helm/software/matita/contribs/procedural/Coq/Reals/Rpower.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: Rpower.v,v 1.17.2.1 2004/07/16 19:31:13 herbelin Exp $ i*)
  34
  35 (*i Due to L.Thery i*)
  36
  37 (*#***********************************************************)
  38
  39 (* Definitions of log and Rpower : R->R->R; main properties *)
  40
  41 (*#***********************************************************)
  42
  43 include "Reals/Rbase.ma".
  44
  45 include "Reals/Rfunctions.ma".
  46
  47 include "Reals/SeqSeries.ma".
  48
  49 include "Reals/Rtrigo.ma".
  50
  51 include "Reals/Ranalysis1.ma".
  52
  53 include "Reals/Exp_prop.ma".
  54
  55 include "Reals/Rsqrt_def.ma".
  56
  57 include "Reals/R_sqrt.ma".
  58
  59 include "Reals/MVT.ma".
  60
  61 include "Reals/Ranalysis4.ma".
  62
  63 (* UNEXPORTED
  64 Open Local Scope R_scope.
  65 *)
  66
  67 inline procedural "cic:/Coq/Reals/Rpower/P_Rmin.con" as lemma.
  68
  69 inline procedural "cic:/Coq/Reals/Rpower/exp_le_3.con" as lemma.
  70
  71 (*#*****************************************************************)
  72
  73 (*                        Properties of  Exp                      *)
  74
  75 (*#*****************************************************************)
  76
  77 inline procedural "cic:/Coq/Reals/Rpower/exp_increasing.con" as theorem.
  78
  79 inline procedural "cic:/Coq/Reals/Rpower/exp_lt_inv.con" as theorem.
  80
  81 inline procedural "cic:/Coq/Reals/Rpower/exp_ineq1.con" as lemma.
  82
  83 inline procedural "cic:/Coq/Reals/Rpower/ln_exists1.con" as lemma.
  84
  85 (*#*********)
  86
  87 inline procedural "cic:/Coq/Reals/Rpower/ln_exists.con" as lemma.
  88
  89 (* Definition of log R+* -> R *)
  90
  91 inline procedural "cic:/Coq/Reals/Rpower/Rln.con" as definition.
  92
  93 (* Extension on R *)
  94
  95 inline procedural "cic:/Coq/Reals/Rpower/ln.con" as definition.
  96
  97 inline procedural "cic:/Coq/Reals/Rpower/exp_ln.con" as lemma.
  98
  99 inline procedural "cic:/Coq/Reals/Rpower/exp_inv.con" as theorem.
 100
 101 inline procedural "cic:/Coq/Reals/Rpower/exp_Ropp.con" as theorem.
 102
 103 (*#*****************************************************************)
 104
 105 (*                        Properties of  Ln                       *)
 106
 107 (*#*****************************************************************)
 108
 109 inline procedural "cic:/Coq/Reals/Rpower/ln_increasing.con" as theorem.
 110
 111 inline procedural "cic:/Coq/Reals/Rpower/ln_exp.con" as theorem.
 112
 113 inline procedural "cic:/Coq/Reals/Rpower/ln_1.con" as theorem.
 114
 115 inline procedural "cic:/Coq/Reals/Rpower/ln_lt_inv.con" as theorem.
 116
 117 inline procedural "cic:/Coq/Reals/Rpower/ln_inv.con" as theorem.
 118
 119 inline procedural "cic:/Coq/Reals/Rpower/ln_mult.con" as theorem.
 120
 121 inline procedural "cic:/Coq/Reals/Rpower/ln_Rinv.con" as theorem.
 122
 123 inline procedural "cic:/Coq/Reals/Rpower/ln_continue.con" as theorem.
 124
 125 (*#*****************************************************************)
 126
 127 (*                        Definition of  Rpower                   *)
 128
 129 (*#*****************************************************************)
 130
 131 inline procedural "cic:/Coq/Reals/Rpower/Rpower.con" as definition.
 132
 133 (* NOTATION
 134 Infix Local "^R" := Rpower (at level 30, right associativity) : R_scope.
 135 *)
 136
 137 (*#*****************************************************************)
 138
 139 (*                        Properties of  Rpower                   *)
 140
 141 (*#*****************************************************************)
 142
 143 inline procedural "cic:/Coq/Reals/Rpower/Rpower_plus.con" as theorem.
 144
 145 inline procedural "cic:/Coq/Reals/Rpower/Rpower_mult.con" as theorem.
 146
 147 inline procedural "cic:/Coq/Reals/Rpower/Rpower_O.con" as theorem.
 148
 149 inline procedural "cic:/Coq/Reals/Rpower/Rpower_1.con" as theorem.
 150
 151 inline procedural "cic:/Coq/Reals/Rpower/Rpower_pow.con" as theorem.
 152
 153 inline procedural "cic:/Coq/Reals/Rpower/Rpower_lt.con" as theorem.
 154
 155 inline procedural "cic:/Coq/Reals/Rpower/Rpower_sqrt.con" as theorem.
 156
 157 inline procedural "cic:/Coq/Reals/Rpower/Rpower_Ropp.con" as theorem.
 158
 159 inline procedural "cic:/Coq/Reals/Rpower/Rle_Rpower.con" as theorem.
 160
 161 inline procedural "cic:/Coq/Reals/Rpower/ln_lt_2.con" as theorem.
 162
 163 (*#*************************************)
 164
 165 (* Differentiability of Ln and Rpower *)
 166
 167 (*#*************************************)
 168
 169 inline procedural "cic:/Coq/Reals/Rpower/limit1_ext.con" as theorem.
 170
 171 inline procedural "cic:/Coq/Reals/Rpower/limit1_imp.con" as theorem.
 172
 173 inline procedural "cic:/Coq/Reals/Rpower/Rinv_Rdiv.con" as theorem.
 174
 175 inline procedural "cic:/Coq/Reals/Rpower/Dln.con" as theorem.
 176
 177 inline procedural "cic:/Coq/Reals/Rpower/derivable_pt_lim_ln.con" as lemma.
 178
 179 inline procedural "cic:/Coq/Reals/Rpower/D_in_imp.con" as theorem.
 180
 181 inline procedural "cic:/Coq/Reals/Rpower/D_in_ext.con" as theorem.
 182
 183 inline procedural "cic:/Coq/Reals/Rpower/Dpower.con" as theorem.
 184
 185 inline procedural "cic:/Coq/Reals/Rpower/derivable_pt_lim_power.con" as theorem.
 186