helm/software/matita/contribs/procedural/Coq/Reals/Rtrigo_calc.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: Rtrigo_calc.v,v 1.15.2.1 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.ma".
  42
  43 include "Reals/R_sqrt.ma".
  44
  45 (* UNEXPORTED
  46 Open Local Scope R_scope.
  47 *)
  48
  49 inline procedural "cic:/Coq/Reals/Rtrigo_calc/tan_PI.con" as lemma.
  50
  51 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sin_3PI2.con" as lemma.
  52
  53 inline procedural "cic:/Coq/Reals/Rtrigo_calc/tan_2PI.con" as lemma.
  54
  55 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sin_cos_PI4.con" as lemma.
  56
  57 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sin_PI3_cos_PI6.con" as lemma.
  58
  59 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sin_PI6_cos_PI3.con" as lemma.
  60
  61 inline procedural "cic:/Coq/Reals/Rtrigo_calc/PI6_RGT_0.con" as lemma.
  62
  63 inline procedural "cic:/Coq/Reals/Rtrigo_calc/PI6_RLT_PI2.con" as lemma.
  64
  65 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sin_PI6.con" as lemma.
  66
  67 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sqrt2_neq_0.con" as lemma.
  68
  69 inline procedural "cic:/Coq/Reals/Rtrigo_calc/R1_sqrt2_neq_0.con" as lemma.
  70
  71 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sqrt3_2_neq_0.con" as lemma.
  72
  73 inline procedural "cic:/Coq/Reals/Rtrigo_calc/Rlt_sqrt2_0.con" as lemma.
  74
  75 inline procedural "cic:/Coq/Reals/Rtrigo_calc/Rlt_sqrt3_0.con" as lemma.
  76
  77 inline procedural "cic:/Coq/Reals/Rtrigo_calc/PI4_RGT_0.con" as lemma.
  78
  79 inline procedural "cic:/Coq/Reals/Rtrigo_calc/cos_PI4.con" as lemma.
  80
  81 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sin_PI4.con" as lemma.
  82
  83 inline procedural "cic:/Coq/Reals/Rtrigo_calc/tan_PI4.con" as lemma.
  84
  85 inline procedural "cic:/Coq/Reals/Rtrigo_calc/cos3PI4.con" as lemma.
  86
  87 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sin3PI4.con" as lemma.
  88
  89 inline procedural "cic:/Coq/Reals/Rtrigo_calc/cos_PI6.con" as lemma.
  90
  91 inline procedural "cic:/Coq/Reals/Rtrigo_calc/tan_PI6.con" as lemma.
  92
  93 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sin_PI3.con" as lemma.
  94
  95 inline procedural "cic:/Coq/Reals/Rtrigo_calc/cos_PI3.con" as lemma.
  96
  97 inline procedural "cic:/Coq/Reals/Rtrigo_calc/tan_PI3.con" as lemma.
  98
  99 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sin_2PI3.con" as lemma.
 100
 101 inline procedural "cic:/Coq/Reals/Rtrigo_calc/cos_2PI3.con" as lemma.
 102
 103 inline procedural "cic:/Coq/Reals/Rtrigo_calc/tan_2PI3.con" as lemma.
 104
 105 inline procedural "cic:/Coq/Reals/Rtrigo_calc/cos_5PI4.con" as lemma.
 106
 107 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sin_5PI4.con" as lemma.
 108
 109 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sin_cos5PI4.con" as lemma.
 110
 111 inline procedural "cic:/Coq/Reals/Rtrigo_calc/Rgt_3PI2_0.con" as lemma.
 112
 113 inline procedural "cic:/Coq/Reals/Rtrigo_calc/Rgt_2PI_0.con" as lemma.
 114
 115 inline procedural "cic:/Coq/Reals/Rtrigo_calc/Rlt_PI_3PI2.con" as lemma.
 116
 117 inline procedural "cic:/Coq/Reals/Rtrigo_calc/Rlt_3PI2_2PI.con" as lemma.
 118
 119 (*#**************************************************************)
 120
 121 (* Radian -> Degree | Degree -> Radian                         *)
 122
 123 (*#**************************************************************)
 124
 125 inline procedural "cic:/Coq/Reals/Rtrigo_calc/plat.con" as definition.
 126
 127 inline procedural "cic:/Coq/Reals/Rtrigo_calc/toRad.con" as definition.
 128
 129 inline procedural "cic:/Coq/Reals/Rtrigo_calc/toDeg.con" as definition.
 130
 131 inline procedural "cic:/Coq/Reals/Rtrigo_calc/rad_deg.con" as lemma.
 132
 133 inline procedural "cic:/Coq/Reals/Rtrigo_calc/toRad_inj.con" as lemma.
 134
 135 inline procedural "cic:/Coq/Reals/Rtrigo_calc/deg_rad.con" as lemma.
 136
 137 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sind.con" as definition.
 138
 139 inline procedural "cic:/Coq/Reals/Rtrigo_calc/cosd.con" as definition.
 140
 141 inline procedural "cic:/Coq/Reals/Rtrigo_calc/tand.con" as definition.
 142
 143 inline procedural "cic:/Coq/Reals/Rtrigo_calc/Rsqr_sin_cos_d_one.con" as lemma.
 144
 145 (*#**************************************************)
 146
 147 (*                Other properties                 *)
 148
 149 (*#**************************************************)
 150
 151 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sin_lb_ge_0.con" as lemma.
 152