rdefinitions.v,v 1.14.2.1 2004/07/16 19:31:12 herbelin Exp $ i*)

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

(*#*          Definitions for the axiomatization          *)

(*                                                       *)

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

include "ZArith/ZArith_base.ma".

inline procedural "cic:/Coq/Reals/Rdefinitions/R.con".

(* Declare Scope positive_scope with Key R *)

(* UNEXPORTED
Delimit Scope R_scope with R.
*)

(* Automatically open scope R_scope for arguments of type R *)

(* UNEXPORTED
Bind Scope R_scope with R.
*)

inline procedural "cic:/Coq/Reals/Rdefinitions/R0.con".

inline procedural "cic:/Coq/Reals/Rdefinitions/R1.con".

inline procedural "cic:/Coq/Reals/Rdefinitions/Rplus.con".

inline procedural "cic:/Coq/Reals/Rdefinitions/Rmult.con".

inline procedural "cic:/Coq/Reals/Rdefinitions/Ropp.con".

inline procedural "cic:/Coq/Reals/Rdefinitions/Rinv.con".

inline procedural "cic:/Coq/Reals/Rdefinitions/Rlt.con".

inline procedural "cic:/Coq/Reals/Rdefinitions/up.con".

(* NOTATION
Infix "+" := Rplus : R_scope.
*)

(* NOTATION
Infix "*" := Rmult : R_scope.
*)

(* NOTATION
Notation "- x" := (Ropp x) : R_scope.
*)

(* NOTATION
Notation "/ x" := (Rinv x) : R_scope.
*)

(* NOTATION
Infix "<" := Rlt : R_scope.
*)

(*i*******************************************************i*)

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

inline procedural "cic:/Coq/Reals/Rdefinitions/Rgt.con" as definition.

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

inline procedural "cic:/Coq/Reals/Rdefinitions/Rle.con" as definition.

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

inline procedural "cic:/Coq/Reals/Rdefinitions/Rge.con" as definition.

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

inline procedural "cic:/Coq/Reals/Rdefinitions/Rminus.con" as definition.

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

inline procedural "cic:/Coq/Reals/Rdefinitions/Rdiv.con" as definition.

(* NOTATION
Infix "-" := Rminus : R_scope.
*)

(* NOTATION
Infix "/" := Rdiv : R_scope.
*)

(* NOTATION
Infix "<=" := Rle : R_scope.
*)

(* NOTATION
Infix ">=" := Rge : R_scope.
*)

(* NOTATION
Infix ">" := Rgt : R_scope.
*)

(* NOTATION
Notation "x <= y <= z" := ((x <= y)%R /\ (y <= z)%R) : R_scope.
*)

(* NOTATION
Notation "x <= y < z" := ((x <= y)%R /\ (y < z)%R) : R_scope.
*)

(* NOTATION
Notation "x < y < z" := ((x < y)%R /\ (y < z)%R) : R_scope.
*)

(* NOTATION
Notation "x < y <= z" := ((x < y)%R /\ (y <= z)%R) : R_scope.
*)