matita/matita/contribs/procedural/Coq/Reals/SeqProp.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: SeqProp.v,v 1.13.2.1 2004/07/16 19:31:15 herbelin Exp $ i*)
  34
  35 include "Reals/Rbase.ma".
  36
  37 include "Reals/Rfunctions.ma".
  38
  39 include "Reals/Rseries.ma".
  40
  41 include "Logic/Classical.ma".
  42
  43 include "Arith/Max.ma".
  44
  45 (* UNEXPORTED
  46 Open Local Scope R_scope.
  47 *)
  48
  49 inline procedural "cic:/Coq/Reals/SeqProp/Un_decreasing.con" as definition.
  50
  51 inline procedural "cic:/Coq/Reals/SeqProp/opp_seq.con" as definition.
  52
  53 inline procedural "cic:/Coq/Reals/SeqProp/has_ub.con" as definition.
  54
  55 inline procedural "cic:/Coq/Reals/SeqProp/has_lb.con" as definition.
  56
  57 (*#*********)
  58
  59 inline procedural "cic:/Coq/Reals/SeqProp/growing_cv.con" as lemma.
  60
  61 inline procedural "cic:/Coq/Reals/SeqProp/decreasing_growing.con" as lemma.
  62
  63 inline procedural "cic:/Coq/Reals/SeqProp/decreasing_cv.con" as lemma.
  64
  65 (*#**********)
  66
  67 inline procedural "cic:/Coq/Reals/SeqProp/maj_sup.con" as lemma.
  68
  69 (*#*********)
  70
  71 inline procedural "cic:/Coq/Reals/SeqProp/min_inf.con" as lemma.
  72
  73 inline procedural "cic:/Coq/Reals/SeqProp/majorant.con" as definition.
  74
  75 inline procedural "cic:/Coq/Reals/SeqProp/minorant.con" as definition.
  76
  77 inline procedural "cic:/Coq/Reals/SeqProp/maj_ss.con" as lemma.
  78
  79 inline procedural "cic:/Coq/Reals/SeqProp/min_ss.con" as lemma.
  80
  81 inline procedural "cic:/Coq/Reals/SeqProp/sequence_majorant.con" as definition.
  82
  83 inline procedural "cic:/Coq/Reals/SeqProp/sequence_minorant.con" as definition.
  84
  85 inline procedural "cic:/Coq/Reals/SeqProp/Wn_decreasing.con" as lemma.
  86
  87 inline procedural "cic:/Coq/Reals/SeqProp/Vn_growing.con" as lemma.
  88
  89 (*#*********)
  90
  91 inline procedural "cic:/Coq/Reals/SeqProp/Vn_Un_Wn_order.con" as lemma.
  92
  93 inline procedural "cic:/Coq/Reals/SeqProp/min_maj.con" as lemma.
  94
  95 inline procedural "cic:/Coq/Reals/SeqProp/maj_min.con" as lemma.
  96
  97 (*#*********)
  98
  99 inline procedural "cic:/Coq/Reals/SeqProp/cauchy_maj.con" as lemma.
 100
 101 (*#*********)
 102
 103 inline procedural "cic:/Coq/Reals/SeqProp/cauchy_opp.con" as lemma.
 104
 105 (*#*********)
 106
 107 inline procedural "cic:/Coq/Reals/SeqProp/cauchy_min.con" as lemma.
 108
 109 (*#*********)
 110
 111 inline procedural "cic:/Coq/Reals/SeqProp/maj_cv.con" as lemma.
 112
 113 (*#*********)
 114
 115 inline procedural "cic:/Coq/Reals/SeqProp/min_cv.con" as lemma.
 116
 117 inline procedural "cic:/Coq/Reals/SeqProp/cond_eq.con" as lemma.
 118
 119 inline procedural "cic:/Coq/Reals/SeqProp/not_Rlt.con" as lemma.
 120
 121 (*#*********)
 122
 123 inline procedural "cic:/Coq/Reals/SeqProp/approx_maj.con" as lemma.
 124
 125 (*#*********)
 126
 127 inline procedural "cic:/Coq/Reals/SeqProp/approx_min.con" as lemma.
 128
 129 (* Unicity of limit for convergent sequences *)
 130
 131 inline procedural "cic:/Coq/Reals/SeqProp/UL_sequence.con" as lemma.
 132
 133 (*#*********)
 134
 135 inline procedural "cic:/Coq/Reals/SeqProp/CV_plus.con" as lemma.
 136
 137 (*#*********)
 138
 139 inline procedural "cic:/Coq/Reals/SeqProp/cv_cvabs.con" as lemma.
 140
 141 (*#*********)
 142
 143 inline procedural "cic:/Coq/Reals/SeqProp/CV_Cauchy.con" as lemma.
 144
 145 (*#*********)
 146
 147 inline procedural "cic:/Coq/Reals/SeqProp/maj_by_pos.con" as lemma.
 148
 149 (*#*********)
 150
 151 inline procedural "cic:/Coq/Reals/SeqProp/CV_mult.con" as lemma.
 152
 153 inline procedural "cic:/Coq/Reals/SeqProp/tech9.con" as lemma.
 154
 155 inline procedural "cic:/Coq/Reals/SeqProp/tech10.con" as lemma.
 156
 157 inline procedural "cic:/Coq/Reals/SeqProp/tech13.con" as lemma.
 158
 159 (*#*********)
 160
 161 inline procedural "cic:/Coq/Reals/SeqProp/growing_ineq.con" as lemma.
 162
 163 (* Un->l => (-Un) -> (-l) *)
 164
 165 inline procedural "cic:/Coq/Reals/SeqProp/CV_opp.con" as lemma.
 166
 167 (*#*********)
 168
 169 inline procedural "cic:/Coq/Reals/SeqProp/decreasing_ineq.con" as lemma.
 170
 171 (*#*********)
 172
 173 inline procedural "cic:/Coq/Reals/SeqProp/CV_minus.con" as lemma.
 174
 175 (* Un -> +oo *)
 176
 177 inline procedural "cic:/Coq/Reals/SeqProp/cv_infty.con" as definition.
 178
 179 (* Un -> +oo => /Un -> O *)
 180
 181 inline procedural "cic:/Coq/Reals/SeqProp/cv_infty_cv_R0.con" as lemma.
 182
 183 (*#*********)
 184
 185 inline procedural "cic:/Coq/Reals/SeqProp/decreasing_prop.con" as lemma.
 186
 187 (* |x|^n/n! -> 0 *)
 188
 189 inline procedural "cic:/Coq/Reals/SeqProp/cv_speed_pow_fact.con" as lemma.
 190