but the ones which do we simply adapt in the usual way.
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/Definitions/J.var" "Definitions__".
+alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Definitions/J.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Definitions/f.var" "Definitions__".
+alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Definitions/f.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Definitions/F.var" "Definitions__".
+alias id "F" = "cic:/CoRN/ftc/MoreFunSeries/Definitions/F.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Definitions/contf.var" "Definitions__".
+alias id "contf" = "cic:/CoRN/ftc/MoreFunSeries/Definitions/contf.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Definitions/contF.var" "Definitions__".
+alias id "contF" = "cic:/CoRN/ftc/MoreFunSeries/Definitions/contF.var".
inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_IR.con".
Limit is defined and works in the same way as before.
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/J.var" "More_Definitions__".
+alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/J.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/f.var" "More_Definitions__".
+alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/f.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/contf.var" "More_Definitions__".
+alias id "contf" = "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/contf.var".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/conv.var" "More_Definitions__".
+alias id "conv" = "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/conv.var".
(* end show *)
Proofs are irrelevant as before---they just have to be present.
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/J.var" "Irrelevance_of_Proofs__".
+alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/J.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/f.var" "Irrelevance_of_Proofs__".
+alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/f.var".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contf.var" "Irrelevance_of_Proofs__".
+alias id "contf" = "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contf.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contf0.var" "Irrelevance_of_Proofs__".
+alias id "contf0" = "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contf0.var".
(* end show *)
-inline "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/F.var" "Irrelevance_of_Proofs__".
+alias id "F" = "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/F.var".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contF.var" "Irrelevance_of_Proofs__".
+alias id "contF" = "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contF.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contF0.var" "Irrelevance_of_Proofs__".
+alias id "contF0" = "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contF0.var".
(* end show *)
Section More_Properties
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/J.var" "More_Properties__".
+alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/J.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/f.var" "More_Properties__".
+alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/f.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/g.var" "More_Properties__".
+alias id "g" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/g.var".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contf.var" "More_Properties__".
+alias id "contf" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contf.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contf0.var" "More_Properties__".
+alias id "contf0" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contf0.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contg.var" "More_Properties__".
+alias id "contg" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contg.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contg0.var" "More_Properties__".
+alias id "contg0" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contg0.var".
(* end show *)
inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_conv_fun_seq'_IR.con".
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/F.var" "More_Properties__".
+alias id "F" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/F.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/G.var" "More_Properties__".
+alias id "G" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/G.var".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contF.var" "More_Properties__".
+alias id "contF" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contF.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contF0.var" "More_Properties__".
+alias id "contF0" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contF0.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contG.var" "More_Properties__".
+alias id "contG" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contG.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contG0.var" "More_Properties__".
+alias id "contG0" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contG0.var".
(* end show *)
Algebraic operations still work well.
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/J.var" "Algebraic_Properties__".
+alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/J.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/f.var" "Algebraic_Properties__".
+alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/f.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/g.var" "Algebraic_Properties__".
+alias id "g" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/g.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contf.var" "Algebraic_Properties__".
+alias id "contf" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contf.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contg.var" "Algebraic_Properties__".
+alias id "contg" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contg.var".
inline "cic:/CoRN/ftc/MoreFunSeries/FLim_unique_IR.con".
inline "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_const_IR.con".
-inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/F.var" "Algebraic_Properties__".
+alias id "F" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/F.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/G.var" "Algebraic_Properties__".
+alias id "G" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/G.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contF.var" "Algebraic_Properties__".
+alias id "contF" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contF.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contG.var" "Algebraic_Properties__".
+alias id "contG" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contG.var".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/convF.var" "Algebraic_Properties__".
+alias id "convF" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/convF.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/convG.var" "Algebraic_Properties__".
+alias id "convG" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/convG.var".
(* end show *)
If we work with the limit function things fit in just as well.
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/J.var" "More_Algebraic_Properties__".
+alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/J.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/f.var" "More_Algebraic_Properties__".
+alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/f.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/g.var" "More_Algebraic_Properties__".
+alias id "g" = "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/g.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/contf.var" "More_Algebraic_Properties__".
+alias id "contf" = "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/contf.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/contg.var" "More_Algebraic_Properties__".
+alias id "contg" = "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/contg.var".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/Hf.var" "More_Algebraic_Properties__".
+alias id "Hf" = "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/Hf.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/Hg.var" "More_Algebraic_Properties__".
+alias id "Hg" = "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/Hg.var".
(* end show *)
Convergence is defined as expected---through convergence in every compact interval.
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/J.var" "Series_Definitions__".
+alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/J.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/f.var" "Series_Definitions__".
+alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/f.var".
inline "cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_IR.con".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/H.var" "Series_Definitions__".
+alias id "H" = "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/H.var".
(* end show *)
Section More_Series_Definitions
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Series_Definitions/J.var" "More_Series_Definitions__".
+alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/More_Series_Definitions/J.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/More_Series_Definitions/f.var" "More_Series_Definitions__".
+alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/More_Series_Definitions/f.var".
(*#*
Absolute convergence still exists.
As before, any series converges to its sum.
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/Convergence_Results/J.var" "Convergence_Results__".
+alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Convergence_Results/J.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Convergence_Results/f.var" "Convergence_Results__".
+alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Convergence_Results/f.var".
inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_conv.con".
Convergence is well defined and preserved by operations.
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/Operations/J.var" "Operations__".
+alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Operations/J.var".
inline "cic:/CoRN/ftc/MoreFunSeries/conv_fun_const_series_IR.con".
inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_zero_IR.con".
-inline "cic:/CoRN/ftc/MoreFunSeries/Operations/f.var" "Operations__".
+alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Operations/f.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Operations/g.var" "Operations__".
+alias id "g" = "cic:/CoRN/ftc/MoreFunSeries/Operations/g.var".
inline "cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_wd_IR.con".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunSeries/Operations/convF.var" "Operations__".
+alias id "convF" = "cic:/CoRN/ftc/MoreFunSeries/Operations/convF.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Operations/convG.var" "Operations__".
+alias id "convG" = "cic:/CoRN/ftc/MoreFunSeries/Operations/convG.var".
(* end show *)
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/Operations/c.var" "Operations__".
+alias id "c" = "cic:/CoRN/ftc/MoreFunSeries/Operations/c.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Operations/H.var" "Operations__".
+alias id "H" = "cic:/CoRN/ftc/MoreFunSeries/Operations/H.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Operations/contH.var" "Operations__".
+alias id "contH" = "cic:/CoRN/ftc/MoreFunSeries/Operations/contH.var".
inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_scal_conv.con".
comparison test (in both versions) and the ratio test.
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/J.var" "Convergence_Criteria__".
+alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/J.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/f.var" "Convergence_Criteria__".
+alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/f.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/contF.var" "Convergence_Criteria__".
+alias id "contF" = "cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/contF.var".
inline "cic:/CoRN/ftc/MoreFunSeries/fun_str_comparison_IR.con".
position. This does not affect convergence or the sum of the series.
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/Insert_Series/J.var" "Insert_Series__".
+alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Insert_Series/J.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Insert_Series/f.var" "Insert_Series__".
+alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Insert_Series/f.var".
-inline "cic:/CoRN/ftc/MoreFunSeries/Insert_Series/convF.var" "Insert_Series__".
+alias id "convF" = "cic:/CoRN/ftc/MoreFunSeries/Insert_Series/convF.var".
inline "cic:/CoRN/ftc/MoreFunSeries/insert_series.con".