some theorems have been moved to more appropriate files in library.

[helm.git] / matita / contribs / CoRN-Decl / ftc / FunctSeries.ma

diff --git a/matita/contribs/CoRN-Decl/ftc/FunctSeries.ma b/matita/contribs/CoRN-Decl/ftc/FunctSeries.ma
index 70dddf1d4c7954348ed46df8c9cd7211fda7145e..917cbe2bcbde4bfa3b5c5f172a2fe589491da743 100644 (file)
--- a/matita/contribs/CoRN-Decl/ftc/FunctSeries.ma
+++ b/matita/contribs/CoRN-Decl/ftc/FunctSeries.ma
@@ -16,22 +16,20 @@
 
 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}% #&sum;<sup>n</sup># *)
 
 (*#* printing Fun_Series_Sum %\ensuremath{\sum_0^{\infty}}% #&sum;<sub>0</sub><sup>&infin;</sup># *)
 
 (* UNEXPORTED
-Section Definitions.
+Section Definitions
 *)
 
 (*#* *Series of Functions
@@ -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.
+alias id "a" = "cic:/CoRN/ftc/FunctSeries/Definitions/a.var".
 
-inline cic:/CoRN/ftc/FunctSeries/b.var.
+alias id "b" = "cic:/CoRN/ftc/FunctSeries/Definitions/b.var".
 
-inline cic:/CoRN/ftc/FunctSeries/Hab.var.
+alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Definitions/Hab.var".
 
 (* begin hide *)
 
-inline cic:/CoRN/ftc/FunctSeries/I.con.
+inline "cic:/CoRN/ftc/FunctSeries/Definitions/I.con" "Definitions__".
 
 (* end hide *)
 
-inline cic:/CoRN/ftc/FunctSeries/f.var.
+alias id "f" = "cic:/CoRN/ftc/FunctSeries/Definitions/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.
@@ -89,24 +87,24 @@ the corresponding series.
 
 (* begin show *)
 
-inline cic:/CoRN/ftc/FunctSeries/H.var.
+alias id "H" = "cic:/CoRN/ftc/FunctSeries/Definitions/H.var".
 
 (* end show *)
 
 (* begin hide *)
 
-inline cic:/CoRN/ftc/FunctSeries/contf.con.
+inline "cic:/CoRN/ftc/FunctSeries/Definitions/contf.con" "Definitions__".
 
-inline cic:/CoRN/ftc/FunctSeries/incf.con.
+inline "cic:/CoRN/ftc/FunctSeries/Definitions/incf.con" "Definitions__".
 
 (* 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.
+End Definitions
 *)
 
 (* UNEXPORTED
@@ -118,27 +116,27 @@ Hint Resolve fun_seq_part_sum_cont: continuous.
 *)
 
 (* UNEXPORTED
-Section More_Definitions.
+Section More_Definitions
 *)
 
-inline cic:/CoRN/ftc/FunctSeries/a.var.
+alias id "a" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/a.var".
 
-inline cic:/CoRN/ftc/FunctSeries/b.var.
+alias id "b" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/b.var".
 
-inline cic:/CoRN/ftc/FunctSeries/Hab.var.
+alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/Hab.var".
 
-inline cic:/CoRN/ftc/FunctSeries/f.var.
+alias id "f" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/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.
+End More_Definitions
 *)
 
 (* UNEXPORTED
-Section Operations.
+Section Operations
 *)
 
 (* **Algebraic Properties
@@ -146,116 +144,116 @@ 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.
+alias id "a" = "cic:/CoRN/ftc/FunctSeries/Operations/a.var".
 
-inline cic:/CoRN/ftc/FunctSeries/b.var.
+alias id "b" = "cic:/CoRN/ftc/FunctSeries/Operations/b.var".
 
-inline cic:/CoRN/ftc/FunctSeries/Hab.var.
+alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Operations/Hab.var".
 
 (* begin hide *)
 
-inline cic:/CoRN/ftc/FunctSeries/I.con.
+inline "cic:/CoRN/ftc/FunctSeries/Operations/I.con" "Operations__".
 
 (* 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.
+alias id "f" = "cic:/CoRN/ftc/FunctSeries/Operations/f.var".
 
