helm/software/matita/contribs/CoRN-Procedural/ftc/StrongIVT.mma

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   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 (* $Id: StrongIVT.v,v 1.5 2004/04/23 10:01:01 lcf Exp $ *)
  20
  21 include "ftc/WeakIVT.ma".
  22
  23 include "ftc/CalculusTheorems.ma".
  24
  25 (* UNEXPORTED
  26 Section IVT'
  27 *)
  28
  29 (*#* ** Strong IVT for partial functions
  30
  31 The IVT can be generalized to arbitrary partial functions; in the first
  32 part, we will simply do that, repeating the previous construction.
  33
  34 The same notations and conventions apply as before.
  35 *)
  36
  37 alias id "a" = "cic:/CoRN/ftc/StrongIVT/IVT'/a.var".
  38
  39 alias id "b" = "cic:/CoRN/ftc/StrongIVT/IVT'/b.var".
  40
  41 alias id "Hab'" = "cic:/CoRN/ftc/StrongIVT/IVT'/Hab'.var".
  42
  43 alias id "Hab" = "cic:/CoRN/ftc/StrongIVT/IVT'/Hab.var".
  44
  45 (* begin hide *)
  46
  47 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/I.con" "IVT'__".
  48
  49 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/I'.con" "IVT'__".
  50
  51 (* end hide *)
  52
  53 alias id "F" = "cic:/CoRN/ftc/StrongIVT/IVT'/F.var".
  54
  55 alias id "contF" = "cic:/CoRN/ftc/StrongIVT/IVT'/contF.var".
  56
  57 (* begin hide *)
  58
  59 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/incF.con" "IVT'__".
  60
  61 (* end hide *)
  62
  63 (* begin show *)
  64
  65 alias id "incrF" = "cic:/CoRN/ftc/StrongIVT/IVT'/incrF.var".
  66
  67 (* end show *)
  68
  69 (* begin hide *)
  70
  71 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/Ha.con" "IVT'__".
  72
  73 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/Hb.con" "IVT'__".
  74
  75 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/HFab'.con" "IVT'__".
  76
  77 (* end hide *)
  78
  79 (* begin show *)
  80
  81 alias id "z" = "cic:/CoRN/ftc/StrongIVT/IVT'/z.var".
  82
  83 alias id "Haz" = "cic:/CoRN/ftc/StrongIVT/IVT'/Haz.var".
  84
  85 alias id "Hzb" = "cic:/CoRN/ftc/StrongIVT/IVT'/Hzb.var".
  86
  87 (* end show *)
  88
  89 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_seq_lemma.con".
  90
  91 (* end hide *)
  92
  93 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_aux_seq_type.ind".
  94
  95 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_iter.con".
  96
  97 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_seq.con".
  98
  99 inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq.con".
 100
 101 inline procedural "cic:/CoRN/ftc/StrongIVT/b'_seq.con".
 102
 103 inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_I.con".
 104
 105 inline procedural "cic:/CoRN/ftc/StrongIVT/b'_seq_I.con".
 106
 107 inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_less_b'_seq.con".
 108
 109 inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_less_z.con".
 110
 111 inline procedural "cic:/CoRN/ftc/StrongIVT/z_less_b'_seq.con".
 112
 113 inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_mon.con".
 114
 115 inline procedural "cic:/CoRN/ftc/StrongIVT/b'_seq_mon.con".
 116
 117 inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_dist_n.con".
 118
 119 inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_dist.con".
 120
 121 inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_Cauchy.con".
 122
 123 inline procedural "cic:/CoRN/ftc/StrongIVT/b'_seq_Cauchy.con".
 124
 125 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/xa.con" "IVT'__".
 126
 127 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/xb.con" "IVT'__".
 128
 129 inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_lim.con".
 130
 131 inline procedural "cic:/CoRN/ftc/StrongIVT/xa'_in_interval.con".
 132
 133 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_I.con".
 134
 135 (* UNEXPORTED
 136 End IVT'
 137 *)
 138
 139 (*#* **Other formulations
 140
 141 We now generalize the various statements of the intermediate value
 142 theorem to more widely applicable forms.
 143 *)
 144
 145 inline procedural "cic:/CoRN/ftc/StrongIVT/Weak_IVT.con".
 146
 147 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT_inc.con".
 148
 149 (* UNEXPORTED
 150 Transparent Min.
 151 *)
 152
 153 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT_dec.con".
 154
 155 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_inc.con".
 156
 157 (* UNEXPORTED
 158 Transparent Min.
 159 *)
 160
 161 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_dec.con".
 162