...

[helm.git] / helm / software / matita / contribs / CoRN-Procedural / ftc / FunctSeries.mma

diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/FunctSeries.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/FunctSeries.mma
index 1ea6562000dbf724fd33a2edf46900aa04ad4066..05ab51726b21ea8a34c6abaab7c17d261c560914 100644 (file)
--- a/helm/software/matita/contribs/CoRN-Procedural/ftc/FunctSeries.mma
+++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/FunctSeries.mma
@@ -51,25 +51,33 @@ defined in a compact interval.  For this, partial sums are defined and
 convergence is simply the convergence of the sequence of partial sums.
 *)
 
-alias id "a" = "cic:/CoRN/ftc/FunctSeries/Definitions/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Definitions/a.var
+*)
 
-alias id "b" = "cic:/CoRN/ftc/FunctSeries/Definitions/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Definitions/b.var
+*)
 
-alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Definitions/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Definitions/Hab.var
+*)
 
 (* begin hide *)
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/Definitions/I.con" "Definitions__".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Definitions/I.con" "Definitions__" as definition.
 
 (* end hide *)
 
-alias id "f" = "cic:/CoRN/ftc/FunctSeries/Definitions/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Definitions/f.var
+*)
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum.con" as definition.
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum_cont.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum_cont.con" as lemma.
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_convergent.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_convergent.con" as definition.
 
 (*#*
 For what comes up next we need to know that the convergence of a
@@ -77,7 +85,7 @@ series of functions implies pointwise convergence of the corresponding
 real number series.
 *)
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_conv_imp_conv.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_conv_imp_conv.con" as lemma.
 
 (*#* We then define the sum of the series as being the pointwise sum of
 the corresponding series.
@@ -85,21 +93,23 @@ the corresponding series.
 
 (* begin show *)
 
-alias id "H" = "cic:/CoRN/ftc/FunctSeries/Definitions/H.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Definitions/H.var
+*)
 
 (* end show *)
 
 (* begin hide *)
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/Definitions/contf.con" "Definitions__".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Definitions/contf.con" "Definitions__" as definition.
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/Definitions/incf.con" "Definitions__".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Definitions/incf.con" "Definitions__" as definition.
 
 (* end hide *)
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_strext.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_strext.con" as lemma.
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum.con" as definition.
 
 (* UNEXPORTED
 End Definitions
@@ -117,17 +127,25 @@ Hint Resolve fun_seq_part_sum_cont: continuous.
 Section More_Definitions
 *)
 
-alias id "a" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Definitions/a.var
+*)
 
-alias id "b" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Definitions/b.var
+*)
 
-alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Definitions/Hab.var
+*)
 
-alias id "f" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Definitions/f.var
+*)
 
 (*#* A series can also be absolutely convergent. *)
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_abs_convergent.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_abs_convergent.con" as definition.
 
 (* UNEXPORTED
 End More_Definitions
@@ -142,70 +160,90 @@ Section Operations
 All of these are analogous to the properties for series of real numbers, so we won't comment much about them.
 *)
 
-alias id "a" = "cic:/CoRN/ftc/FunctSeries/Operations/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/a.var
+*)
 
-alias id "b" = "cic:/CoRN/ftc/FunctSeries/Operations/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/b.var
+*)
 
-alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Operations/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/Hab.var
+*)
 
 (* begin hide *)
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/Operations/I.con" "Operations__".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Operations/I.con" "Operations__" as definition.
 
 (* end hide *)
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum_n.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum_n.con" as lemma.
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_const_series.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_const_series.con" as lemma.
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/fun_const_series_sum.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/fun_const_series_sum.con" as lemma.
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/conv_zero_fun_series.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/conv_zero_fun_series.con" as lemma.
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_zero.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_zero.con" as lemma.
 
 (* begin show *)
 
-alias id "f" = "cic:/CoRN/ftc/FunctSeries/Operations/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/f.var
+*)
 
-alias id "g" = "cic:/CoRN/ftc/FunctSeries/Operations/g.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/g.var
+*)
 
 (* end show *)
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_convergent_wd.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_convergent_wd.con" as lemma.
 
