X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fcontribs%2FCoRN-Decl%2Fftc%2FFunctSeries.ma;h=917cbe2bcbde4bfa3b5c5f172a2fe589491da743;hb=0a9ed4329c069d2e06902934b6d1d58d3690959c;hp=2ce9fa143c23f1ea8ecf2ab887a6c5775b41377e;hpb=62596f4e0a109e43c9df5da20571827c8b905ce4;p=helm.git diff --git a/matita/contribs/CoRN-Decl/ftc/FunctSeries.ma b/matita/contribs/CoRN-Decl/ftc/FunctSeries.ma index 2ce9fa143..917cbe2bc 100644 --- a/matita/contribs/CoRN-Decl/ftc/FunctSeries.ma +++ b/matita/contribs/CoRN-Decl/ftc/FunctSeries.ma @@ -53,11 +53,11 @@ 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/Definitions/a.var" "Definitions__". +alias id "a" = "cic:/CoRN/ftc/FunctSeries/Definitions/a.var". -inline "cic:/CoRN/ftc/FunctSeries/Definitions/b.var" "Definitions__". +alias id "b" = "cic:/CoRN/ftc/FunctSeries/Definitions/b.var". -inline "cic:/CoRN/ftc/FunctSeries/Definitions/Hab.var" "Definitions__". +alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Definitions/Hab.var". (* begin hide *) @@ -65,7 +65,7 @@ inline "cic:/CoRN/ftc/FunctSeries/Definitions/I.con" "Definitions__". (* end hide *) -inline "cic:/CoRN/ftc/FunctSeries/Definitions/f.var" "Definitions__". +alias id "f" = "cic:/CoRN/ftc/FunctSeries/Definitions/f.var". inline "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum.con". @@ -87,7 +87,7 @@ the corresponding series. (* begin show *) -inline "cic:/CoRN/ftc/FunctSeries/Definitions/H.var" "Definitions__". +alias id "H" = "cic:/CoRN/ftc/FunctSeries/Definitions/H.var". (* end show *) @@ -119,13 +119,13 @@ Hint Resolve fun_seq_part_sum_cont: continuous. Section More_Definitions *) -inline "cic:/CoRN/ftc/FunctSeries/More_Definitions/a.var" "More_Definitions__". +alias id "a" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/a.var". -inline "cic:/CoRN/ftc/FunctSeries/More_Definitions/b.var" "More_Definitions__". +alias id "b" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/b.var". -inline "cic:/CoRN/ftc/FunctSeries/More_Definitions/Hab.var" "More_Definitions__". +alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/Hab.var". -inline "cic:/CoRN/ftc/FunctSeries/More_Definitions/f.var" "More_Definitions__". +alias id "f" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/f.var". (*#* A series can also be absolutely convergent. *) @@ -144,11 +144,11 @@ 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/Operations/a.var" "Operations__". +alias id "a" = "cic:/CoRN/ftc/FunctSeries/Operations/a.var". -inline "cic:/CoRN/ftc/FunctSeries/Operations/b.var" "Operations__". +alias id "b" = "cic:/CoRN/ftc/FunctSeries/Operations/b.var". -inline "cic:/CoRN/ftc/FunctSeries/Operations/Hab.var" "Operations__". +alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Operations/Hab.var". (* begin hide *) @@ -168,9 +168,9 @@ inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_zero.con". (* begin show *) -inline "cic:/CoRN/ftc/FunctSeries/Operations/f.var" "Operations__". +alias id "f" = "cic:/CoRN/ftc/FunctSeries/Operations/f.var". -inline "cic:/CoRN/ftc/FunctSeries/Operations/g.var" "Operations__". +alias id "g" = "cic:/CoRN/ftc/FunctSeries/Operations/g.var". (* end show *) @@ -178,9 +178,9 @@ inline "cic:/CoRN/ftc/FunctSeries/fun_series_convergent_wd.con". (* begin show *) -inline "cic:/CoRN/ftc/FunctSeries/Operations/convF.var" "Operations__". +alias id "convF" = "cic:/CoRN/ftc/FunctSeries/Operations/convF.var". -inline "cic:/CoRN/ftc/FunctSeries/Operations/convG.var" "Operations__". +alias id "convG" = "cic:/CoRN/ftc/FunctSeries/Operations/convG.var". (* end