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

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  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: Rprod.v,v 1.10.2.1 2004/07/16 19:31:13 herbelin Exp $ i*)
  34
  35 include "Arith/Compare.ma".
  36
  37 include "Reals/Rbase.ma".
  38
  39 include "Reals/Rfunctions.ma".
  40
  41 include "Reals/Rseries.ma".
  42
  43 include "Reals/PartSum.ma".
  44
  45 include "Reals/Binomial.ma".
  46
  47 (* UNEXPORTED
  48 Open Local Scope R_scope.
  49 *)
  50
  51 (* TT Ak; 1<=k<=N *)
  52
  53 inline procedural "cic:/Coq/Reals/Rprod/prod_f_SO.con" as definition.
  54
  55 (*#*********)
  56
  57 inline procedural "cic:/Coq/Reals/Rprod/prod_SO_split.con" as lemma.
  58
  59 (*#*********)
  60
  61 inline procedural "cic:/Coq/Reals/Rprod/prod_SO_pos.con" as lemma.
  62
  63 (*#*********)
  64
  65 inline procedural "cic:/Coq/Reals/Rprod/prod_SO_Rle.con" as lemma.
  66
  67 (* Application to factorial *)
  68
  69 inline procedural "cic:/Coq/Reals/Rprod/fact_prodSO.con" as lemma.
  70
  71 inline procedural "cic:/Coq/Reals/Rprod/le_n_2n.con" as lemma.
  72
  73 (* We prove that (N!)\178\<=(2N-k)!*k! forall k in [|O;2N|] *)
  74
  75 inline procedural "cic:/Coq/Reals/Rprod/RfactN_fact2N_factk.con" as lemma.
  76
  77 (*#*********)
  78
  79 inline procedural "cic:/Coq/Reals/Rprod/INR_fact_lt_0.con" as lemma.
  80
  81 (* We have the following inequality : (C 2N k) <= (C 2N N) forall k in [|O;2N|] *)
  82
  83 inline procedural "cic:/Coq/Reals/Rprod/C_maj.con" as lemma.
  84