 (* begin show *)
 
-alias id "convF" = "cic:/CoRN/ftc/FunctSeries/Operations/convF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/convF.var
+*)
 
-alias id "convG" = "cic:/CoRN/ftc/FunctSeries/Operations/convG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/convG.var
+*)
 
 (* end show *)
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_wd'.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_wd'.con" as lemma.
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_plus.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_plus.con" as lemma.
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_plus.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_plus.con" as lemma.
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_minus.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_minus.con" as lemma.
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_min.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_min.con" as lemma.
 
 (*#*
 %\begin{convention}% Let [c:IR].
 %\end{convention}%
 *)
 
-alias id "c" = "cic:/CoRN/ftc/FunctSeries/Operations/c.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/c.var
+*)
 
-alias id "H" = "cic:/CoRN/ftc/FunctSeries/Operations/H.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/H.var
+*)
 
-alias id "contH" = "cic:/CoRN/ftc/FunctSeries/Operations/contH.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/contH.var
+*)
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_scal.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_scal.con" as lemma.
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_scal.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_scal.con" as lemma.
 
 (* UNEXPORTED
 End Operations
@@ -215,25 +253,35 @@ End Operations
 Section More_Operations
 *)
 
-alias id "a" = "cic:/CoRN/ftc/FunctSeries/More_Operations/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Operations/a.var
+*)
 
-alias id "b" = "cic:/CoRN/ftc/FunctSeries/More_Operations/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Operations/b.var
+*)
 
-alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/More_Operations/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Operations/Hab.var
+*)
 
 (* begin hide *)
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/More_Operations/I.con" "More_Operations__".
+inline procedural "cic:/CoRN/ftc/FunctSeries/More_Operations/I.con" "More_Operations__" as definition.
 
 (* end hide *)
 
-alias id "f" = "cic:/CoRN/ftc/FunctSeries/More_Operations/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Operations/f.var
+*)
 
-alias id "convF" = "cic:/CoRN/ftc/FunctSeries/More_Operations/convF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Operations/convF.var
+*)
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_inv.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_inv.con" as lemma.
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_inv.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_inv.con" as lemma.
 
 (* UNEXPORTED
 End More_Operations
@@ -243,15 +291,25 @@ End More_Operations
 Section Other_Results
 *)
 
-alias id "a" = "cic:/CoRN/ftc/FunctSeries/Other_Results/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Other_Results/a.var
+*)
 
-alias id "b" = "cic:/CoRN/ftc/FunctSeries/Other_Results/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Other_Results/b.var
+*)
 
-alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Other_Results/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Other_Results/Hab.var
+*)
 
-alias id "f" = "cic:/CoRN/ftc/FunctSeries/Other_Results/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Other_Results/f.var
+*)
 
-alias id "convF" = "cic:/CoRN/ftc/FunctSeries/Other_Results/convF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Other_Results/convF.var
+*)
 
 (*#*
 The following relate the sum series with the limit of the sequence of
@@ -259,15 +317,15 @@ partial sums; as a corollary we get the continuity of the sum of the
 series.
 *)
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_char'.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_char'.con" as lemma.
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_conv.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_conv.con" as lemma.
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_cont.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_cont.con" as lemma.
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_char.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_char.con" as lemma.
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_as_Lim.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_as_Lim.con" as lemma.
 
 (* UNEXPORTED
 End Other_Results
@@ -286,21 +344,31 @@ 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.
 *)
 
-alias id "a" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/a.var
+*)
 
-alias id "b" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/b.var
+*)
 
-alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/Hab.var
+*)
 
 (* begin hide *)
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/I.con" "Convergence_Criteria__".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/I.con" "Convergence_Criteria__" as definition.
 
 (* end hide *)
 
-alias id "f" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/f.var
+*)
 
-alias id "contF" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/contF.var
+*)
 
 (* UNEXPORTED
 Opaque Frestr.
@@ -342,21 +410,21 @@ Transparent fun_seq_part_sum.
 Opaque fun_seq_part_sum.
 *)
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/fun_str_comparison.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/fun_str_comparison.con" as lemma.
 
 (* UNEXPORTED
 Transparent FAbs.
 *)
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/fun_comparison.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/fun_comparison.con" as lemma.
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/abs_imp_conv.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/abs_imp_conv.con" as lemma.
 
 (* UNEXPORTED
 Opaque FAbs.
 *)
 
-inline procedural "cic:/CoRN/ftc/FunctSeries/fun_ratio_test_conv.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/fun_ratio_test_conv.con" as lemma.
 
 (* UNEXPORTED
 End Convergence_Criteria