show *) @@ -199,11 +199,11 @@ inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_min.con". %\end{convention}% *) -inline "cic:/CoRN/ftc/FunctSeries/Operations/c.var" "Operations__". +alias id "c" = "cic:/CoRN/ftc/FunctSeries/Operations/c.var". -inline "cic:/CoRN/ftc/FunctSeries/Operations/H.var" "Operations__". +alias id "H" = "cic:/CoRN/ftc/FunctSeries/Operations/H.var". -inline "cic:/CoRN/ftc/FunctSeries/Operations/contH.var" "Operations__". +alias id "contH" = "cic:/CoRN/ftc/FunctSeries/Operations/contH.var". inline "cic:/CoRN/ftc/FunctSeries/conv_fun_series_scal.con". @@ -217,11 +217,11 @@ End Operations Section More_Operations *) -inline "cic:/CoRN/ftc/FunctSeries/More_Operations/a.var" "More_Operations__". +alias id "a" = "cic:/CoRN/ftc/FunctSeries/More_Operations/a.var". -inline "cic:/CoRN/ftc/FunctSeries/More_Operations/b.var" "More_Operations__". +alias id "b" = "cic:/CoRN/ftc/FunctSeries/More_Operations/b.var". -inline "cic:/CoRN/ftc/FunctSeries/More_Operations/Hab.var" "More_Operations__". +alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/More_Operations/Hab.var". (* begin hide *) @@ -229,9 +229,9 @@ inline "cic:/CoRN/ftc/FunctSeries/More_Operations/I.con" "More_Operations__". (* end hide *) -inline "cic:/CoRN/ftc/FunctSeries/More_Operations/f.var" "More_Operations__". +alias id "f" = "cic:/CoRN/ftc/FunctSeries/More_Operations/f.var". -inline "cic:/CoRN/ftc/FunctSeries/More_Operations/convF.var" "More_Operations__". +alias id "convF" = "cic:/CoRN/ftc/FunctSeries/More_Operations/convF.var". inline "cic:/CoRN/ftc/FunctSeries/conv_fun_series_inv.con". @@ -245,15 +245,15 @@ End More_Operations Section Other_Results *) -inline "cic:/CoRN/ftc/FunctSeries/Other_Results/a.var" "Other_Results__". +alias id "a" = "cic:/CoRN/ftc/FunctSeries/Other_Results/a.var". -inline "cic:/CoRN/ftc/FunctSeries/Other_Results/b.var" "Other_Results__". +alias id "b" = "cic:/CoRN/ftc/FunctSeries/Other_Results/b.var". -inline "cic:/CoRN/ftc/FunctSeries/Other_Results/Hab.var" "Other_Results__". +alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Other_Results/Hab.var". -inline "cic:/CoRN/ftc/FunctSeries/Other_Results/f.var" "Other_Results__". +alias id "f" = "cic:/CoRN/ftc/FunctSeries/Other_Results/f.var". -inline "cic:/CoRN/ftc/FunctSeries/Other_Results/convF.var" "Other_Results__". +alias id "convF" = "cic:/CoRN/ftc/FunctSeries/Other_Results/convF.var". (*#* The following relate the sum series with the limit of the sequence of @@ -288,11 +288,11 @@ 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/Convergence_Criteria/a.var" "Convergence_Criteria__". +alias id "a" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/a.var". -inline "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/b.var" "Convergence_Criteria__". +alias id "b" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/b.var". -inline "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/Hab.var" "Convergence_Criteria__". +alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/Hab.var". (* begin hide *) @@ -300,9 +300,9 @@ inline "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/I.con" "Convergence_Crite (* end hide *) -inline "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/f.var" "Convergence_Criteria__". +alias id "f" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/f.var". -inline "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/contF.var" "Convergence_Criteria__". +alias id "contF" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/contF.var". (* UNEXPORTED Opaque Frestr.