1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
17 set "baseuri" "cic:/matita/CoRN-Decl/ftc/Taylor".
21 (* $Id: Taylor.v,v 1.10 2004/04/23 10:01:01 lcf Exp $ *)
23 include "ftc/TaylorLemma.ma".
26 Opaque Min Max N_Deriv.
30 Section More_Taylor_Defs.
35 The generalization to arbitrary intervals just needs a few more definitions.
37 %\begin{convention}% Let [I] be a proper interval, [F:PartIR] and
38 [a,b:IR] be points of [I].
42 inline "cic:/CoRN/ftc/Taylor/I.var".
44 inline "cic:/CoRN/ftc/Taylor/pI.var".
46 inline "cic:/CoRN/ftc/Taylor/F.var".
50 inline "cic:/CoRN/ftc/Taylor/deriv_Sn.con".
54 inline "cic:/CoRN/ftc/Taylor/a.var".
56 inline "cic:/CoRN/ftc/Taylor/b.var".
58 inline "cic:/CoRN/ftc/Taylor/Ha.var".
60 inline "cic:/CoRN/ftc/Taylor/Hb.var".
64 inline "cic:/CoRN/ftc/Taylor/fi.con".
66 inline "cic:/CoRN/ftc/Taylor/funct_i.con".
70 inline "cic:/CoRN/ftc/Taylor/Taylor_Seq'.con".
74 inline "cic:/CoRN/ftc/Taylor/TaylorB.con".
78 inline "cic:/CoRN/ftc/Taylor/Taylor_Rem.con".
82 inline "cic:/CoRN/ftc/Taylor/Taylor_Sumx_lemma.con".
84 inline "cic:/CoRN/ftc/Taylor/Taylor_lemma_ap.con".
88 inline "cic:/CoRN/ftc/Taylor/Taylor'.con".
95 Section Taylor_Theorem.
99 And finally the ``nice'' version, when we know the expression of the
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].
107 inline "cic:/CoRN/ftc/Taylor/I.var".
109 inline "cic:/CoRN/ftc/Taylor/pI.var".
111 inline "cic:/CoRN/ftc/Taylor/F.var".
113 inline "cic:/CoRN/ftc/Taylor/n.var".
115 inline "cic:/CoRN/ftc/Taylor/f.var".
117 inline "cic:/CoRN/ftc/Taylor/goodF.var".
119 inline "cic:/CoRN/ftc/Taylor/goodF'.var".
121 inline "cic:/CoRN/ftc/Taylor/derF.var".
123 inline "cic:/CoRN/ftc/Taylor/F'.var".
125 inline "cic:/CoRN/ftc/Taylor/derF'.var".
127 inline "cic:/CoRN/ftc/Taylor/a.var".
129 inline "cic:/CoRN/ftc/Taylor/b.var".
131 inline "cic:/CoRN/ftc/Taylor/Ha.var".
133 inline "cic:/CoRN/ftc/Taylor/Hb.var".
137 inline "cic:/CoRN/ftc/Taylor/funct_i.con".
139 inline "cic:/CoRN/ftc/Taylor/Taylor_Seq.con".
141 inline "cic:/CoRN/ftc/Taylor/deriv_Sn.con".
145 inline "cic:/CoRN/ftc/Taylor/Taylor_aux.con".
151 inline "cic:/CoRN/ftc/Taylor/Taylor.con".