helm/software/matita/contribs/procedural/CoRN/ftc/Taylor.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 "CoRN.ma".
  18
  19 (* $Id: Taylor.v,v 1.10 2004/04/23 10:01:01 lcf Exp $ *)
  20
  21 include "ftc/TaylorLemma.ma".
  22
  23 (* UNEXPORTED
  24 Opaque Min Max N_Deriv.
  25 *)
  26
  27 (* UNEXPORTED
  28 Section More_Taylor_Defs
  29 *)
  30
  31 (*#* **General case
  32
  33 The generalization to arbitrary intervals just needs a few more definitions.
  34
  35 %\begin{convention}% Let [I] be a proper interval, [F:PartIR] and
  36 [a,b:IR] be points of [I].
  37 %\end{convention}%
  38 *)
  39
  40 (* UNEXPORTED
  41 cic:/CoRN/ftc/Taylor/More_Taylor_Defs/I.var
  42 *)
  43
  44 (* UNEXPORTED
  45 cic:/CoRN/ftc/Taylor/More_Taylor_Defs/pI.var
  46 *)
  47
  48 (* UNEXPORTED
  49 cic:/CoRN/ftc/Taylor/More_Taylor_Defs/F.var
  50 *)
  51
  52 (* begin show *)
  53
  54 inline procedural "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/deriv_Sn.con" "More_Taylor_Defs__" as definition.
  55
  56 (* end show *)
  57
  58 (* UNEXPORTED
  59 cic:/CoRN/ftc/Taylor/More_Taylor_Defs/a.var
  60 *)
  61
  62 (* UNEXPORTED
  63 cic:/CoRN/ftc/Taylor/More_Taylor_Defs/b.var
  64 *)
  65
  66 (* UNEXPORTED
  67 cic:/CoRN/ftc/Taylor/More_Taylor_Defs/Ha.var
  68 *)
  69
  70 (* UNEXPORTED
  71 cic:/CoRN/ftc/Taylor/More_Taylor_Defs/Hb.var
  72 *)
  73
  74 (* begin show *)
  75
  76 inline procedural "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/fi.con" "More_Taylor_Defs__" as definition.
  77
  78 inline procedural "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/funct_i.con" "More_Taylor_Defs__" as definition.
  79
  80 (* end show *)
  81
  82 inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Seq'.con" as definition.
  83
  84 (* begin hide *)
  85
  86 inline procedural "cic:/CoRN/ftc/Taylor/TaylorB.con" as lemma.
  87
  88 (* end hide *)
  89
  90 inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Rem.con" as definition.
  91
  92 (* begin hide *)
  93
  94 inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Sumx_lemma.con" as lemma.
  95
  96 inline procedural "cic:/CoRN/ftc/Taylor/Taylor_lemma_ap.con" as lemma.
  97
  98 (* end hide *)
  99
 100 inline procedural "cic:/CoRN/ftc/Taylor/Taylor'.con" as theorem.
 101
 102 (* UNEXPORTED
 103 End More_Taylor_Defs
 104 *)
 105
 106 (* UNEXPORTED
 107 Section Taylor_Theorem
 108 *)
 109
 110 (*#*
 111 And finally the ``nice'' version, when we know the expression of the
 112 derivatives of [F].
 113
 114 %\begin{convention}% Let [f] be the sequence of derivatives of [F] of
 115 order up to [n] and [F'] be the nth-derivative of [F].
 116 %\end{convention}%
 117 *)
 118
 119 (* UNEXPORTED
 120 cic:/CoRN/ftc/Taylor/Taylor_Theorem/I.var
 121 *)
 122
 123 (* UNEXPORTED
 124 cic:/CoRN/ftc/Taylor/Taylor_Theorem/pI.var
 125 *)
 126
 127 (* UNEXPORTED
 128 cic:/CoRN/ftc/Taylor/Taylor_Theorem/F.var
 129 *)
 130
 131 (* UNEXPORTED
 132 cic:/CoRN/ftc/Taylor/Taylor_Theorem/n.var
 133 *)
 134
 135 (* UNEXPORTED
 136 cic:/CoRN/ftc/Taylor/Taylor_Theorem/f.var
 137 *)
 138
 139 (* UNEXPORTED
 140 cic:/CoRN/ftc/Taylor/Taylor_Theorem/goodF.var
 141 *)
 142
 143 (* UNEXPORTED
 144 cic:/CoRN/ftc/Taylor/Taylor_Theorem/goodF'.var
 145 *)
 146
 147 (* UNEXPORTED
 148 cic:/CoRN/ftc/Taylor/Taylor_Theorem/derF.var
 149 *)
 150
 151 (* UNEXPORTED
 152 cic:/CoRN/ftc/Taylor/Taylor_Theorem/F'.var
 153 *)
 154
 155 (* UNEXPORTED
 156 cic:/CoRN/ftc/Taylor/Taylor_Theorem/derF'.var
 157 *)
 158
 159 (* UNEXPORTED
 160 cic:/CoRN/ftc/Taylor/Taylor_Theorem/a.var
 161 *)
 162
 163 (* UNEXPORTED
 164 cic:/CoRN/ftc/Taylor/Taylor_Theorem/b.var
 165 *)
 166
 167 (* UNEXPORTED
 168 cic:/CoRN/ftc/Taylor/Taylor_Theorem/Ha.var
 169 *)
 170
 171 (* UNEXPORTED
 172 cic:/CoRN/ftc/Taylor/Taylor_Theorem/Hb.var
 173 *)
 174
 175 (* begin show *)
 176
 177 inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Theorem/funct_i.con" "Taylor_Theorem__" as definition.
 178
 179 inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Seq.con" as definition.
 180
 181 inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Theorem/deriv_Sn.con" "Taylor_Theorem__" as definition.
 182
 183 (* end show *)
 184
 185 inline procedural "cic:/CoRN/ftc/Taylor/Taylor_aux.con" as lemma.
 186
 187 (* UNEXPORTED
 188 Transparent N_Deriv.
 189 *)
 190
 191 inline procedural "cic:/CoRN/ftc/Taylor/Taylor.con" as theorem.
 192
 193 (* UNEXPORTED
 194 End Taylor_Theorem
 195 *)
 196