helm/software/matita/contribs/procedural/Coq/Reals/RiemannInt.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.v,v 1.18.2.1 2004/07/16 19:31:13 herbelin Exp $ i*)
  34
  35 include "Reals/Rfunctions.ma".
  36
  37 include "Reals/SeqSeries.ma".
  38
  39 include "Reals/Ranalysis.ma".
  40
  41 include "Reals/Rbase.ma".
  42
  43 include "Reals/RiemannInt_SF.ma".
  44
  45 include "Logic/Classical_Prop.ma".
  46
  47 include "Logic/Classical_Pred_Type.ma".
  48
  49 include "Arith/Max.ma".
  50
  51 (* UNEXPORTED
  52 Open Local Scope R_scope.
  53 *)
  54
  55 (* UNEXPORTED
  56 Set Implicit Arguments.
  57 *)
  58
  59 (*#*******************************************)
  60
  61 (*            Riemann's Integral            *)
  62
  63 (*#*******************************************)
  64
  65 inline procedural "cic:/Coq/Reals/RiemannInt/Riemann_integrable.con" as definition.
  66
  67 inline procedural "cic:/Coq/Reals/RiemannInt/phi_sequence.con" as definition.
  68
  69 inline procedural "cic:/Coq/Reals/RiemannInt/phi_sequence_prop.con" as lemma.
  70
  71 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P1.con" as lemma.
  72
  73 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P2.con" as lemma.
  74
  75 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P3.con" as lemma.
  76
  77 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_exists.con" as lemma.
  78
  79 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P4.con" as lemma.
  80
  81 inline procedural "cic:/Coq/Reals/RiemannInt/RinvN_pos.con" as lemma.
  82
  83 inline procedural "cic:/Coq/Reals/RiemannInt/RinvN.con" as definition.
  84
  85 inline procedural "cic:/Coq/Reals/RiemannInt/RinvN_cv.con" as lemma.
  86
  87 (*#*********)
  88
  89 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt.con" as definition.
  90
  91 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P5.con" as lemma.
  92
  93 (*#*************************************)
  94
  95 (* C\176\([a,b]) is included in L1([a,b]) *)
  96
  97 (*#*************************************)
  98
  99 inline procedural "cic:/Coq/Reals/RiemannInt/maxN.con" as lemma.
 100
 101 inline procedural "cic:/Coq/Reals/RiemannInt/SubEquiN.con" as definition.
 102
 103 inline procedural "cic:/Coq/Reals/RiemannInt/max_N.con" as definition.
 104
 105 inline procedural "cic:/Coq/Reals/RiemannInt/SubEqui.con" as definition.
 106
 107 inline procedural "cic:/Coq/Reals/RiemannInt/Heine_cor1.con" as lemma.
 108
 109 inline procedural "cic:/Coq/Reals/RiemannInt/Heine_cor2.con" as lemma.
 110
 111 inline procedural "cic:/Coq/Reals/RiemannInt/SubEqui_P1.con" as lemma.
 112
 113 inline procedural "cic:/Coq/Reals/RiemannInt/SubEqui_P2.con" as lemma.
 114
 115 inline procedural "cic:/Coq/Reals/RiemannInt/SubEqui_P3.con" as lemma.
 116
 117 inline procedural "cic:/Coq/Reals/RiemannInt/SubEqui_P4.con" as lemma.
 118
 119 inline procedural "cic:/Coq/Reals/RiemannInt/SubEqui_P5.con" as lemma.
 120
 121 inline procedural "cic:/Coq/Reals/RiemannInt/SubEqui_P6.con" as lemma.
 122
 123 inline procedural "cic:/Coq/Reals/RiemannInt/SubEqui_P7.con" as lemma.
 124
 125 inline procedural "cic:/Coq/Reals/RiemannInt/SubEqui_P8.con" as lemma.
 126
 127 inline procedural "cic:/Coq/Reals/RiemannInt/SubEqui_P9.con" as lemma.
 128
 129 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P6.con" as lemma.
 130
 131 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P7.con" as lemma.
 132
 133 inline procedural "cic:/Coq/Reals/RiemannInt/continuity_implies_RiemannInt.con" as lemma.
 134
 135 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P8.con" as lemma.
 136
 137 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P9.con" as lemma.
 138
 139 inline procedural "cic:/Coq/Reals/RiemannInt/Req_EM_T.con" as lemma.
 140
 141 (* L1([a,b]) is a vectorial space *)
 142
 143 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P10.con" as lemma.
 144
 145 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P11.con" as lemma.
 146
 147 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P12.con" as lemma.
 148
 149 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P13.con" as lemma.
 150
 151 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P14.con" as lemma.
 152
 153 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P15.con" as lemma.
 154
 155 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P16.con" as lemma.
 156
 157 inline procedural "cic:/Coq/Reals/RiemannInt/Rle_cv_lim.con" as lemma.
 158
 159 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P17.con" as lemma.
 160
 161 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P18.con" as lemma.
 162
 163 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P19.con" as lemma.
 164
 165 inline procedural "cic:/Coq/Reals/RiemannInt/FTC_P1.con" as lemma.
 166
 167 inline procedural "cic:/Coq/Reals/RiemannInt/primitive.con" as definition.
 168
 169 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P20.con" as lemma.
 170
 171 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P21.con" as lemma.
 172
 173 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P22.con" as lemma.
 174
 175 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P23.con" as lemma.
 176
 177 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P24.con" as lemma.
 178
 179 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P25.con" as lemma.
 180
 181 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P26.con" as lemma.
 182
 183 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P27.con" as lemma.
 184
 185 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P28.con" as lemma.
 186
 187 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P29.con" as lemma.
 188
 189 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P30.con" as lemma.
 190
 191 inline procedural "cic:/Coq/Reals/RiemannInt/C1_fun.ind".
 192
 193 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P31.con" as lemma.
 194
 195 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P32.con" as lemma.
 196
 197 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P33.con" as lemma.
 198
 199 inline procedural "cic:/Coq/Reals/RiemannInt/FTC_Riemann.con" as lemma.
 200