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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 *)
11 (* v GNU General Public License Version 2 *)
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15 (* This file was automatically generated: do not edit *********************)
19 (*#***********************************************************************)
21 (* v * The Coq Proof Assistant / The Coq Development Team *)
23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
25 (* \VV/ **************************************************************)
27 (* // * This file is distributed under the terms of the *)
29 (* * GNU Lesser General Public License Version 2.1 *)
31 (*#***********************************************************************)
33 (*i $Id: Alembert.v,v 1.14.2.1 2004/07/16 19:31:10 herbelin Exp $ i*)
35 include "Reals/Rbase.ma".
37 include "Reals/Rfunctions.ma".
39 include "Reals/Rseries.ma".
41 include "Reals/SeqProp.ma".
43 include "Reals/PartSum.ma".
45 include "Arith/Max.ma".
48 Open Local Scope R_scope.
51 (*#**************************************************)
53 (* Various versions of the criterion of D'Alembert *)
55 (*#**************************************************)
57 inline procedural "cic:/Coq/Reals/Alembert/Alembert_C1.con" as lemma.
59 inline procedural "cic:/Coq/Reals/Alembert/Alembert_C2.con" as lemma.
61 inline procedural "cic:/Coq/Reals/Alembert/AlembertC3_step1.con" as lemma.
63 inline procedural "cic:/Coq/Reals/Alembert/AlembertC3_step2.con" as lemma.
65 (* An useful criterion of convergence for power series *)
67 inline procedural "cic:/Coq/Reals/Alembert/Alembert_C3.con" as theorem.
69 inline procedural "cic:/Coq/Reals/Alembert/Alembert_C4.con" as lemma.
71 inline procedural "cic:/Coq/Reals/Alembert/Alembert_C5.con" as lemma.
73 (* Convergence of power series in D(O,1/k) *)
75 (* k=0 is described in Alembert_C3 *)
77 inline procedural "cic:/Coq/Reals/Alembert/Alembert_C6.con" as lemma.