helm/software/matita/contribs/CoRN-Procedural/reals/CSumsReals.mma

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   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                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 (* This file was automatically generated: do not edit *********************)
  16
  17 include "CoRN.ma".
  18
  19 (* $Id: CSumsReals.v,v 1.5 2004/04/23 10:01:04 lcf Exp $ *)
  20
  21 include "reals/CReals1.ma".
  22
  23 (*#* * Sums over Reals
  24
  25 %\begin{convention}% Let [c] be a real.
  26 %\end{convention}%
  27
  28 Here we prove that
  29 $\Sigma_{m\leq i \leq n}~c^k = \frac{c^{n+1}-c^m}{c-1}.$
  30 #sum_(m&le; i &le; n) c^k = frac (c^(n+1) -c^m) (c-1)#
  31 *)
  32
  33 (* UNEXPORTED
  34 Section Sums_over_Reals
  35 *)
  36
  37 alias id "c" = "cic:/CoRN/reals/CSumsReals/Sums_over_Reals/c.var".
  38
  39 inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_c_exp.con".
  40
  41 (* UNEXPORTED
  42 Hint Resolve Sum0_c_exp.
  43 *)
  44
  45 inline procedural "cic:/CoRN/reals/CSumsReals/Sum_c_exp.con".
  46
  47 (* UNEXPORTED
  48 Hint Resolve Sum_c_exp.
  49 *)
  50
  51 (*#* The following formulation is often more useful if [c [<] 1]. *)
  52
  53 inline procedural "cic:/CoRN/reals/CSumsReals/Sum_c_exp'.con".
  54
  55 (* UNEXPORTED
  56 Hint Resolve Sum_c_exp'.
  57 *)
  58
  59 (* UNEXPORTED
  60 End Sums_over_Reals
  61 *)
  62
  63 (* UNEXPORTED
  64 Hint Resolve Sum0_c_exp Sum_c_exp Sum_c_exp': algebra.
  65 *)
  66
  67 inline procedural "cic:/CoRN/reals/CSumsReals/diff_is_Sum0.con".
  68
  69 inline procedural "cic:/CoRN/reals/CSumsReals/diff_is_sum.con".
  70
  71 inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_pres_less.con".
  72
  73 inline procedural "cic:/CoRN/reals/CSumsReals/Sum_pres_less.con".
  74
  75 inline procedural "cic:/CoRN/reals/CSumsReals/Sum_pres_leEq.con".
  76
  77 inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_comm_scal.con".
  78
  79 (* UNEXPORTED
  80 Hint Resolve Sum0_comm_scal: algebra.
  81 *)
  82
  83 inline procedural "cic:/CoRN/reals/CSumsReals/Sum_comm_scal.con".
  84
  85 inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_comm_scal'.con".
  86
  87 inline procedural "cic:/CoRN/reals/CSumsReals/Sum_comm_scal'.con".
  88
  89 inline procedural "cic:/CoRN/reals/CSumsReals/Sumx_comm_scal'.con".
  90
  91 inline procedural "cic:/CoRN/reals/CSumsReals/Sum2_comm_scal'.con".
  92