set "baseuri" "cic:/matita/CoRN-Decl/ftc/MoreFunctions".
-include "CoRN_notation.ma".
+include "CoRN.ma".
(* $Id: MoreFunctions.v,v 1.5 2004/04/20 22:38:50 hinderer Exp $ *)
*)
(* UNEXPORTED
-Section Basic_Results.
+Section Basic_Results
*)
(*#* *More about Functions
**Continuity
*)
-inline "cic:/CoRN/ftc/MoreFunctions/I.var".
+alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Basic_Results/I.var".
(*#*
Trivial stuff.
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/MoreFunctions/cI.var".
+alias id "cI" = "cic:/CoRN/ftc/MoreFunctions/Basic_Results/cI.var".
-inline "cic:/CoRN/ftc/MoreFunctions/F.var".
+alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Basic_Results/F.var".
-inline "cic:/CoRN/ftc/MoreFunctions/contF.var".
+alias id "contF" = "cic:/CoRN/ftc/MoreFunctions/Basic_Results/contF.var".
inline "cic:/CoRN/ftc/MoreFunctions/continuous_compact.con".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunctions/Hinc.var".
+alias id "Hinc" = "cic:/CoRN/ftc/MoreFunctions/Basic_Results/Hinc.var".
(* end show *)
inline "cic:/CoRN/ftc/MoreFunctions/FNorm_bnd_AbsIR.con".
(* UNEXPORTED
-End Basic_Results.
+End Basic_Results
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Other_Results.
+Section Other_Results
*)
(*#*
The usual stuff.
*)
-inline "cic:/CoRN/ftc/MoreFunctions/I.var".
+alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Other_Results/I.var".
-inline "cic:/CoRN/ftc/MoreFunctions/F.var".
+alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Other_Results/F.var".
-inline "cic:/CoRN/ftc/MoreFunctions/G.var".
+alias id "G" = "cic:/CoRN/ftc/MoreFunctions/Other_Results/G.var".
inline "cic:/CoRN/ftc/MoreFunctions/Continuous_wd.con".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunctions/contF.var".
+alias id "contF" = "cic:/CoRN/ftc/MoreFunctions/Other_Results/contF.var".
-inline "cic:/CoRN/ftc/MoreFunctions/contG.var".
+alias id "contG" = "cic:/CoRN/ftc/MoreFunctions/Other_Results/contG.var".
(* end show *)
inline "cic:/CoRN/ftc/MoreFunctions/Continuous_recip.con".
(* UNEXPORTED
-End Other_Results.
+End Other_Results
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Corollaries.
+Section Corollaries
*)
-inline "cic:/CoRN/ftc/MoreFunctions/I.var".
+alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Corollaries/I.var".
-inline "cic:/CoRN/ftc/MoreFunctions/cI.var".
+alias id "cI" = "cic:/CoRN/ftc/MoreFunctions/Corollaries/cI.var".
-inline "cic:/CoRN/ftc/MoreFunctions/F.var".
+alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Corollaries/F.var".
-inline "cic:/CoRN/ftc/MoreFunctions/G.var".
+alias id "G" = "cic:/CoRN/ftc/MoreFunctions/Corollaries/G.var".
-inline "cic:/CoRN/ftc/MoreFunctions/contF.var".
+alias id "contF" = "cic:/CoRN/ftc/MoreFunctions/Corollaries/contF.var".
-inline "cic:/CoRN/ftc/MoreFunctions/contG.var".
+alias id "contG" = "cic:/CoRN/ftc/MoreFunctions/Corollaries/contG.var".
inline "cic:/CoRN/ftc/MoreFunctions/Continuous_div.con".
inline "cic:/CoRN/ftc/MoreFunctions/FNorm_wd.con".
(* UNEXPORTED
-End Corollaries.
+End Corollaries
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Sums.
+Section Sums
*)
-inline "cic:/CoRN/ftc/MoreFunctions/I.var".
+alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Sums/I.var".
inline "cic:/CoRN/ftc/MoreFunctions/Continuous_Sumx.con".
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/MoreFunctions/f.var".
+alias id "f" = "cic:/CoRN/ftc/MoreFunctions/Sums/f.var".
-inline "cic:/CoRN/ftc/MoreFunctions/contF.var".
+alias id "contF" = "cic:/CoRN/ftc/MoreFunctions/Sums/contF.var".
inline "cic:/CoRN/ftc/MoreFunctions/Continuous_Sum0.con".
inline "cic:/CoRN/ftc/MoreFunctions/Continuous_Sum.con".
