X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FCoRN-Decl%2Fftc%2FFunctSeries.ma;h=869a6a3f98864fee0881a09dcd8b2311c0c39460;hb=80110e17ef1d38d71473e9471ce15beddde663bb;hp=70dddf1d4c7954348ed46df8c9cd7211fda7145e;hpb=3199f2a8428b5d19a3a803c1b03d9f90e4120f74;p=helm.git diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/FunctSeries.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/FunctSeries.ma index 70dddf1d4..869a6a3f9 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/FunctSeries.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/FunctSeries.ma @@ -16,15 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/FunctSeries". +include "CoRN.ma". + (* $Id: FunctSeries.v,v 1.6 2004/04/23 10:00:58 lcf Exp $ *) -(* INCLUDE -FunctSequence -*) +include "ftc/FunctSequence.ma". -(* INCLUDE -Series -*) +include "reals/Series.ma". (*#* printing fun_seq_part_sum %\ensuremath{\sum^n}% #∑n# *) @@ -55,25 +53,25 @@ defined in a compact interval. For this, partial sums are defined and convergence is simply the convergence of the sequence of partial sums. *) -inline cic:/CoRN/ftc/FunctSeries/a.var. +inline "cic:/CoRN/ftc/FunctSeries/a.var". -inline cic:/CoRN/ftc/FunctSeries/b.var. +inline "cic:/CoRN/ftc/FunctSeries/b.var". -inline cic:/CoRN/ftc/FunctSeries/Hab.var. +inline "cic:/CoRN/ftc/FunctSeries/Hab.var". (* begin hide *) -inline cic:/CoRN/ftc/FunctSeries/I.con. +inline "cic:/CoRN/ftc/FunctSeries/I.con". (* end hide *) -inline cic:/CoRN/ftc/FunctSeries/f.var. +inline "cic:/CoRN/ftc/FunctSeries/f.var". -inline cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum.con. +inline "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum.con". -inline cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum_cont.con. +inline "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum_cont.con". -inline cic:/CoRN/ftc/FunctSeries/fun_series_convergent.con. +inline "cic:/CoRN/ftc/FunctSeries/fun_series_convergent.con". (*#* For what comes up next we need to know that the convergence of a @@ -81,7 +79,7 @@ series of functions implies pointwise convergence of the corresponding real number series. *) -inline cic:/CoRN/ftc/FunctSeries/fun_series_conv_imp_conv.con. +inline "cic:/CoRN/ftc/FunctSeries/fun_series_conv_imp_conv.con". (*#* We then define the sum of the series as being the pointwise sum of the corresponding series. @@ -89,21 +87,21 @@ the corresponding series. (* begin show *) -inline cic:/CoRN/ftc/FunctSeries/H.var. +inline "cic:/CoRN/ftc/FunctSeries/H.var". (* end show *) (* begin hide *) -inline cic:/CoRN/ftc/FunctSeries/contf.con. +inline "cic:/CoRN/ftc/FunctSeries/contf.con". -inline cic:/CoRN/ftc/FunctSeries/incf.con. +inline "cic:/CoRN/ftc/FunctSeries/incf.con". (* end hide *) -inline cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_strext.con. +inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_strext.con". -inline cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum.con. +inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum.con". (* UNEXPORTED End Definitions. @@ -121,17 +119,17 @@ Hint Resolve fun_seq_part_sum_cont: continuous. Section More_Definitions. *) -inline cic:/CoRN/ftc/FunctSeries/a.var. +inline "cic:/CoRN/ftc/FunctSeries/a.var". -inline cic:/CoRN/ftc/FunctSeries/b.var. +inline "cic:/CoRN/ftc/FunctSeries/b.var". -inline cic:/CoRN/ftc/FunctSeries/Hab.var. +inline "cic:/CoRN/ftc/FunctSeries/Hab.var". -inline cic:/CoRN/ftc/FunctSeries/f.var. +inline "cic:/CoRN/ftc/FunctSeries/f.var". (*#* A