helm/software/matita/contribs/CoRN-Decl/complex/AbsCC.ma

   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 set "baseuri" "cic:/matita/CoRN-Decl/complex/AbsCC".
  18
  19 include "CoRN.ma".
  20
  21 (* $Id: AbsCC.v,v 1.2 2004/04/23 10:00:54 lcf Exp $ *)
  22
  23 include "complex/CComplex.ma".
  24
  25 (*#* * Absolute value on [CC]
  26 ** Properties of [AbsCC] *)
  27
  28 (* UNEXPORTED
  29 Section AbsCC_properties
  30 *)
  31
  32 inline "cic:/CoRN/complex/AbsCC/AbsCC_nonneg.con".
  33
  34 inline "cic:/CoRN/complex/AbsCC/AbsCC_ap_zero_imp_pos.con".
  35
  36 inline "cic:/CoRN/complex/AbsCC/AbsCC_wd.con".
  37
  38 (* UNEXPORTED
  39 Hint Resolve AbsCC_wd: algebra_c.
  40 *)
  41
  42 inline "cic:/CoRN/complex/AbsCC/cc_inv_abs.con".
  43
  44 (* UNEXPORTED
  45 Hint Resolve cc_inv_abs: algebra.
  46 *)
  47
  48 inline "cic:/CoRN/complex/AbsCC/cc_minus_abs.con".
  49
  50 inline "cic:/CoRN/complex/AbsCC/cc_mult_abs.con".
  51
  52 (* UNEXPORTED
  53 Hint Resolve cc_mult_abs: algebra.
  54 *)
  55
  56 inline "cic:/CoRN/complex/AbsCC/AbsCC_minzero.con".
  57
  58 inline "cic:/CoRN/complex/AbsCC/AbsCC_IR.con".
  59
  60 (* UNEXPORTED
  61 Hint Resolve AbsCC_IR: algebra.
  62 *)
  63
  64 inline "cic:/CoRN/complex/AbsCC/cc_div_abs.con".
  65
  66 inline "cic:/CoRN/complex/AbsCC/cc_div_abs'.con".
  67
  68 inline "cic:/CoRN/complex/AbsCC/AbsCC_zero.con".
  69
  70 (* UNEXPORTED
  71 Hint Resolve AbsCC_zero: algebra.
  72 *)
  73
  74 inline "cic:/CoRN/complex/AbsCC/AbsCC_one.con".
  75
  76 inline "cic:/CoRN/complex/AbsCC/cc_pow_abs.con".
  77
  78 inline "cic:/CoRN/complex/AbsCC/AbsCC_pos.con".
  79
  80 inline "cic:/CoRN/complex/AbsCC/AbsCC_ap_zero.con".
  81
  82 inline "cic:/CoRN/complex/AbsCC/AbsCC_small_imp_eq.con".
  83
  84 (* begin hide *)
  85
  86 inline "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_1_1_2.con" "AbsCC_properties__".
  87
  88 (* end hide *)
  89
  90 (* UNEXPORTED
  91 Hint Resolve l_1_1_2: algebra.
  92 *)
  93
  94 inline "cic:/CoRN/complex/AbsCC/AbsCC_square_Re_Im.con".
  95
  96 (* UNEXPORTED
  97 Hint Resolve AbsCC_square_Re_Im: algebra.
  98 *)
  99
 100 (* begin hide *)
 101
 102 inline "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_1_2_3_CC.con" "AbsCC_properties__".
 103
 104 (* end hide *)
 105
 106 (* UNEXPORTED
 107 Hint Resolve l_1_2_3_CC: algebra.
 108 *)
 109
 110 inline "cic:/CoRN/complex/AbsCC/AbsCC_mult_conj.con".
 111
 112 (* UNEXPORTED
 113 Hint Resolve CC_conj_mult: algebra.
 114 *)
 115
 116 (* begin hide *)
 117
 118 inline "cic:/CoRN/complex/AbsCC/l_2_1_2.con".
 119
 120 (* UNEXPORTED
 121 Hint Resolve l_2_1_2: algebra.
 122 *)
 123
 124 (* end hide *)
 125
 126 inline "cic:/CoRN/complex/AbsCC/AbsCC_mult_square.con".
 127
 128 inline "cic:/CoRN/complex/AbsCC/AbsCC_square_ap_zero.con".
 129
 130 inline "cic:/CoRN/complex/AbsCC/cc_recip_char.con".
 131
 132 inline "cic:/CoRN/complex/AbsCC/AbsCC_strext.con".
 133
 134 inline "cic:/CoRN/complex/AbsCC/AbsSmallCC.con".
 135
 136 inline "cic:/CoRN/complex/AbsCC/Cexis_AFS_CC.con".
 137
 138 (* The following lemmas are just auxiliary results *)
 139
 140 (* begin hide *)
 141
 142 inline "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_4_1_2.con" "AbsCC_properties__".
 143
 144 inline "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_4_2_3.con" "AbsCC_properties__".
 145
 146 inline "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_4_3_4.con" "AbsCC_properties__".
 147
 148 (* end hide *)
 149
 150 (* UNEXPORTED
 151 End AbsCC_properties
 152 *)
 153
 154 (* UNEXPORTED
 155 Hint Resolve AbsCC_wd: algebra_c.
 156 *)
 157
 158 (* UNEXPORTED
 159 Hint Resolve cc_inv_abs cc_mult_abs cc_div_abs cc_div_abs' cc_pow_abs
 160   AbsCC_zero AbsCC_one AbsCC_IR AbsCC_mult_conj AbsCC_mult_square
 161   cc_recip_char: algebra.
 162 *)
 163
 164 (*#* ** The triangle inequality *)
 165
 166 inline "cic:/CoRN/complex/AbsCC/triangle.con".
 167
 168 inline "cic:/CoRN/complex/AbsCC/triangle_Sum.con".
 169