helm/software/matita/contribs/procedural/Coq/Reals/Rsqrt_def.mma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  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: Rsqrt_def.v,v 1.14.2.1 2004/07/16 19:31:13 herbelin Exp $ i*)
  34
  35 include "Bool/Sumbool.ma".
  36
  37 include "Reals/Rbase.ma".
  38
  39 include "Reals/Rfunctions.ma".
  40
  41 include "Reals/SeqSeries.ma".
  42
  43 include "Reals/Ranalysis1.ma".
  44
  45 (* UNEXPORTED
  46 Open Local Scope R_scope.
  47 *)
  48
  49 inline procedural "cic:/Coq/Reals/Rsqrt_def/Dichotomy_lb.con" as definition.
  50
  51 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_lb.con" as definition.
  52
  53 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_up.con" as definition.
  54
  55 (*#*********)
  56
  57 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_comp.con" as lemma.
  58
  59 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_lb_growing.con" as lemma.
  60
  61 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_up_decreasing.con" as lemma.
  62
  63 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_lb_maj_y.con" as lemma.
  64
  65 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_lb_maj.con" as lemma.
  66
  67 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_up_min_x.con" as lemma.
  68
  69 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_up_min.con" as lemma.
  70
  71 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_lb_cv.con" as lemma.
  72
  73 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_up_cv.con" as lemma.
  74
  75 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_lb_dicho_up.con" as lemma.
  76
  77 inline procedural "cic:/Coq/Reals/Rsqrt_def/pow_2_n.con" as definition.
  78
  79 inline procedural "cic:/Coq/Reals/Rsqrt_def/pow_2_n_neq_R0.con" as lemma.
  80
  81 inline procedural "cic:/Coq/Reals/Rsqrt_def/pow_2_n_growing.con" as lemma.
  82
  83 inline procedural "cic:/Coq/Reals/Rsqrt_def/pow_2_n_infty.con" as lemma.
  84
  85 inline procedural "cic:/Coq/Reals/Rsqrt_def/cv_dicho.con" as lemma.
  86
  87 inline procedural "cic:/Coq/Reals/Rsqrt_def/cond_positivity.con" as definition.
  88
  89 (* Sequential caracterisation of continuity *)
  90
  91 inline procedural "cic:/Coq/Reals/Rsqrt_def/continuity_seq.con" as lemma.
  92
  93 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_lb_car.con" as lemma.
  94
  95 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_up_car.con" as lemma.
  96
  97 (* Intermediate Value Theorem *)
  98
  99 inline procedural "cic:/Coq/Reals/Rsqrt_def/IVT.con" as lemma.
 100
 101 inline procedural "cic:/Coq/Reals/Rsqrt_def/IVT_cor.con" as lemma.
 102
 103 (* We can now define the square root function as the reciprocal transformation of the square root function *)
 104
 105 inline procedural "cic:/Coq/Reals/Rsqrt_def/Rsqrt_exists.con" as lemma.
 106
 107 (* Definition of the square root: R+->R *)
 108
 109 inline procedural "cic:/Coq/Reals/Rsqrt_def/Rsqrt.con" as definition.
 110
 111 (*#*********)
 112
 113 inline procedural "cic:/Coq/Reals/Rsqrt_def/Rsqrt_positivity.con" as lemma.
 114
 115 (*#*********)
 116
 117 inline procedural "cic:/Coq/Reals/Rsqrt_def/Rsqrt_Rsqrt.con" as lemma.
 118