helm/software/matita/contribs/procedural/Coq/Reals/NewtonInt.mma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
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  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: NewtonInt.v,v 1.11.2.1 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/SeqSeries.ma".
  40
  41 include "Reals/Rtrigo.ma".
  42
  43 include "Reals/Ranalysis.ma".
  44
  45 (* UNEXPORTED
  46 Open Local Scope R_scope.
  47 *)
  48
  49 (*#******************************************)
  50
  51 (*            Newton's Integral            *)
  52
  53 (*#******************************************)
  54
  55 inline procedural "cic:/Coq/Reals/NewtonInt/Newton_integrable.con" as definition.
  56
  57 inline procedural "cic:/Coq/Reals/NewtonInt/NewtonInt.con" as definition.
  58
  59 (* If f is differentiable, then f' is Newton integrable (Tautology ?) *)
  60
  61 inline procedural "cic:/Coq/Reals/NewtonInt/FTCN_step1.con" as lemma.
  62
  63 (* By definition, we have the Fondamental Theorem of Calculus *)
  64
  65 inline procedural "cic:/Coq/Reals/NewtonInt/FTC_Newton.con" as lemma.
  66
  67 (* $\int_a^a f$ exists forall a:R and f:R->R *)
  68
  69 inline procedural "cic:/Coq/Reals/NewtonInt/NewtonInt_P1.con" as lemma.
  70
  71 (* $\int_a^a f = 0$ *)
  72
  73 inline procedural "cic:/Coq/Reals/NewtonInt/NewtonInt_P2.con" as lemma.
  74
  75 (* If $\int_a^b f$ exists, then $\int_b^a f$ exists too *)
  76
  77 inline procedural "cic:/Coq/Reals/NewtonInt/NewtonInt_P3.con" as lemma.
  78
  79 (* $\int_a^b f = -\int_b^a f$ *)
  80
  81 inline procedural "cic:/Coq/Reals/NewtonInt/NewtonInt_P4.con" as lemma.
  82
  83 (* The set of Newton integrable functions is a vectorial space *)
  84
  85 inline procedural "cic:/Coq/Reals/NewtonInt/NewtonInt_P5.con" as lemma.
  86
  87 (*#*********)
  88
  89 inline procedural "cic:/Coq/Reals/NewtonInt/antiderivative_P1.con" as lemma.
  90
  91 (* $\int_a^b \lambda f + g = \lambda \int_a^b f + \int_a^b f *)
  92
  93 inline procedural "cic:/Coq/Reals/NewtonInt/NewtonInt_P6.con" as lemma.
  94
  95 inline procedural "cic:/Coq/Reals/NewtonInt/antiderivative_P2.con" as lemma.
  96
  97 inline procedural "cic:/Coq/Reals/NewtonInt/antiderivative_P3.con" as lemma.
  98
  99 inline procedural "cic:/Coq/Reals/NewtonInt/antiderivative_P4.con" as lemma.
 100
 101 inline procedural "cic:/Coq/Reals/NewtonInt/NewtonInt_P7.con" as lemma.
 102
 103 inline procedural "cic:/Coq/Reals/NewtonInt/NewtonInt_P8.con" as lemma.
 104
 105 (* Chasles' relation *)
 106
 107 inline procedural "cic:/Coq/Reals/NewtonInt/NewtonInt_P9.con" as lemma.
 108