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[helm.git] / matita / contribs / CoRN-Decl / reals / CSumsReals.ma

diff --git a/matita/contribs/CoRN-Decl/reals/CSumsReals.ma b/matita/contribs/CoRN-Decl/reals/CSumsReals.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+set "baseuri" "cic:/matita/CoRN-Decl/reals/CSumsReals".
+
+include "CoRN.ma".
+
+(* $Id: CSumsReals.v,v 1.5 2004/04/23 10:01:04 lcf Exp $ *)
+
+include "reals/CReals1.ma".
+
+(*#* * Sums over Reals
+
+%\begin{convention}% Let [c] be a real.
+%\end{convention}%
+
+Here we prove that
+$\Sigma_{m\leq i \leq n}~c^k = \frac{c^{n+1}-c^m}{c-1}.$
+#sum_(m≤ i ≤ n) c^k = frac (c^(n+1) -c^m) (c-1)#
+*)
+
+(* UNEXPORTED
+Section Sums_over_Reals
+*)
+
+alias id "c" = "cic:/CoRN/reals/CSumsReals/Sums_over_Reals/c.var".
+
+inline "cic:/CoRN/reals/CSumsReals/Sum0_c_exp.con".
+
+(* UNEXPORTED
+Hint Resolve Sum0_c_exp.
+*)
+
+inline "cic:/CoRN/reals/CSumsReals/Sum_c_exp.con".
+
+(* UNEXPORTED
+Hint Resolve Sum_c_exp.
+*)
+
+(*#* The following formulation is often more useful if [c [<] 1]. *)
+
+inline "cic:/CoRN/reals/CSumsReals/Sum_c_exp'.con".
+
+(* UNEXPORTED
+Hint Resolve Sum_c_exp'.
+*)
+
+(* UNEXPORTED
+End Sums_over_Reals
+*)
+
+(* UNEXPORTED
+Hint Resolve Sum0_c_exp Sum_c_exp Sum_c_exp': algebra.
+*)
+
+inline "cic:/CoRN/reals/CSumsReals/diff_is_Sum0.con".
+
+inline "cic:/CoRN/reals/CSumsReals/diff_is_sum.con".
+
+inline "cic:/CoRN/reals/CSumsReals/Sum0_pres_less.con".
+
+inline "cic:/CoRN/reals/CSumsReals/Sum_pres_less.con".
+
+inline "cic:/CoRN/reals/CSumsReals/Sum_pres_leEq.con".
+
+inline "cic:/CoRN/reals/CSumsReals/Sum0_comm_scal.con".
+
+(* UNEXPORTED
+Hint Resolve Sum0_comm_scal: algebra.
+*)
+
+inline "cic:/CoRN/reals/CSumsReals/Sum_comm_scal.con".
+
+inline "cic:/CoRN/reals/CSumsReals/Sum0_comm_scal'.con".
+
+inline "cic:/CoRN/reals/CSumsReals/Sum_comm_scal'.con".
+
+inline "cic:/CoRN/reals/CSumsReals/Sumx_comm_scal'.con".
+
+inline "cic:/CoRN/reals/CSumsReals/Sum2_comm_scal'.con".
+