set "baseuri" "cic:/matita/CoRN-Decl/transc/TaylorSeries".
+include "CoRN_notation.ma".
+
(* $Id: TaylorSeries.v,v 1.7 2004/04/23 10:01:08 lcf Exp $ *)
-(* INCLUDE
-PowerSeries
-*)
+include "transc/PowerSeries.ma".
-(* INCLUDE
-Taylor
-*)
+include "ftc/Taylor.ma".
(*#* *Taylor Series
Section Definitions.
*)
-inline cic:/CoRN/transc/TaylorSeries/J.var.
+inline "cic:/CoRN/transc/TaylorSeries/J.var".
-inline cic:/CoRN/transc/TaylorSeries/pJ.var.
+inline "cic:/CoRN/transc/TaylorSeries/pJ.var".
-inline cic:/CoRN/transc/TaylorSeries/F.var.
+inline "cic:/CoRN/transc/TaylorSeries/F.var".
-inline cic:/CoRN/transc/TaylorSeries/diffF.var.
+inline "cic:/CoRN/transc/TaylorSeries/diffF.var".
-inline cic:/CoRN/transc/TaylorSeries/a.var.
+inline "cic:/CoRN/transc/TaylorSeries/a.var".
-inline cic:/CoRN/transc/TaylorSeries/Ha.var.
+inline "cic:/CoRN/transc/TaylorSeries/Ha.var".
-inline cic:/CoRN/transc/TaylorSeries/Taylor_Series'.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series'.con".
(*#*
%\begin{convention}% Assume also that [f] is the sequence of
%\end{convention}%
*)
-inline cic:/CoRN/transc/TaylorSeries/f.var.
+inline "cic:/CoRN/transc/TaylorSeries/f.var".
-inline cic:/CoRN/transc/TaylorSeries/derF.var.
+inline "cic:/CoRN/transc/TaylorSeries/derF.var".
-inline cic:/CoRN/transc/TaylorSeries/Taylor_Series.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series.con".
(* UNEXPORTED
Opaque N_Deriv.
(*#* Characterizations of the Taylor remainder. *)
-inline cic:/CoRN/transc/TaylorSeries/Taylor_Rem_char.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_Rem_char.con".
-inline cic:/CoRN/transc/TaylorSeries/abs_Taylor_Rem_char.con.
+inline "cic:/CoRN/transc/TaylorSeries/abs_Taylor_Rem_char.con".
(* UNEXPORTED
End Definitions.
[F].
*)
-inline cic:/CoRN/transc/TaylorSeries/H.var.
+inline "cic:/CoRN/transc/TaylorSeries/H.var".
-inline cic:/CoRN/transc/TaylorSeries/F.var.
+inline "cic:/CoRN/transc/TaylorSeries/F.var".
-inline cic:/CoRN/transc/TaylorSeries/a.var.
+inline "cic:/CoRN/transc/TaylorSeries/a.var".
-inline cic:/CoRN/transc/TaylorSeries/Ha.var.
+inline "cic:/CoRN/transc/TaylorSeries/Ha.var".
-inline cic:/CoRN/transc/TaylorSeries/f.var.
+inline "cic:/CoRN/transc/TaylorSeries/f.var".
-inline cic:/CoRN/transc/TaylorSeries/derF.var.
+inline "cic:/CoRN/transc/TaylorSeries/derF.var".
-inline cic:/CoRN/transc/TaylorSeries/Taylor_Series_imp_cont.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series_imp_cont.con".
-inline cic:/CoRN/transc/TaylorSeries/Taylor_Series_lemma_cont.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series_lemma_cont.con".
-inline cic:/CoRN/transc/TaylorSeries/Taylor_bnd.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_bnd.con".
(* begin show *)
-inline cic:/CoRN/transc/TaylorSeries/bndf.var.
+inline "cic:/CoRN/transc/TaylorSeries/bndf.var".
(* end show *)
(* begin hide *)
-inline cic:/CoRN/transc/TaylorSeries/H1.con.
+inline "cic:/CoRN/transc/TaylorSeries/H1.con".
(* UNEXPORTED
Transparent nexp_op.
*)
-inline cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_lemma1.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_lemma1.con".
-inline cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_lemma2.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_lemma2.con".
(* end hide *)
Opaque nexp_op.
*)
-inline cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_IR.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_IR.con".
(* begin hide *)
Transparent nexp_op.
*)
-inline cic:/CoRN/transc/TaylorSeries/Taylor_majoration_lemma.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_majoration_lemma.con".
(* UNEXPORTED
Opaque N_Deriv fac.
*)
-inline cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_lemma3.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_lemma3.con".
(* end hide *)
(* begin show *)
-inline cic:/CoRN/transc/TaylorSeries/Hf.var.
+inline "cic:/CoRN/transc/TaylorSeries/Hf.var".
(* end show *)
Opaque mult.
*)
-inline cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_to_fun.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_to_fun.con".
(* UNEXPORTED
End Convergence_in_IR.
give some helpful lemmas.
*)
-inline cic:/CoRN/transc/TaylorSeries/Taylor_bnd_trans.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_bnd_trans.con".
(* begin hide *)
Opaque nexp_op.
*)
-inline cic:/CoRN/transc/TaylorSeries/convergence_lemma.con.
+inline "cic:/CoRN/transc/TaylorSeries/convergence_lemma.con".
(* end hide *)
-inline cic:/CoRN/transc/TaylorSeries/bnd_imp_Taylor_bnd.con.
+inline "cic:/CoRN/transc/TaylorSeries/bnd_imp_Taylor_bnd.con".
(*#*
Finally, a uniqueness criterium: two functions [F] and [G] are equal,
Taylor series converge to themselves.
*)
-inline cic:/CoRN/transc/TaylorSeries/F.var.
+inline "cic:/CoRN/transc/TaylorSeries/F.var".
-inline cic:/CoRN/transc/TaylorSeries/G.var.
+inline "cic:/CoRN/transc/TaylorSeries/G.var".
-inline cic:/CoRN/transc/TaylorSeries/a.var.
+inline "cic:/CoRN/transc/TaylorSeries/a.var".
-inline cic:/CoRN/transc/TaylorSeries/f.var.
+inline "cic:/CoRN/transc/TaylorSeries/f.var".
-inline cic:/CoRN/transc/TaylorSeries/g.var.
+inline "cic:/CoRN/transc/TaylorSeries/g.var".
-inline cic:/CoRN/transc/TaylorSeries/derF.var.
+inline "cic:/CoRN/transc/TaylorSeries/derF.var".
-inline cic:/CoRN/transc/TaylorSeries/derG.var.
+inline "cic:/CoRN/transc/TaylorSeries/derG.var".
-inline cic:/CoRN/transc/TaylorSeries/bndf.var.
+inline "cic:/CoRN/transc/TaylorSeries/bndf.var".
-inline cic:/CoRN/transc/TaylorSeries/bndg.var.
+inline "cic:/CoRN/transc/TaylorSeries/bndg.var".
(* begin show *)
-inline cic:/CoRN/transc/TaylorSeries/Heq.var.
+inline "cic:/CoRN/transc/TaylorSeries/Heq.var".
(* end show *)
(* begin hide *)
-inline cic:/CoRN/transc/TaylorSeries/Hf.con.
+inline "cic:/CoRN/transc/TaylorSeries/Hf.con".
(* end hide *)
-inline cic:/CoRN/transc/TaylorSeries/Taylor_unique_crit.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_unique_crit.con".
(* UNEXPORTED
End Other_Results.