helm/software/matita/contribs/procedural/Coq/Reals/Rtopology.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: Rtopology.v,v 1.19.2.1 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/Ranalysis1.ma".
  40
  41 include "Reals/RList.ma".
  42
  43 include "Logic/Classical_Prop.ma".
  44
  45 include "Logic/Classical_Pred_Type.ma".
  46
  47 (* UNEXPORTED
  48 Open Local Scope R_scope.
  49 *)
  50
  51 inline procedural "cic:/Coq/Reals/Rtopology/included.con" as definition.
  52
  53 inline procedural "cic:/Coq/Reals/Rtopology/disc.con" as definition.
  54
  55 inline procedural "cic:/Coq/Reals/Rtopology/neighbourhood.con" as definition.
  56
  57 inline procedural "cic:/Coq/Reals/Rtopology/open_set.con" as definition.
  58
  59 inline procedural "cic:/Coq/Reals/Rtopology/complementary.con" as definition.
  60
  61 inline procedural "cic:/Coq/Reals/Rtopology/closed_set.con" as definition.
  62
  63 inline procedural "cic:/Coq/Reals/Rtopology/intersection_domain.con" as definition.
  64
  65 inline procedural "cic:/Coq/Reals/Rtopology/union_domain.con" as definition.
  66
  67 inline procedural "cic:/Coq/Reals/Rtopology/interior.con" as definition.
  68
  69 inline procedural "cic:/Coq/Reals/Rtopology/interior_P1.con" as lemma.
  70
  71 inline procedural "cic:/Coq/Reals/Rtopology/interior_P2.con" as lemma.
  72
  73 inline procedural "cic:/Coq/Reals/Rtopology/point_adherent.con" as definition.
  74
  75 inline procedural "cic:/Coq/Reals/Rtopology/adherence.con" as definition.
  76
  77 inline procedural "cic:/Coq/Reals/Rtopology/adherence_P1.con" as lemma.
  78
  79 inline procedural "cic:/Coq/Reals/Rtopology/included_trans.con" as lemma.
  80
  81 inline procedural "cic:/Coq/Reals/Rtopology/interior_P3.con" as lemma.
  82
  83 inline procedural "cic:/Coq/Reals/Rtopology/complementary_P1.con" as lemma.
  84
  85 inline procedural "cic:/Coq/Reals/Rtopology/adherence_P2.con" as lemma.
  86
  87 inline procedural "cic:/Coq/Reals/Rtopology/adherence_P3.con" as lemma.
  88
  89 inline procedural "cic:/Coq/Reals/Rtopology/eq_Dom.con" as definition.
  90
  91 (* NOTATION
  92 Infix "=_D" := eq_Dom (at level 70, no associativity).
  93 *)
  94
  95 inline procedural "cic:/Coq/Reals/Rtopology/open_set_P1.con" as lemma.
  96
  97 inline procedural "cic:/Coq/Reals/Rtopology/closed_set_P1.con" as lemma.
  98
  99 inline procedural "cic:/Coq/Reals/Rtopology/neighbourhood_P1.con" as lemma.
 100
 101 inline procedural "cic:/Coq/Reals/Rtopology/open_set_P2.con" as lemma.
 102
 103 inline procedural "cic:/Coq/Reals/Rtopology/open_set_P3.con" as lemma.
 104
 105 inline procedural "cic:/Coq/Reals/Rtopology/open_set_P4.con" as lemma.
 106
 107 inline procedural "cic:/Coq/Reals/Rtopology/open_set_P5.con" as lemma.
 108
 109 inline procedural "cic:/Coq/Reals/Rtopology/disc_P1.con" as lemma.
 110
 111 inline procedural "cic:/Coq/Reals/Rtopology/continuity_P1.con" as lemma.
 112
 113 inline procedural "cic:/Coq/Reals/Rtopology/image_rec.con" as definition.
 114
 115 (*#*********)
 116
 117 inline procedural "cic:/Coq/Reals/Rtopology/continuity_P2.con" as lemma.
 118
 119 (*#*********)
 120
 121 inline procedural "cic:/Coq/Reals/Rtopology/continuity_P3.con" as lemma.
 122
 123 (*#*********)
 124
 125 inline procedural "cic:/Coq/Reals/Rtopology/Rsepare.con" as theorem.
 126
 127 inline procedural "cic:/Coq/Reals/Rtopology/family.ind".
 128
 129 inline procedural "cic:/Coq/Reals/Rtopology/family_open_set.con" as definition.
 130
 131 inline procedural "cic:/Coq/Reals/Rtopology/domain_finite.con" as definition.
 132
 133 inline procedural "cic:/Coq/Reals/Rtopology/family_finite.con" as definition.
 134
 135 inline procedural "cic:/Coq/Reals/Rtopology/covering.con" as definition.
