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-(************************************************************************)
-(* 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 1.1.2.1 2004/07/16 19:31:34 herbelin Exp $ i*)
-
-
-(*********************************************************)
-(** Definitions for the axiomatization *)
-(* *)
-(*********************************************************)
-
-Require Export ZArith_base.
-
-Parameter R:Set.
-
-(* Declare Scope positive_scope with Key R *)
-Delimits Scope R_scope with R.
-
-(* Automatically open scope R_scope for arguments of type R *)
-Bind Scope R_scope with R.
-
-Parameter R0:R.
-Parameter R1:R.
-Parameter Rplus:R->R->R.
-Parameter Rmult:R->R->R.
-Parameter Ropp:R->R.
-Parameter Rinv:R->R.
-Parameter Rlt:R->R->Prop.
-Parameter up:R->Z.
-
-V8Infix "+" Rplus : R_scope.
-V8Infix "*" Rmult : R_scope.
-V8Notation "- x" := (Ropp x) : R_scope.
-V8Notation "/ x" := (Rinv x) : R_scope.
-
-V8Infix "<" Rlt : R_scope.
-
-(*i*******************************************************i*)
-
-(**********)
-Definition Rgt:R->R->Prop:=[r1,r2:R](Rlt r2 r1).
-
-(**********)
-Definition Rle:R->R->Prop:=[r1,r2:R]((Rlt r1 r2)\/(r1==r2)).
-
-(**********)
-Definition Rge:R->R->Prop:=[r1,r2:R]((Rgt r1 r2)\/(r1==r2)).
-
-(**********)
-Definition Rminus:R->R->R:=[r1,r2:R](Rplus r1 (Ropp r2)).
-
-(**********)
-Definition Rdiv:R->R->R:=[r1,r2:R](Rmult r1 (Rinv r2)).
-
-V8Infix "-" Rminus : R_scope.
-V8Infix "/" Rdiv : R_scope.
-
-V8Infix "<=" Rle : R_scope.
-V8Infix ">=" Rge : R_scope.
-V8Infix ">" Rgt : R_scope.
-
-V8Notation "x <= y <= z" := (Rle x y)/\(Rle y z) : R_scope.
-V8Notation "x <= y < z" := (Rle x y)/\(Rlt y z) : R_scope.
-V8Notation "x < y < z" := (Rlt x y)/\(Rlt y z) : R_scope.
-V8Notation "x < y <= z" := (Rlt x y)/\(Rle y z) : R_scope.