helm/software/matita/contribs/procedural/Coq/Reals/Alembert.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 "Coq.ma".
  18
  19 (*#***********************************************************************)
  20
  21 (*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
  22
  23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
  24
  25 (*   \VV/  **************************************************************)
  26
  27 (*    //   *      This file is distributed under the terms of the       *)
  28
  29 (*         *       GNU Lesser General Public License Version 2.1        *)
  30
  31 (*#***********************************************************************)
  32
  33 (*i $Id: Alembert.v,v 1.14.2.1 2004/07/16 19:31:10 herbelin Exp $ i*)
  34
  35 include "Reals/Rbase.ma".
  36
  37 include "Reals/Rfunctions.ma".
  38
  39 include "Reals/Rseries.ma".
  40
  41 include "Reals/SeqProp.ma".
  42
  43 include "Reals/PartSum.ma".
  44
  45 include "Arith/Max.ma".
  46
  47 (* UNEXPORTED
  48 Open Local Scope R_scope.
  49 *)
  50
  51 (*#**************************************************)
  52
  53 (* Various versions of the criterion of D'Alembert *)
  54
  55 (*#**************************************************)
  56
  57 inline procedural "cic:/Coq/Reals/Alembert/Alembert_C1.con" as lemma.
  58
  59 inline procedural "cic:/Coq/Reals/Alembert/Alembert_C2.con" as lemma.
  60
  61 inline procedural "cic:/Coq/Reals/Alembert/AlembertC3_step1.con" as lemma.
  62
  63 inline procedural "cic:/Coq/Reals/Alembert/AlembertC3_step2.con" as lemma.
  64
  65 (* An useful criterion of convergence for power series *)
  66
  67 inline procedural "cic:/Coq/Reals/Alembert/Alembert_C3.con" as theorem.
  68
  69 inline procedural "cic:/Coq/Reals/Alembert/Alembert_C4.con" as lemma.
  70
  71 inline procedural "cic:/Coq/Reals/Alembert/Alembert_C5.con" as lemma.
  72
  73 (* Convergence of power series in D(O,1/k) *)
  74
  75 (*     k=0 is described in Alembert_C3     *)
  76
  77 inline procedural "cic:/Coq/Reals/Alembert/Alembert_C6.con" as lemma.
  78