-inline cic:/CoRN/ftc/FunctSeries/g.var.
+alias id "g" = "cic:/CoRN/ftc/FunctSeries/Operations/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.
+alias id "convF" = "cic:/CoRN/ftc/FunctSeries/Operations/convF.var".
 
-inline cic:/CoRN/ftc/FunctSeries/convG.var.
+alias id "convG" = "cic:/CoRN/ftc/FunctSeries/Operations/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.
+alias id "c" = "cic:/CoRN/ftc/FunctSeries/Operations/c.var".
 
-inline cic:/CoRN/ftc/FunctSeries/H.var.
+alias id "H" = "cic:/CoRN/ftc/FunctSeries/Operations/H.var".
 
-inline cic:/CoRN/ftc/FunctSeries/contH.var.
+alias id "contH" = "cic:/CoRN/ftc/FunctSeries/Operations/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.
+End Operations
 *)
 
 (* UNEXPORTED
-Section More_Operations.
+Section More_Operations
 *)
 
-inline cic:/CoRN/ftc/FunctSeries/a.var.
+alias id "a" = "cic:/CoRN/ftc/FunctSeries/More_Operations/a.var".
 
-inline cic:/CoRN/ftc/FunctSeries/b.var.
+alias id "b" = "cic:/CoRN/ftc/FunctSeries/More_Operations/b.var".
 
-inline cic:/CoRN/ftc/FunctSeries/Hab.var.
+alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/More_Operations/Hab.var".
 
 (* begin hide *)
 
-inline cic:/CoRN/ftc/FunctSeries/I.con.
+inline "cic:/CoRN/ftc/FunctSeries/More_Operations/I.con" "More_Operations__".
 
 (* end hide *)
 
-inline cic:/CoRN/ftc/FunctSeries/f.var.
+alias id "f" = "cic:/CoRN/ftc/FunctSeries/More_Operations/f.var".
 
-inline cic:/CoRN/ftc/FunctSeries/convF.var.
+alias id "convF" = "cic:/CoRN/ftc/FunctSeries/More_Operations/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.
+End More_Operations
 *)
 
 (* UNEXPORTED
-Section Other_Results.
+Section Other_Results
 *)
 
-inline cic:/CoRN/ftc/FunctSeries/a.var.
+alias id "a" = "cic:/CoRN/ftc/FunctSeries/Other_Results/a.var".
 
-inline cic:/CoRN/ftc/FunctSeries/b.var.
+alias id "b" = "cic:/CoRN/ftc/FunctSeries/Other_Results/b.var".
 
-inline cic:/CoRN/ftc/FunctSeries/Hab.var.
+alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Other_Results/Hab.var".
 
-inline cic:/CoRN/ftc/FunctSeries/f.var.
+alias id "f" = "cic:/CoRN/ftc/FunctSeries/Other_Results/f.var".
 
-inline cic:/CoRN/ftc/FunctSeries/convF.var.
+alias id "convF" = "cic:/CoRN/ftc/FunctSeries/Other_Results/convF.var".
 
 (*#*
 The following relate the sum series with the limit of the sequence of
@@ -263,18 +261,18 @@ 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.
+End Other_Results
 *)
 
 (* UNEXPORTED
@@ -282,7 +280,7 @@ Hint Resolve Fun_Series_Sum_cont: continuous.
 *)
 
 (* UNEXPORTED
-Section Convergence_Criteria.
+Section Convergence_Criteria
 *)
 
 (*#* **Convergence Criteria
@@ -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.
+alias id "a" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/a.var".
 
-inline cic:/CoRN/ftc/FunctSeries/b.var.
+alias id "b" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/b.var".
 
-inline cic:/CoRN/ftc/FunctSeries/Hab.var.
+alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/Hab.var".
 
 (* begin hide *)
 
-inline cic:/CoRN/ftc/FunctSeries/I.con.
+inline "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/I.con" "Convergence_Criteria__".
 
 (* end hide *)
 
-inline cic:/CoRN/ftc/FunctSeries/f.var.
+alias id "f" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/f.var".
 
-inline cic:/CoRN/ftc/FunctSeries/contF.var.
+alias id "contF" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/contF.var".
 
 (* UNEXPORTED
 Opaque Frestr.
@@ -346,23 +344,23 @@ 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.
+End Convergence_Criteria
 *)