series can also be absolutely convergent. *) -inline cic:/CoRN/ftc/FunctSeries/fun_series_abs_convergent.con. +inline "cic:/CoRN/ftc/FunctSeries/fun_series_abs_convergent.con". (* UNEXPORTED End More_Definitions. @@ -146,70 +144,70 @@ Section Operations. All of these are analogous to the properties for series of real numbers, so we won't comment much about them. *) -inline cic:/CoRN/ftc/FunctSeries/a.var. +inline "cic:/CoRN/ftc/FunctSeries/a.var". -inline cic:/CoRN/ftc/FunctSeries/b.var. +inline "cic:/CoRN/ftc/FunctSeries/b.var". -inline cic:/CoRN/ftc/FunctSeries/Hab.var. +inline "cic:/CoRN/ftc/FunctSeries/Hab.var". (* begin hide *) -inline cic:/CoRN/ftc/FunctSeries/I.con. +inline "cic:/CoRN/ftc/FunctSeries/I.con". (* end hide *) -inline cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum_n.con. +inline "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum_n.con". -inline cic:/CoRN/ftc/FunctSeries/conv_fun_const_series.con. +inline "cic:/CoRN/ftc/FunctSeries/conv_fun_const_series.con". -inline cic:/CoRN/ftc/FunctSeries/fun_const_series_sum.con. +inline "cic:/CoRN/ftc/FunctSeries/fun_const_series_sum.con". -inline cic:/CoRN/ftc/FunctSeries/conv_zero_fun_series.con. +inline "cic:/CoRN/ftc/FunctSeries/conv_zero_fun_series.con". -inline cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_zero.con. +inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_zero.con". (* begin show *) -inline cic:/CoRN/ftc/FunctSeries/f.var. +inline "cic:/CoRN/ftc/FunctSeries/f.var". -inline cic:/CoRN/ftc/FunctSeries/g.var. +inline "cic:/CoRN/ftc/FunctSeries/g.var". (* end show *) -inline cic:/CoRN/ftc/FunctSeries/fun_series_convergent_wd.con. +inline "cic:/CoRN/ftc/FunctSeries/fun_series_convergent_wd.con". (* begin show *) -inline cic:/CoRN/ftc/FunctSeries/convF.var. +inline "cic:/CoRN/ftc/FunctSeries/convF.var". -inline cic:/CoRN/ftc/FunctSeries/convG.var. +inline "cic:/CoRN/ftc/FunctSeries/convG.var". (* end show *) -inline cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_wd'.con. +inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_wd'.con". -inline cic:/CoRN/ftc/FunctSeries/conv_fun_series_plus.con. +inline "cic:/CoRN/ftc/FunctSeries/conv_fun_series_plus.con". -inline cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_plus.con. +inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_plus.con". -inline cic:/CoRN/ftc/FunctSeries/conv_fun_series_minus.con. +inline "cic:/CoRN/ftc/FunctSeries/conv_fun_series_minus.con". -inline cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_min.con. +inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_min.con". (*#* %\begin{convention}% Let [c:IR]. %\end{convention}% *) -inline cic:/CoRN/ftc/FunctSeries/c.var. +inline "cic:/CoRN/ftc/FunctSeries/c.var". -inline cic:/CoRN/ftc/FunctSeries/H.var. +inline "cic:/CoRN/ftc/FunctSeries/H.var". -inline cic:/CoRN/ftc/FunctSeries/contH.var. +inline "cic:/CoRN/ftc/FunctSeries/contH.var". -inline cic:/CoRN/ftc/FunctSeries/conv_fun_series_scal.con. +inline "cic:/CoRN/ftc/FunctSeries/conv_fun_series_scal.con". -inline cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_scal.con. +inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_scal.con". (* UNEXPORTED End Operations. @@ -219,25 +217,25 @@ End Operations. Section More_Operations. *) -inline cic:/CoRN/ftc/FunctSeries/a.var. +inline "cic:/CoRN/ftc/FunctSeries/a.var". -inline cic:/CoRN/ftc/FunctSeries/b.var. +inline "cic:/CoRN/ftc/FunctSeries/b.var". -inline