(* UNEXPORTED
-End Sums.
+End Sums
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Basic_Properties.
+Section Basic_Properties
*)
(*#* **Derivative
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/MoreFunctions/I.var".
+alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/I.var".
-inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
+alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/pI.var".
-inline "cic:/CoRN/ftc/MoreFunctions/F.var".
+alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/F.var".
-inline "cic:/CoRN/ftc/MoreFunctions/G.var".
+alias id "G" = "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/G.var".
-inline "cic:/CoRN/ftc/MoreFunctions/H.var".
+alias id "H" = "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/H.var".
inline "cic:/CoRN/ftc/MoreFunctions/Derivative_wdl.con".
inline "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Continuous'.con".
(* UNEXPORTED
-End Basic_Properties.
+End Basic_Properties
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section More_Results.
+Section More_Results
*)
-inline "cic:/CoRN/ftc/MoreFunctions/I.var".
+alias id "I" = "cic:/CoRN/ftc/MoreFunctions/More_Results/I.var".
-inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
+alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/More_Results/pI.var".
(*#*
%\begin{convention}% Assume that [F'] and [G'] are derivatives of [F] and [G], respectively, in [I].
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/MoreFunctions/F.var".
+alias id "F" = "cic:/CoRN/ftc/MoreFunctions/More_Results/F.var".
-inline "cic:/CoRN/ftc/MoreFunctions/F'.var".
+alias id "F'" = "cic:/CoRN/ftc/MoreFunctions/More_Results/F'.var".
-inline "cic:/CoRN/ftc/MoreFunctions/G.var".
+alias id "G" = "cic:/CoRN/ftc/MoreFunctions/More_Results/G.var".
-inline "cic:/CoRN/ftc/MoreFunctions/G'.var".
+alias id "G'" = "cic:/CoRN/ftc/MoreFunctions/More_Results/G'.var".
-inline "cic:/CoRN/ftc/MoreFunctions/derF.var".
+alias id "derF" = "cic:/CoRN/ftc/MoreFunctions/More_Results/derF.var".
-inline "cic:/CoRN/ftc/MoreFunctions/derG.var".
+alias id "derG" = "cic:/CoRN/ftc/MoreFunctions/More_Results/derG.var".
inline "cic:/CoRN/ftc/MoreFunctions/included_imp_Derivative.con".
inline "cic:/CoRN/ftc/MoreFunctions/Derivative_recip.con".
(* UNEXPORTED
-End More_Results.
+End More_Results
*)
(* UNEXPORTED
-Section More_Corollaries.
+Section More_Corollaries
*)
-inline "cic:/CoRN/ftc/MoreFunctions/I.var".
+alias id "I" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/I.var".
-inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
+alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/pI.var".
-inline "cic:/CoRN/ftc/MoreFunctions/F.var".
+alias id "F" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/F.var".
-inline "cic:/CoRN/ftc/MoreFunctions/F'.var".
+alias id "F'" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/F'.var".
-inline "cic:/CoRN/ftc/MoreFunctions/G.var".
+alias id "G" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/G.var".
-inline "cic:/CoRN/ftc/MoreFunctions/G'.var".
+alias id "G'" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/G'.var".
-inline "cic:/CoRN/ftc/MoreFunctions/derF.var".
+alias id "derF" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/derF.var".
-inline "cic:/CoRN/ftc/MoreFunctions/derG.var".
+alias id "derG" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/derG.var".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunctions/Gbnd.var".
+alias id "Gbnd" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/Gbnd.var".
(* end show *)
inline "cic:/CoRN/ftc/MoreFunctions/Derivative_div.con".
(* UNEXPORTED
-End More_Corollaries.
+End More_Corollaries
*)
(* UNEXPORTED
-Section More_Sums.
+Section More_Sums
*)
-inline "cic:/CoRN/ftc/MoreFunctions/I.var".
+alias id "I" = "cic:/CoRN/ftc/MoreFunctions/More_Sums/I.var".
-inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
+alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/More_Sums/pI.var".
inline "cic:/CoRN/ftc/MoreFunctions/Derivative_Sumx.con".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunctions/f.var".
+alias id "f" = "cic:/CoRN/ftc/MoreFunctions/More_Sums/f.var".
-inline "cic:/CoRN/ftc/MoreFunctions/f'.var".
+alias id "f'" = "cic:/CoRN/ftc/MoreFunctions/More_Sums/f'.var".
-inline "cic:/CoRN/ftc/MoreFunctions/derF.var".
+alias id "derF" = "cic:/CoRN/ftc/MoreFunctions/More_Sums/derF.var".