 136
 137 inline procedural "cic:/Coq/Reals/Rtopology/covering_open_set.con" as definition.
 138
 139 inline procedural "cic:/Coq/Reals/Rtopology/covering_finite.con" as definition.
 140
 141 inline procedural "cic:/Coq/Reals/Rtopology/restriction_family.con" as lemma.
 142
 143 inline procedural "cic:/Coq/Reals/Rtopology/subfamily.con" as definition.
 144
 145 inline procedural "cic:/Coq/Reals/Rtopology/compact.con" as definition.
 146
 147 (*#*********)
 148
 149 inline procedural "cic:/Coq/Reals/Rtopology/family_P1.con" as lemma.
 150
 151 inline procedural "cic:/Coq/Reals/Rtopology/bounded.con" as definition.
 152
 153 inline procedural "cic:/Coq/Reals/Rtopology/open_set_P6.con" as lemma.
 154
 155 (*#*********)
 156
 157 inline procedural "cic:/Coq/Reals/Rtopology/compact_P1.con" as lemma.
 158
 159 (*#*********)
 160
 161 inline procedural "cic:/Coq/Reals/Rtopology/compact_P2.con" as lemma.
 162
 163 (*#*********)
 164
 165 inline procedural "cic:/Coq/Reals/Rtopology/compact_EMP.con" as lemma.
 166
 167 inline procedural "cic:/Coq/Reals/Rtopology/compact_eqDom.con" as lemma.
 168
 169 (* Borel-Lebesgue's lemma *)
 170
 171 inline procedural "cic:/Coq/Reals/Rtopology/compact_P3.con" as lemma.
 172
 173 inline procedural "cic:/Coq/Reals/Rtopology/compact_P4.con" as lemma.
 174
 175 (*#*********)
 176
 177 inline procedural "cic:/Coq/Reals/Rtopology/compact_P5.con" as lemma.
 178
 179 (*#*********)
 180
 181 inline procedural "cic:/Coq/Reals/Rtopology/compact_carac.con" as lemma.
 182
 183 inline procedural "cic:/Coq/Reals/Rtopology/image_dir.con" as definition.
 184
 185 (*#*********)
 186
 187 inline procedural "cic:/Coq/Reals/Rtopology/continuity_compact.con" as lemma.
 188
 189 inline procedural "cic:/Coq/Reals/Rtopology/Rlt_Rminus.con" as lemma.
 190
 191 inline procedural "cic:/Coq/Reals/Rtopology/prolongement_C0.con" as lemma.
 192
 193 (*#*********)
 194
 195 inline procedural "cic:/Coq/Reals/Rtopology/continuity_ab_maj.con" as lemma.
 196
 197 (*#*********)
 198
 199 inline procedural "cic:/Coq/Reals/Rtopology/continuity_ab_min.con" as lemma.
 200
 201 (*#*******************************************************)
 202
 203 (*         Proof of Bolzano-Weierstrass theorem         *)
 204
 205 (*#*******************************************************)
 206
 207 inline procedural "cic:/Coq/Reals/Rtopology/ValAdh.con" as definition.
 208
 209 inline procedural "cic:/Coq/Reals/Rtopology/intersection_family.con" as definition.
 210
 211 inline procedural "cic:/Coq/Reals/Rtopology/ValAdh_un_exists.con" as lemma.
 212
 213 inline procedural "cic:/Coq/Reals/Rtopology/ValAdh_un.con" as definition.
 214
 215 inline procedural "cic:/Coq/Reals/Rtopology/ValAdh_un_prop.con" as lemma.
 216
 217 inline procedural "cic:/Coq/Reals/Rtopology/adherence_P4.con" as lemma.
 218
 219 inline procedural "cic:/Coq/Reals/Rtopology/family_closed_set.con" as definition.
 220
 221 inline procedural "cic:/Coq/Reals/Rtopology/intersection_vide_in.con" as definition.
 222
 223 inline procedural "cic:/Coq/Reals/Rtopology/intersection_vide_finite_in.con" as definition.
 224
 225 (*#*********)
 226
 227 inline procedural "cic:/Coq/Reals/Rtopology/compact_P6.con" as lemma.
 228
 229 inline procedural "cic:/Coq/Reals/Rtopology/Bolzano_Weierstrass.con" as theorem.
 230
 231 (*#*******************************************************)
 232
 233 (*               Proof of Heine's theorem               *)
 234
 235 (*#*******************************************************)
 236
 237 inline procedural "cic:/Coq/Reals/Rtopology/uniform_continuity.con" as definition.
 238
 239 inline procedural "cic:/Coq/Reals/Rtopology/is_lub_u.con" as lemma.
 240
 241 inline procedural "cic:/Coq/Reals/Rtopology/domain_P1.con" as lemma.
 242
 243 inline procedural "cic:/Coq/Reals/Rtopology/Heine.con" as theorem.
 244