cic:/CoRN/ftc/FunctSeries/Hab.var. +inline "cic:/CoRN/ftc/FunctSeries/Hab.var". (* begin hide *) -inline cic:/CoRN/ftc/FunctSeries/I.con. +inline "cic:/CoRN/ftc/FunctSeries/I.con". (* end hide *) -inline cic:/CoRN/ftc/FunctSeries/f.var. +inline "cic:/CoRN/ftc/FunctSeries/f.var". -inline cic:/CoRN/ftc/FunctSeries/convF.var. +inline "cic:/CoRN/ftc/FunctSeries/convF.var". -inline cic:/CoRN/ftc/FunctSeries/conv_fun_series_inv.con. +inline "cic:/CoRN/ftc/FunctSeries/conv_fun_series_inv.con". -inline cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_inv.con. +inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_inv.con". (* UNEXPORTED End More_Operations. @@ -247,15 +245,15 @@ End More_Operations. Section Other_Results. *) -inline cic:/CoRN/ftc/FunctSeries/a.var. +inline "cic:/CoRN/ftc/FunctSeries/a.var". -inline cic:/CoRN/ftc/FunctSeries/b.var. +inline "cic:/CoRN/ftc/FunctSeries/b.var". -inline cic:/CoRN/ftc/FunctSeries/Hab.var. +inline "cic:/CoRN/ftc/FunctSeries/Hab.var". -inline cic:/CoRN/ftc/FunctSeries/f.var. +inline "cic:/CoRN/ftc/FunctSeries/f.var". -inline cic:/CoRN/ftc/FunctSeries/convF.var. +inline "cic:/CoRN/ftc/FunctSeries/convF.var". (*#* The following relate the sum series with the limit of the sequence of @@ -263,15 +261,15 @@ partial sums; as a corollary we get the continuity of the sum of the series. *) -inline cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_char'.con. +inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_char'.con". -inline cic:/CoRN/ftc/FunctSeries/fun_series_conv.con. +inline "cic:/CoRN/ftc/FunctSeries/fun_series_conv.con". -inline cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_cont.con. +inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_cont.con". -inline cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_char.con. +inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_char.con". -inline cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_as_Lim.con. +inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_as_Lim.con". (* UNEXPORTED End Other_Results. @@ -290,21 +288,21 @@ Section Convergence_Criteria. Most of the convergence criteria for series of real numbers carry over to series of real-valued functions, so again we just present them without comments. *) -inline cic:/CoRN/ftc/FunctSeries/a.var. +inline "cic:/CoRN/ftc/FunctSeries/a.var". -inline cic:/CoRN/ftc/FunctSeries/b.var. +inline "cic:/CoRN/ftc/FunctSeries/b.var". -inline cic:/CoRN/ftc/FunctSeries/Hab.var. +inline "cic:/CoRN/ftc/FunctSeries/Hab.var". (* begin hide *) -inline cic:/CoRN/ftc/FunctSeries/I.con. +inline "cic:/CoRN/ftc/FunctSeries/I.con". (* end hide *) -inline cic:/CoRN/ftc/FunctSeries/f.var. +inline "cic:/CoRN/ftc/FunctSeries/f.var". -inline cic:/CoRN/ftc/FunctSeries/contF.var. +inline "cic:/CoRN/ftc/FunctSeries/contF.var". (* UNEXPORTED Opaque Frestr. @@ -346,21 +344,21 @@ Transparent fun_seq_part_sum. Opaque fun_seq_part_sum. *) -inline cic:/CoRN/ftc/FunctSeries/fun_str_comparison.con. +inline "cic:/CoRN/ftc/FunctSeries/fun_str_comparison.con". (* UNEXPORTED Transparent FAbs. *) -inline cic:/CoRN/ftc/FunctSeries/fun_comparison.con. +inline "cic:/CoRN/ftc/FunctSeries/fun_comparison.con". -inline cic:/CoRN/ftc/FunctSeries/abs_imp_conv.con. +inline "cic:/CoRN/ftc/FunctSeries/abs_imp_conv.con". (* UNEXPORTED Opaque FAbs. *) -inline cic:/CoRN/ftc/FunctSeries/fun_ratio_test_conv.con. +inline "cic:/CoRN/ftc/FunctSeries/fun_ratio_test_conv.con". (* UNEXPORTED End Convergence_Criteria.