helm/software/matita/contribs/procedural/CoRN/ftc/StrongIVT.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 "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 (* UNEXPORTED
  38 cic:/CoRN/ftc/StrongIVT/IVT'/a.var
  39 *)
  40
  41 (* UNEXPORTED
  42 cic:/CoRN/ftc/StrongIVT/IVT'/b.var
  43 *)
  44
  45 (* UNEXPORTED
  46 cic:/CoRN/ftc/StrongIVT/IVT'/Hab'.var
  47 *)
  48
  49 (* UNEXPORTED
  50 cic:/CoRN/ftc/StrongIVT/IVT'/Hab.var
  51 *)
  52
  53 (* begin hide *)
  54
  55 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/I.con" "IVT'__" as definition.
  56
  57 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/I'.con" "IVT'__" as definition.
  58
  59 (* end hide *)
  60
  61 (* UNEXPORTED
  62 cic:/CoRN/ftc/StrongIVT/IVT'/F.var
  63 *)
  64
  65 (* UNEXPORTED
  66 cic:/CoRN/ftc/StrongIVT/IVT'/contF.var
  67 *)
  68
  69 (* begin hide *)
  70
  71 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/incF.con" "IVT'__" as definition.
  72
  73 (* end hide *)
  74
  75 (* begin show *)
  76
  77 (* UNEXPORTED
  78 cic:/CoRN/ftc/StrongIVT/IVT'/incrF.var
  79 *)
  80
  81 (* end show *)
  82
  83 (* begin hide *)
  84
  85 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/Ha.con" "IVT'__" as definition.
  86
  87 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/Hb.con" "IVT'__" as definition.
  88
  89 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/HFab'.con" "IVT'__" as definition.
  90
  91 (* end hide *)
  92
  93 (* begin show *)
  94
  95 (* UNEXPORTED
  96 cic:/CoRN/ftc/StrongIVT/IVT'/z.var
  97 *)
  98
  99 (* UNEXPORTED
 100 cic:/CoRN/ftc/StrongIVT/IVT'/Haz.var
 101 *)
 102
 103 (* UNEXPORTED
 104 cic:/CoRN/ftc/StrongIVT/IVT'/Hzb.var
 105 *)
 106
 107 (* end show *)
 108
 109 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_seq_lemma.con" as lemma.
 110
 111 (* end hide *)
 112
 113 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_aux_seq_type.ind".
 114
 115 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_iter.con" as definition.
 116
 117 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_seq.con" as definition.
 118
 119 inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq.con" as definition.
 120
 121 inline procedural "cic:/CoRN/ftc/StrongIVT/b'_seq.con" as definition.
 122
 123 inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_I.con" as definition.
 124
 125 inline procedural "cic:/CoRN/ftc/StrongIVT/b'_seq_I.con" as definition.
 126
 127 inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_less_b'_seq.con" as lemma.
 128
 129 inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_less_z.con" as lemma.
 130
 131 inline procedural "cic:/CoRN/ftc/StrongIVT/z_less_b'_seq.con" as lemma.
 132
 133 inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_mon.con" as lemma.
 134
 135 inline procedural "cic:/CoRN/ftc/StrongIVT/b'_seq_mon.con" as lemma.
 136
 137 inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_dist_n.con" as lemma.
 138
 139 inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_dist.con" as lemma.
 140
 141 inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_Cauchy.con" as lemma.
 142
 143 inline procedural "cic:/CoRN/ftc/StrongIVT/b'_seq_Cauchy.con" as lemma.
 144
 145 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/xa.con" "IVT'__" as definition.
 146
 147 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/xb.con" "IVT'__" as definition.
 148
 149 inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_lim.con" as lemma.
 150
 151 inline procedural "cic:/CoRN/ftc/StrongIVT/xa'_in_interval.con" as lemma.
 152
 153 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_I.con" as lemma.
 154
 155 (* UNEXPORTED
 156 End IVT'
 157 *)
 158
 159 (*#* **Other formulations
 160
 161 We now generalize the various statements of the intermediate value
 162 theorem to more widely applicable forms.
 163 *)
 164
 165 inline procedural "cic:/CoRN/ftc/StrongIVT/Weak_IVT.con" as lemma.
 166
 167 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT_inc.con" as lemma.
 168
 169 (* UNEXPORTED
 170 Transparent Min.
 171 *)
 172
 173 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT_dec.con" as lemma.
 174
 175 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_inc.con" as lemma.
 176
 177 (* UNEXPORTED
 178 Transparent Min.
 179 *)
 180
 181 inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_dec.con" as lemma.
 182