helm/software/matita/contribs/procedural/Coq/Reals/MVT.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: MVT.v,v 1.10.2.1 2004/07/16 19:31:10 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/Rtopology.ma".
  42
  43 (* UNEXPORTED
  44 Open Local Scope R_scope.
  45 *)
  46
  47 (* The Mean Value Theorem *)
  48
  49 inline procedural "cic:/Coq/Reals/MVT/MVT.con" as theorem.
  50
  51 (* Corollaries ... *)
  52
  53 inline procedural "cic:/Coq/Reals/MVT/MVT_cor1.con" as lemma.
  54
  55 inline procedural "cic:/Coq/Reals/MVT/MVT_cor2.con" as theorem.
  56
  57 inline procedural "cic:/Coq/Reals/MVT/MVT_cor3.con" as lemma.
  58
  59 inline procedural "cic:/Coq/Reals/MVT/Rolle.con" as lemma.
  60
  61 (*#*********)
  62
  63 inline procedural "cic:/Coq/Reals/MVT/nonneg_derivative_1.con" as lemma.
  64
  65 (*#*********)
  66
  67 inline procedural "cic:/Coq/Reals/MVT/nonpos_derivative_0.con" as lemma.
  68
  69 (*#*********)
  70
  71 inline procedural "cic:/Coq/Reals/MVT/increasing_decreasing_opp.con" as lemma.
  72
  73 (*#*********)
  74
  75 inline procedural "cic:/Coq/Reals/MVT/nonpos_derivative_1.con" as lemma.
  76
  77 (*#*********)
  78
  79 inline procedural "cic:/Coq/Reals/MVT/positive_derivative.con" as lemma.
  80
  81 (*#*********)
  82
  83 inline procedural "cic:/Coq/Reals/MVT/strictincreasing_strictdecreasing_opp.con" as lemma.
  84
  85 (*#*********)
  86
  87 inline procedural "cic:/Coq/Reals/MVT/negative_derivative.con" as lemma.
  88
  89 (*#*********)
  90
  91 inline procedural "cic:/Coq/Reals/MVT/null_derivative_0.con" as lemma.
  92
  93 (*#*********)
  94
  95 inline procedural "cic:/Coq/Reals/MVT/increasing_decreasing.con" as lemma.
  96
  97 (*#*********)
  98
  99 inline procedural "cic:/Coq/Reals/MVT/null_derivative_1.con" as lemma.
 100
 101 (*#*********)
 102
 103 inline procedural "cic:/Coq/Reals/MVT/derive_increasing_interv_ax.con" as lemma.
 104
 105 (*#*********)
 106
 107 inline procedural "cic:/Coq/Reals/MVT/derive_increasing_interv.con" as lemma.
 108
 109 (*#*********)
 110
 111 inline procedural "cic:/Coq/Reals/MVT/derive_increasing_interv_var.con" as lemma.
 112
 113 (*#*********)
 114
 115 (*#*********)
 116
 117 inline procedural "cic:/Coq/Reals/MVT/IAF.con" as theorem.
 118
 119 inline procedural "cic:/Coq/Reals/MVT/IAF_var.con" as lemma.
 120
 121 (* If f has a null derivative in ]a,b[ and is continue in [a,b], *)
 122
 123 (* then f is constant on [a,b] *)
 124
 125 inline procedural "cic:/Coq/Reals/MVT/null_derivative_loc.con" as lemma.
 126
 127 (* Unicity of the antiderivative *)
 128
 129 inline procedural "cic:/Coq/Reals/MVT/antiderivative_Ucte.con" as lemma.
 130