helm/software/matita/contribs/procedural/CoRN/reals/CSumsReals.mma

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  11 (*        v         GNU General Public License Version 2                  *)
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  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 (* UNEXPORTED
  38 cic:/CoRN/reals/CSumsReals/Sums_over_Reals/c.var
  39 *)
  40
  41 inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_c_exp.con" as lemma.
  42
  43 (* UNEXPORTED
  44 Hint Resolve Sum0_c_exp.
  45 *)
  46
  47 inline procedural "cic:/CoRN/reals/CSumsReals/Sum_c_exp.con" as lemma.
  48
  49 (* UNEXPORTED
  50 Hint Resolve Sum_c_exp.
  51 *)
  52
  53 (*#* The following formulation is often more useful if [c [<] 1]. *)
  54
  55 inline procedural "cic:/CoRN/reals/CSumsReals/Sum_c_exp'.con" as lemma.
  56
  57 (* UNEXPORTED
  58 Hint Resolve Sum_c_exp'.
  59 *)
  60
  61 (* UNEXPORTED
  62 End Sums_over_Reals
  63 *)
  64
  65 (* UNEXPORTED
  66 Hint Resolve Sum0_c_exp Sum_c_exp Sum_c_exp': algebra.
  67 *)
  68
  69 inline procedural "cic:/CoRN/reals/CSumsReals/diff_is_Sum0.con" as lemma.
  70
  71 inline procedural "cic:/CoRN/reals/CSumsReals/diff_is_sum.con" as lemma.
  72
  73 inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_pres_less.con" as lemma.
  74
  75 inline procedural "cic:/CoRN/reals/CSumsReals/Sum_pres_less.con" as lemma.
  76
  77 inline procedural "cic:/CoRN/reals/CSumsReals/Sum_pres_leEq.con" as lemma.
  78
  79 inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_comm_scal.con" as lemma.
  80
  81 (* UNEXPORTED
  82 Hint Resolve Sum0_comm_scal: algebra.
  83 *)
  84
  85 inline procedural "cic:/CoRN/reals/CSumsReals/Sum_comm_scal.con" as lemma.
  86
  87 inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_comm_scal'.con" as lemma.
  88
  89 inline procedural "cic:/CoRN/reals/CSumsReals/Sum_comm_scal'.con" as lemma.
  90
  91 inline procedural "cic:/CoRN/reals/CSumsReals/Sumx_comm_scal'.con" as lemma.
  92
  93 inline procedural "cic:/CoRN/reals/CSumsReals/Sum2_comm_scal'.con" as lemma.
  94