helm/software/matita/contribs/procedural/Coq/Reals/Raxioms.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: Raxioms.v,v 1.20.2.1 2004/07/16 19:31:12 herbelin Exp $ i*)
  34
  35 (*#********************************************************)
  36
  37 (*#*    Axiomatisation of the classical reals             *)
  38
  39 (*#********************************************************)
  40
  41 include "ZArith/ZArith_base.ma".
  42
  43 include "Reals/Rdefinitions.ma".
  44
  45 (* UNEXPORTED
  46 Open Local Scope R_scope.
  47 *)
  48
  49 (*#********************************************************)
  50
  51 (*               Field axioms                            *)
  52
  53 (*#********************************************************)
  54
  55 (*#********************************************************)
  56
  57 (*#*      Addition                                        *)
  58
  59 (*#********************************************************)
  60
  61 (*#*********)
  62
  63 inline procedural "cic:/Coq/Reals/Raxioms/Rplus_comm.con".
  64
  65 (* UNEXPORTED
  66 Hint Resolve Rplus_comm: real.
  67 *)
  68
  69 (*#*********)
  70
  71 inline procedural "cic:/Coq/Reals/Raxioms/Rplus_assoc.con".
  72
  73 (* UNEXPORTED
  74 Hint Resolve Rplus_assoc: real.
  75 *)
  76
  77 (*#*********)
  78
  79 inline procedural "cic:/Coq/Reals/Raxioms/Rplus_opp_r.con".
  80
  81 (* UNEXPORTED
  82 Hint Resolve Rplus_opp_r: real v62.
  83 *)
  84
  85 (*#*********)
  86
  87 inline procedural "cic:/Coq/Reals/Raxioms/Rplus_0_l.con".
  88
  89 (* UNEXPORTED
  90 Hint Resolve Rplus_0_l: real.
  91 *)
  92
  93 (*#**********************************************************)
  94
  95 (*#*       Multiplication                                   *)
  96
  97 (*#**********************************************************)
  98
  99 (*#*********)
 100
 101 inline procedural "cic:/Coq/Reals/Raxioms/Rmult_comm.con".
 102
 103 (* UNEXPORTED
 104 Hint Resolve Rmult_comm: real v62.
 105 *)
 106
 107 (*#*********)
 108
 109 inline procedural "cic:/Coq/Reals/Raxioms/Rmult_assoc.con".
 110
 111 (* UNEXPORTED
 112 Hint Resolve Rmult_assoc: real v62.
 113 *)
 114
 115 (*#*********)
 116
 117 inline procedural "cic:/Coq/Reals/Raxioms/Rinv_l.con".
 118
 119 (* UNEXPORTED
 120 Hint Resolve Rinv_l: real.
 121 *)
 122
 123 (*#*********)
 124
 125 inline procedural "cic:/Coq/Reals/Raxioms/Rmult_1_l.con".
 126
 127 (* UNEXPORTED
 128 Hint Resolve Rmult_1_l: real.
 129 *)
 130
 131 (*#*********)
 132
 133 inline procedural "cic:/Coq/Reals/Raxioms/R1_neq_R0.con".
 134
 135 (* UNEXPORTED
 136 Hint Resolve R1_neq_R0: real.
 137 *)
 138
 139 (*#********************************************************)
 140
 141 (*#*      Distributivity                                  *)
 142
 143 (*#********************************************************)
 144
 145 (*#*********)
 146
 147 inline procedural "cic:/Coq/Reals/Raxioms/Rmult_plus_distr_l.con".
 148
 149 (* UNEXPORTED
 150 Hint Resolve Rmult_plus_distr_l: real v62.
 151 *)
 152
 153 (*#********************************************************)
 154
 155 (*#*      Order axioms                                    *)
 156
 157 (*#********************************************************)
 158
 159 (*#********************************************************)
 160
 161 (*#*      Total Order                                     *)
 162
 163 (*#********************************************************)
 164
 165 (*#*********)
 166
 167 inline procedural "cic:/Coq/Reals/Raxioms/total_order_T.con".
 168
 169 (*#********************************************************)
 170
 171 (*#*      Lower                                           *)
 172
 173 (*#********************************************************)
 174
 175 (*#*********)
 176
 177 inline procedural "cic:/Coq/Reals/Raxioms/Rlt_asym.con".
 178
 179 (*#*********)
 180
 181 inline procedural "cic:/Coq/Reals/Raxioms/Rlt_trans.con".
 182
 183 (*#*********)
 184
 185 inline procedural "cic:/Coq/Reals/Raxioms/Rplus_lt_compat_l.con".
 186
 187 (*#*********)
 188
 189 inline procedural "cic:/Coq/Reals/Raxioms/Rmult_lt_compat_l.con".
 190
 191 (* UNEXPORTED
 192 Hint Resolve Rlt_asym Rplus_lt_compat_l Rmult_lt_compat_l: real.
 193 *)
 194
 195 (*#*********************************************************)
 196
 197 (*#*      Injection from N to R                            *)
 198
 199 (*#*********************************************************)
 200
 201 (*#*********)
 202
 203 inline procedural "cic:/Coq/Reals/Raxioms/INR.con" as definition.
 204
 205 (* UNEXPORTED
 206 Arguments Scope INR [nat_scope].
 207 *)
 208
 209 (*#*********************************************************)
 210
 211 (*#*      Injection from [Z] to [R]                        *)
 212
 213 (*#*********************************************************)
 214
 215 (*#*********)
 216
 217 inline procedural "cic:/Coq/Reals/Raxioms/IZR.con" as definition.
 218
 219 (* UNEXPORTED
 220 Arguments Scope IZR [Z_scope].
 221 *)
 222
 223 (*#*********************************************************)
 224
 225 (*#*      [R] Archimedian                                  *)
 226
 227 (*#*********************************************************)
 228
 229 (*#*********)
 230
 231 inline procedural "cic:/Coq/Reals/Raxioms/archimed.con".
 232
 233 (*#*********************************************************)
 234
 235 (*#*      [R] Complete                                     *)
 236
 237 (*#*********************************************************)
 238
 239 (*#*********)
 240
 241 inline procedural "cic:/Coq/Reals/Raxioms/is_upper_bound.con" as definition.
 242
 243 (*#*********)
 244
 245 inline procedural "cic:/Coq/Reals/Raxioms/bound.con" as definition.
 246
 247 (*#*********)
 248
 249 inline procedural "cic:/Coq/Reals/Raxioms/is_lub.con" as definition.
 250
 251 (*#*********)
 252
 253 inline procedural "cic:/Coq/Reals/Raxioms/completeness.con".
 254