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

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   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: Rtrigo_def.v,v 1.17.2.1 2004/07/16 19:31:14 herbelin Exp $ i*)
  34
  35 include "Reals/Rbase.ma".
  36
  37 include "Reals/Rfunctions.ma".
  38
  39 include "Reals/SeqSeries.ma".
  40
  41 include "Reals/Rtrigo_fun.ma".
  42
  43 include "Arith/Max.ma".
  44
  45 (* UNEXPORTED
  46 Open Local Scope R_scope.
  47 *)
  48
  49 (*#****************************)
  50
  51 (* Definition of exponential *)
  52
  53 (*#****************************)
  54
  55 inline procedural "cic:/Coq/Reals/Rtrigo_def/exp_in.con" as definition.
  56
  57 inline procedural "cic:/Coq/Reals/Rtrigo_def/exp_cof_no_R0.con" as lemma.
  58
  59 inline procedural "cic:/Coq/Reals/Rtrigo_def/exist_exp.con" as lemma.
  60
  61 inline procedural "cic:/Coq/Reals/Rtrigo_def/exp.con" as definition.
  62
  63 inline procedural "cic:/Coq/Reals/Rtrigo_def/pow_i.con" as lemma.
  64
  65 (*i Calculus of $e^0$ *)
  66
  67 inline procedural "cic:/Coq/Reals/Rtrigo_def/exist_exp0.con" as lemma.
  68
  69 inline procedural "cic:/Coq/Reals/Rtrigo_def/exp_0.con" as lemma.
  70
  71 (*#*************************************)
  72
  73 (* Definition of hyperbolic functions *)
  74
  75 (*#*************************************)
  76
  77 inline procedural "cic:/Coq/Reals/Rtrigo_def/cosh.con" as definition.
  78
  79 inline procedural "cic:/Coq/Reals/Rtrigo_def/sinh.con" as definition.
  80
  81 inline procedural "cic:/Coq/Reals/Rtrigo_def/tanh.con" as definition.
  82
  83 inline procedural "cic:/Coq/Reals/Rtrigo_def/cosh_0.con" as lemma.
  84
  85 inline procedural "cic:/Coq/Reals/Rtrigo_def/sinh_0.con" as lemma.
  86
  87 inline procedural "cic:/Coq/Reals/Rtrigo_def/cos_n.con" as definition.
  88
  89 inline procedural "cic:/Coq/Reals/Rtrigo_def/simpl_cos_n.con" as lemma.
  90
  91 inline procedural "cic:/Coq/Reals/Rtrigo_def/archimed_cor1.con" as lemma.
  92
  93 inline procedural "cic:/Coq/Reals/Rtrigo_def/Alembert_cos.con" as lemma.
  94
  95 inline procedural "cic:/Coq/Reals/Rtrigo_def/cosn_no_R0.con" as lemma.
  96
  97 (*#*********)
  98
  99 inline procedural "cic:/Coq/Reals/Rtrigo_def/cos_in.con" as definition.
 100
 101 (*#*********)
 102
 103 inline procedural "cic:/Coq/Reals/Rtrigo_def/exist_cos.con" as lemma.
 104
 105 (* Definition of cosinus *)
 106
 107 (*#************************)
 108
 109 inline procedural "cic:/Coq/Reals/Rtrigo_def/cos.con" as definition.
 110
 111 inline procedural "cic:/Coq/Reals/Rtrigo_def/sin_n.con" as definition.
 112
 113 inline procedural "cic:/Coq/Reals/Rtrigo_def/simpl_sin_n.con" as lemma.
 114
 115 inline procedural "cic:/Coq/Reals/Rtrigo_def/Alembert_sin.con" as lemma.
 116
 117 inline procedural "cic:/Coq/Reals/Rtrigo_def/sin_no_R0.con" as lemma.
 118
 119 (*#*********)
 120
 121 inline procedural "cic:/Coq/Reals/Rtrigo_def/sin_in.con" as definition.
 122
 123 (*#*********)
 124
 125 inline procedural "cic:/Coq/Reals/Rtrigo_def/exist_sin.con" as lemma.
 126
 127 (*#**********************)
 128
 129 (* Definition of sinus *)
 130
 131 inline procedural "cic:/Coq/Reals/Rtrigo_def/sin.con" as definition.
 132
 133 (*#********************************************)
 134
 135 (*                 PROPERTIES                *)
 136
 137 (*#********************************************)
 138
 139 inline procedural "cic:/Coq/Reals/Rtrigo_def/cos_sym.con" as lemma.
 140
 141 inline procedural "cic:/Coq/Reals/Rtrigo_def/sin_antisym.con" as lemma.
 142
 143 inline procedural "cic:/Coq/Reals/Rtrigo_def/sin_0.con" as lemma.
 144
 145 inline procedural "cic:/Coq/Reals/Rtrigo_def/exist_cos0.con" as lemma.
 146
 147 (* Calculus of (cos 0) *)
 148
 149 inline procedural "cic:/Coq/Reals/Rtrigo_def/cos_0.con" as lemma.
 150