helm/software/matita/contribs/procedural/Coq/Reals/RiemannInt_SF.mma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 (* This file was automatically generated: do not edit *********************)
  16
  17 include "Coq.ma".
  18
  19 (*#***********************************************************************)
  20
  21 (*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
  22
  23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
  24
  25 (*   \VV/  **************************************************************)
  26
  27 (*    //   *      This file is distributed under the terms of the       *)
  28
  29 (*         *       GNU Lesser General Public License Version 2.1        *)
  30
  31 (*#***********************************************************************)
  32
  33 (*i $Id: RiemannInt_SF.v,v 1.16.2.1 2004/07/16 19:31:13 herbelin Exp $ i*)
  34
  35 include "Reals/Rbase.ma".
  36
  37 include "Reals/Rfunctions.ma".
  38
  39 include "Reals/Ranalysis.ma".
  40
  41 include "Logic/Classical_Prop.ma".
  42
  43 (* UNEXPORTED
  44 Open Local Scope R_scope.
  45 *)
  46
  47 (* UNEXPORTED
  48 Set Implicit Arguments.
  49 *)
  50
  51 (*#*************************************************)
  52
  53 (* Each bounded subset of N has a maximal element *)
  54
  55 (*#*************************************************)
  56
  57 inline procedural "cic:/Coq/Reals/RiemannInt_SF/Nbound.con" as definition.
  58
  59 inline procedural "cic:/Coq/Reals/RiemannInt_SF/IZN_var.con" as lemma.
  60
  61 inline procedural "cic:/Coq/Reals/RiemannInt_SF/Nzorn.con" as lemma.
  62
  63 (*#******************************************)
  64
  65 (*             Step functions              *)
  66
  67 (*#******************************************)
  68
  69 inline procedural "cic:/Coq/Reals/RiemannInt_SF/open_interval.con" as definition.
  70
  71 inline procedural "cic:/Coq/Reals/RiemannInt_SF/co_interval.con" as definition.
  72
  73 inline procedural "cic:/Coq/Reals/RiemannInt_SF/adapted_couple.con" as definition.
  74
  75 inline procedural "cic:/Coq/Reals/RiemannInt_SF/adapted_couple_opt.con" as definition.
  76
  77 inline procedural "cic:/Coq/Reals/RiemannInt_SF/is_subdivision.con" as definition.
  78
  79 inline procedural "cic:/Coq/Reals/RiemannInt_SF/IsStepFun.con" as definition.
  80
  81 (* Class of step functions *)
  82
  83 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun.ind".
  84
  85 inline procedural "cic:/Coq/Reals/RiemannInt_SF/subdivision.con" as definition.
  86
  87 inline procedural "cic:/Coq/Reals/RiemannInt_SF/subdivision_val.con" as definition.
  88
  89 inline procedural "cic:/Coq/Reals/RiemannInt_SF/Int_SF.con" as definition.
  90
  91 (* Integral of step functions *)
  92
  93 inline procedural "cic:/Coq/Reals/RiemannInt_SF/RiemannInt_SF.con" as definition.
  94
  95 (*#*******************************)
  96
  97 (* Properties of step functions *)
  98
  99 (*#*******************************)
 100
 101 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P1.con" as lemma.
 102
 103 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P2.con" as lemma.
 104
 105 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P3.con" as lemma.
 106
 107 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P4.con" as lemma.
 108
 109 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P5.con" as lemma.
 110
 111 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P6.con" as lemma.
 112
 113 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P7.con" as lemma.
 114
 115 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P8.con" as lemma.
 116
 117 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P9.con" as lemma.
 118
 119 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P10.con" as lemma.
 120
 121 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P11.con" as lemma.
 122
 123 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P12.con" as lemma.
 124
 125 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P13.con" as lemma.
 126
 127 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P14.con" as lemma.
 128
 129 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P15.con" as lemma.
 130
 131 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P16.con" as lemma.
 132
 133 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P17.con" as lemma.
 134
 135 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P18.con" as lemma.
 136
 137 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P19.con" as lemma.
 138
 139 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P20.con" as lemma.
 140
 141 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P21.con" as lemma.
 142
 143 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P22.con" as lemma.
 144
 145 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P23.con" as lemma.
 146
 147 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P24.con" as lemma.
 148
 149 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P25.con" as lemma.
 150
 151 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P26.con" as lemma.
 152
 153 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P27.con" as lemma.
 154
 155 (* The set of step functions on [a,b] is a vectorial space *)
 156
 157 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P28.con" as lemma.
 158
 159 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P29.con" as lemma.
 160
 161 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P30.con" as lemma.
 162
 163 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P31.con" as lemma.
 164
 165 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P32.con" as lemma.
 166
 167 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P33.con" as lemma.
 168
 169 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P34.con" as lemma.
 170
 171 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P35.con" as lemma.
 172
 173 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P36.con" as lemma.
 174
 175 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P37.con" as lemma.
 176
 177 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P38.con" as lemma.
 178
 179 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P39.con" as lemma.
 180
 181 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P40.con" as lemma.
 182
 183 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P41.con" as lemma.
 184
 185 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P42.con" as lemma.
 186
 187 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P43.con" as lemma.
 188
 189 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P44.con" as lemma.
 190
 191 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P45.con" as lemma.
 192
 193 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P46.con" as lemma.
 194