1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
19 (*#***********************************************************************)
21 (* v * The Coq Proof Assistant / The Coq Development Team *)
23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
25 (* \VV/ **************************************************************)
27 (* // * This file is distributed under the terms of the *)
29 (* * GNU Lesser General Public License Version 2.1 *)
31 (*#***********************************************************************)
33 (*i $Id: Rbasic_fun.v,v 1.22.2.1 2004/07/16 19:31:12 herbelin Exp $ i*)
35 (*#********************************************************)
37 (*#* Complements for the real numbers *)
41 (*#********************************************************)
43 include "Reals/Rbase.ma".
45 include "Reals/R_Ifp.ma".
48 Open Local Scope R_scope.
55 (*#******************************)
59 (*#******************************)
63 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rmin.con" as definition.
67 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rmin_Rgt_l.con" as lemma.
71 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rmin_Rgt_r.con" as lemma.
75 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rmin_Rgt.con" as lemma.
79 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rmin_l.con" as lemma.
83 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rmin_r.con" as lemma.
87 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rmin_comm.con" as lemma.
91 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rmin_stable_in_posreal.con" as lemma.
93 (*#******************************)
97 (*#******************************)
101 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rmax.con" as definition.
105 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rmax_Rle.con" as lemma.
107 inline procedural "cic:/Coq/Reals/Rbasic_fun/RmaxLess1.con" as lemma.
109 inline procedural "cic:/Coq/Reals/Rbasic_fun/RmaxLess2.con" as lemma.
111 inline procedural "cic:/Coq/Reals/Rbasic_fun/RmaxSym.con" as lemma.
113 inline procedural "cic:/Coq/Reals/Rbasic_fun/RmaxRmult.con" as lemma.
115 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rmax_stable_in_negreal.con" as lemma.
117 (*#******************************)
121 (*#******************************)
125 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rcase_abs.con" as lemma.
129 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rabs.con" as definition.
133 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rabs_R0.con" as lemma.
135 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rabs_R1.con" as lemma.
139 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rabs_no_R0.con" as lemma.
143 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rabs_left.con" as lemma.
147 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rabs_right.con" as lemma.
149 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rabs_left1.con" as lemma.
153 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rabs_pos.con" as lemma.
155 inline procedural "cic:/Coq/Reals/Rbasic_fun/RRle_abs.con" as lemma.
159 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rabs_pos_eq.con" as lemma.
163 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rabs_Rabsolu.con" as lemma.
167 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rabs_pos_lt.con" as lemma.
171 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rabs_minus_sym.con" as lemma.
175 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rabs_mult.con" as lemma.
179 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rabs_Rinv.con" as lemma.
181 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rabs_Ropp.con" as lemma.
185 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rabs_triang.con" as lemma.
189 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rabs_triang_inv.con" as lemma.
191 (* ||a|-|b||<=|a-b| *)
193 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rabs_triang_inv2.con" as lemma.
197 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rabs_def1.con" as lemma.
201 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rabs_def2.con" as lemma.
203 inline procedural "cic:/Coq/Reals/Rbasic_fun/RmaxAbs.con" as lemma.
205 inline procedural "cic:/Coq/Reals/Rbasic_fun/Rabs_Zabs.con" as lemma.