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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 *)
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15 (* This file was automatically generated: do not edit *********************)
17 set "baseuri" "cic:/matita/CoRN-Decl/ftc/Taylor".
19 (* $Id: Taylor.v,v 1.10 2004/04/23 10:01:01 lcf Exp $ *)
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.