helm/software/matita/contribs/CoRN-Decl/ftc/Taylor.ma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  14
  15 (* This file was automatically generated: do not edit *********************)
  16
  17 set "baseuri" "cic:/matita/CoRN-Decl/ftc/Taylor".
  18
  19 include "CoRN.ma".
  20
  21 (* $Id: Taylor.v,v 1.10 2004/04/23 10:01:01 lcf Exp $ *)
  22
  23 include "ftc/TaylorLemma.ma".
  24
  25 (* UNEXPORTED
  26 Opaque Min Max N_Deriv.
  27 *)
  28
  29 (* UNEXPORTED
  30 Section More_Taylor_Defs
  31 *)
  32
  33 (*#* **General case
  34
  35 The generalization to arbitrary intervals just needs a few more definitions.
  36
  37 %\begin{convention}% Let [I] be a proper interval, [F:PartIR] and
  38 [a,b:IR] be points of [I].
  39 %\end{convention}%
  40 *)
  41
  42 inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/I.var" "More_Taylor_Defs__".
  43
  44 inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/pI.var" "More_Taylor_Defs__".
  45
  46 inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/F.var" "More_Taylor_Defs__".
  47
  48 (* begin show *)
  49
  50 inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/deriv_Sn.con" "More_Taylor_Defs__".
  51
  52 (* end show *)
  53
  54 inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/a.var" "More_Taylor_Defs__".
  55
  56 inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/b.var" "More_Taylor_Defs__".
  57
  58 inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/Ha.var" "More_Taylor_Defs__".
  59
  60 inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/Hb.var" "More_Taylor_Defs__".
  61
  62 (* begin show *)
  63
  64 inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/fi.con" "More_Taylor_Defs__".
  65
  66 inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/funct_i.con" "More_Taylor_Defs__".
  67
  68 (* end show *)
  69
  70 inline "cic:/CoRN/ftc/Taylor/Taylor_Seq'.con".
  71
  72 (* begin hide *)
  73
  74 inline "cic:/CoRN/ftc/Taylor/TaylorB.con".
  75
  76 (* end hide *)
  77
  78 inline "cic:/CoRN/ftc/Taylor/Taylor_Rem.con".
  79
  80 (* begin hide *)
  81
  82 inline "cic:/CoRN/ftc/Taylor/Taylor_Sumx_lemma.con".
  83
  84 inline "cic:/CoRN/ftc/Taylor/Taylor_lemma_ap.con".
  85
  86 (* end hide *)
  87
  88 inline "cic:/CoRN/ftc/Taylor/Taylor'.con".
  89
  90 (* UNEXPORTED
  91 End More_Taylor_Defs
  92 *)
  93
  94 (* UNEXPORTED
  95 Section Taylor_Theorem
  96 *)
  97
  98 (*#*
  99 And finally the ``nice'' version, when we know the expression of the
 100 derivatives of [F].
 101
 102 %\begin{convention}% Let [f] be the sequence of derivatives of [F] of
 103 order up to [n] and [F'] be the nth-derivative of [F].
 104 %\end{convention}%
 105 *)
 106
 107 inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/I.var" "Taylor_Theorem__".
 108
 109 inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/pI.var" "Taylor_Theorem__".
 110
 111 inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/F.var" "Taylor_Theorem__".
 112
 113 inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/n.var" "Taylor_Theorem__".
 114
 115 inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/f.var" "Taylor_Theorem__".
 116
 117 inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/goodF.var" "Taylor_Theorem__".
 118
 119 inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/goodF'.var" "Taylor_Theorem__".
 120
 121 inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/derF.var" "Taylor_Theorem__".
 122
 123 inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/F'.var" "Taylor_Theorem__".
 124
 125 inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/derF'.var" "Taylor_Theorem__".
 126
 127 inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/a.var" "Taylor_Theorem__".
 128
 129 inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/b.var" "Taylor_Theorem__".
 130
 131 inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/Ha.var" "Taylor_Theorem__".
 132
 133 inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/Hb.var" "Taylor_Theorem__".
 134
 135 (* begin show *)
 136
 137 inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/funct_i.con" "Taylor_Theorem__".
 138
 139 inline "cic:/CoRN/ftc/Taylor/Taylor_Seq.con".
 140
 141 inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/deriv_Sn.con" "Taylor_Theorem__".
 142
 143 (* end show *)
 144
 145 inline "cic:/CoRN/ftc/Taylor/Taylor_aux.con".
 146
 147 (* UNEXPORTED
 148 Transparent N_Deriv.
 149 *)
 150
 151 inline "cic:/CoRN/ftc/Taylor/Taylor.con".
 152
 153 (* UNEXPORTED
 154 End Taylor_Theorem
 155 *)
 156