helm/software/matita/contribs/CoRN-Procedural/algebra/COrdAbs.mma

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   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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  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 "CoRN.ma".
  18
  19 include "algebra/COrdFields2.ma".
  20
  21 (*#*
  22 ** Properties of [AbsSmall]
  23 *)
  24
  25 (* Begin_SpecReals *)
  26
  27 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall.con".
  28
  29 (* UNEXPORTED
  30 Implicit Arguments AbsSmall [R].
  31 *)
  32
  33 (* End_SpecReals *)
  34
  35 (* UNEXPORTED
  36 Section AbsSmall_properties
  37 *)
  38
  39 (*#*
  40 %\begin{convention}% Let [R] be an ordered field.
  41 %\end{convention}%
  42 *)
  43
  44 alias id "R" = "cic:/CoRN/algebra/COrdAbs/AbsSmall_properties/R.var".
  45
  46 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdr.con".
  47
  48 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdr_unfolded.con".
  49
  50 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdl.con".
  51
  52 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdl_unfolded.con".
  53
  54 (* UNEXPORTED
  55 Declare Left Step AbsSmall_wdl_unfolded.
  56 *)
  57
  58 (* UNEXPORTED
  59 Declare Right Step AbsSmall_wdr_unfolded.
  60 *)
  61
  62 (* begin hide *)
  63
  64 (* NOTATION
  65 Notation ZeroR := (Zero:R).
  66 *)
  67
  68 (* end hide *)
  69
  70 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_leEq_trans.con".
  71
  72 inline procedural "cic:/CoRN/algebra/COrdAbs/zero_AbsSmall.con".
  73
  74 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_trans.con".
  75
  76 inline procedural "cic:/CoRN/algebra/COrdAbs/leEq_imp_AbsSmall.con".
  77
  78 inline procedural "cic:/CoRN/algebra/COrdAbs/inv_resp_AbsSmall.con".
  79
  80 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_minus.con".
  81
  82 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_plus.con".
  83
  84 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_eps_div_two.con".
  85
  86 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_x_plus_delta.con".
  87
  88 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_x_minus_delta.con".
  89
  90 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_x_plus_eps_div2.con".
  91
  92 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_x_minus_eps_div2.con".
  93
  94 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_intermediate.con".
  95
  96 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_eps_div2.con".
  97
  98 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_nonneg.con".
  99
 100 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_mult.con".
 101
 102 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_cancel_mult.con".
 103
 104 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_approach_zero.con".
 105
 106 (* UNEXPORTED
 107 End AbsSmall_properties
 108 *)
 109
 110 (* UNEXPORTED
 111 Declare Left Step AbsSmall_wdl_unfolded.
 112 *)
 113
 114 (* UNEXPORTED
 115 Declare Right Step AbsSmall_wdr_unfolded.
 116 *)
 117
 118 (*#* ** Properties of [AbsBig] *)
 119
 120 inline procedural "cic:/CoRN/algebra/COrdAbs/absBig.con".
 121
 122 (* NOTATION
 123 Notation AbsBig := (absBig _).
 124 *)
 125
 126 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBigSmall_minus.con".
 127
 128 (* UNEXPORTED
 129 Section absBig_wd_properties
 130 *)
 131
 132 (*#*
 133 %\begin{convention}% Let [R] be an ordered field.
 134 %\end{convention}%
 135 *)
 136
 137 alias id "R" = "cic:/CoRN/algebra/COrdAbs/absBig_wd_properties/R.var".
 138
 139 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBig_wdr.con".
 140
 141 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBig_wdl.con".
 142
 143 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBig_wdr_unfolded.con".
 144
 145 inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBig_wdl_unfolded.con".
 146
 147 (* UNEXPORTED
 148 End absBig_wd_properties
 149 *)
 150
 151 (* UNEXPORTED
 152 Declare Left Step AbsBig_wdl_unfolded.
 153 *)
 154
 155 (* UNEXPORTED
 156 Declare Right Step AbsBig_wdr_unfolded.
 157 *)
 158