(* end show *)
inline "cic:/CoRN/ftc/MoreFunctions/Derivative_Sum.con".
(* UNEXPORTED
-End More_Sums.
+End More_Sums
*)
(* UNEXPORTED
-Section Diffble_Basic_Properties.
+Section Diffble_Basic_Properties
*)
(*#* **Differentiability
Mutatis mutandis for differentiability.
*)
-inline "cic:/CoRN/ftc/MoreFunctions/I.var".
+alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/I.var".
-inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
+alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/pI.var".
inline "cic:/CoRN/ftc/MoreFunctions/Diffble_imp_inc.con".
inline "cic:/CoRN/ftc/MoreFunctions/Diffble_wd.con".
-inline "cic:/CoRN/ftc/MoreFunctions/F.var".
+alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/F.var".
-inline "cic:/CoRN/ftc/MoreFunctions/G.var".
+alias id "G" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/G.var".
-inline "cic:/CoRN/ftc/MoreFunctions/diffF.var".
+alias id "diffF" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/diffF.var".
-inline "cic:/CoRN/ftc/MoreFunctions/diffG.var".
+alias id "diffG" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/diffG.var".
(*#*
%\begin{convention}% Assume [F] and [G] are differentiable in [I].
inline "cic:/CoRN/ftc/MoreFunctions/Diffble_recip.con".
(* UNEXPORTED
-End Diffble_Basic_Properties.
+End Diffble_Basic_Properties
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Diffble_Corollaries.
+Section Diffble_Corollaries
*)
-inline "cic:/CoRN/ftc/MoreFunctions/I.var".
+alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/I.var".
-inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
+alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/pI.var".
-inline "cic:/CoRN/ftc/MoreFunctions/F.var".
+alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/F.var".
-inline "cic:/CoRN/ftc/MoreFunctions/G.var".
+alias id "G" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/G.var".
-inline "cic:/CoRN/ftc/MoreFunctions/diffF.var".
+alias id "diffF" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/diffF.var".
-inline "cic:/CoRN/ftc/MoreFunctions/diffG.var".
+alias id "diffG" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/diffG.var".
inline "cic:/CoRN/ftc/MoreFunctions/Diffble_div.con".
inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Sum.con".
(* UNEXPORTED
-End Diffble_Corollaries.
+End Diffble_Corollaries
*)
(* UNEXPORTED
-Section Nth_Derivative.
+Section Nth_Derivative
*)
(*#* **Nth Derivative
Higher order derivatives pose more interesting problems. It turns out that it really becomes necessary to generalize our [n_deriv] operator to any interval.
*)
-inline "cic:/CoRN/ftc/MoreFunctions/I.var".
+alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/I.var".
-inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
+alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/pI.var".
(* UNEXPORTED
-Section Definitions.
+Section Definitions
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/MoreFunctions/n.var".
+alias id "n" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Definitions/n.var".
-inline "cic:/CoRN/ftc/MoreFunctions/F.var".
+alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Definitions/F.var".
-inline "cic:/CoRN/ftc/MoreFunctions/diffF.var".
+alias id "diffF" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Definitions/diffF.var".
inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv_fun.con".
inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv.con".
(* UNEXPORTED
-End Definitions.
+End Definitions
*)
(* UNEXPORTED
-Section Basic_Results.
+Section Basic_Results
*)
(*#*
inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_plus.con".
(* UNEXPORTED
-End Basic_Results.
+End Basic_Results
*)
(* UNEXPORTED
-Section More_Results.
+Section More_Results
*)
(*#*
inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_Sn.con".
(* UNEXPORTED
-End More_Results.
+End More_Results
*)
(* UNEXPORTED
-Section Derivating_Diffble.
+Section Derivating_Diffble
*)
(*#*
As a special case we get a differentiation operator%\ldots%#...#
*)
-inline "cic:/CoRN/ftc/MoreFunctions/F.var".
+alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Derivating_Diffble/F.var".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunctions/diffF.var".
+alias id "diffF" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Derivating_Diffble/diffF.var".
(* end show *)
inline "cic:/CoRN/ftc/MoreFunctions/Deriv.con".
(* UNEXPORTED
-End Derivating_Diffble.
+End Derivating_Diffble
*)
(* UNEXPORTED
-Section Corollaries.
+Section Corollaries
*)
(*#*
inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Continuous'.con".
(* UNEXPORTED
-End Corollaries.
+End Corollaries
*)
(* UNEXPORTED
-End Nth_Derivative.
+End Nth_Derivative
*)
(* UNEXPORTED