matita/contribs/CoRN-Decl/reals/CSumsReals.ma

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  14
  15 (* This file was automatically generated: do not edit *********************)
  16
  17 set "baseuri" "cic:/matita/CoRN-Decl/reals/CSumsReals".
  18
  19 include "CoRN.ma".
  20
  21 (* $Id: CSumsReals.v,v 1.5 2004/04/23 10:01:04 lcf Exp $ *)
  22
  23 include "reals/CReals1.ma".
  24
  25 (*#* * Sums over Reals
  26
  27 %\begin{convention}% Let [c] be a real.
  28 %\end{convention}%
  29
  30 Here we prove that
  31 $\Sigma_{m\leq i \leq n}~c^k = \frac{c^{n+1}-c^m}{c-1}.$
  32 #sum_(m&le; i &le; n) c^k = frac (c^(n+1) -c^m) (c-1)#
  33 *)
  34
  35 (* UNEXPORTED
  36 Section Sums_over_Reals
  37 *)
  38
  39 alias id "c" = "cic:/CoRN/reals/CSumsReals/Sums_over_Reals/c.var".
  40
  41 inline "cic:/CoRN/reals/CSumsReals/Sum0_c_exp.con".
  42
  43 (* UNEXPORTED
  44 Hint Resolve Sum0_c_exp.
  45 *)
  46
  47 inline "cic:/CoRN/reals/CSumsReals/Sum_c_exp.con".
  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 "cic:/CoRN/reals/CSumsReals/Sum_c_exp'.con".
  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 "cic:/CoRN/reals/CSumsReals/diff_is_Sum0.con".
  70
  71 inline "cic:/CoRN/reals/CSumsReals/diff_is_sum.con".
  72
  73 inline "cic:/CoRN/reals/CSumsReals/Sum0_pres_less.con".
  74
  75 inline "cic:/CoRN/reals/CSumsReals/Sum_pres_less.con".
  76
  77 inline "cic:/CoRN/reals/CSumsReals/Sum_pres_leEq.con".
  78
  79 inline "cic:/CoRN/reals/CSumsReals/Sum0_comm_scal.con".
  80
  81 (* UNEXPORTED
  82 Hint Resolve Sum0_comm_scal: algebra.
  83 *)
  84
  85 inline "cic:/CoRN/reals/CSumsReals/Sum_comm_scal.con".
  86
  87 inline "cic:/CoRN/reals/CSumsReals/Sum0_comm_scal'.con".
  88
  89 inline "cic:/CoRN/reals/CSumsReals/Sum_comm_scal'.con".
  90
  91 inline "cic:/CoRN/reals/CSumsReals/Sumx_comm_scal'.con".
  92
  93 inline "cic:/CoRN/reals/CSumsReals/Sum2_comm_scal'.con".
  94