set "baseuri" "cic:/matita/CoRN-Decl/ftc/MoreFunctions".
+include "CoRN.ma".
+
(* $Id: MoreFunctions.v,v 1.5 2004/04/20 22:38:50 hinderer Exp $ *)
(*#* printing FNorm %\ensuremath{\|\cdot\|_{\infty}}% *)
-(* INCLUDE
-MoreIntervals
-*)
+include "ftc/MoreIntervals.ma".
(* UNEXPORTED
Opaque Min Max.
**Continuity
*)
-inline cic:/CoRN/ftc/MoreFunctions/I.var.
+inline "cic:/CoRN/ftc/MoreFunctions/I.var".
(*#*
Trivial stuff.
*)
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_imp_inc.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_imp_inc.con".
(*#*
%\begin{convention}% Assume that [I] is compact and [F] is continuous in [I].
%\end{convention}%
*)
-inline cic:/CoRN/ftc/MoreFunctions/cI.var.
+inline "cic:/CoRN/ftc/MoreFunctions/cI.var".
-inline cic:/CoRN/ftc/MoreFunctions/F.var.
+inline "cic:/CoRN/ftc/MoreFunctions/F.var".
-inline cic:/CoRN/ftc/MoreFunctions/contF.var.
+inline "cic:/CoRN/ftc/MoreFunctions/contF.var".
-inline cic:/CoRN/ftc/MoreFunctions/continuous_compact.con.
+inline "cic:/CoRN/ftc/MoreFunctions/continuous_compact.con".
(* begin show *)
-inline cic:/CoRN/ftc/MoreFunctions/Hinc.var.
+inline "cic:/CoRN/ftc/MoreFunctions/Hinc.var".
(* end show *)
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_I_imp_tb_image.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_I_imp_tb_image.con".
-inline cic:/CoRN/ftc/MoreFunctions/FNorm.con.
+inline "cic:/CoRN/ftc/MoreFunctions/FNorm.con".
-inline cic:/CoRN/ftc/MoreFunctions/FNorm_bnd_AbsIR.con.
+inline "cic:/CoRN/ftc/MoreFunctions/FNorm_bnd_AbsIR.con".
(* UNEXPORTED
End Basic_Results.
The usual stuff.
*)
-inline cic:/CoRN/ftc/MoreFunctions/I.var.
+inline "cic:/CoRN/ftc/MoreFunctions/I.var".
-inline cic:/CoRN/ftc/MoreFunctions/F.var.
+inline "cic:/CoRN/ftc/MoreFunctions/F.var".
-inline cic:/CoRN/ftc/MoreFunctions/G.var.
+inline "cic:/CoRN/ftc/MoreFunctions/G.var".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_wd.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_wd.con".
(* begin show *)
-inline cic:/CoRN/ftc/MoreFunctions/contF.var.
+inline "cic:/CoRN/ftc/MoreFunctions/contF.var".
-inline cic:/CoRN/ftc/MoreFunctions/contG.var.
+inline "cic:/CoRN/ftc/MoreFunctions/contG.var".
(* end show *)
-inline cic:/CoRN/ftc/MoreFunctions/included_imp_Continuous.con.
+inline "cic:/CoRN/ftc/MoreFunctions/included_imp_Continuous.con".
-inline cic:/CoRN/ftc/MoreFunctions/Included_imp_Continuous.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Included_imp_Continuous.con".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_const.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_const.con".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_id.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_id.con".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_plus.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_plus.con".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_inv.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_inv.con".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_minus.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_minus.con".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_mult.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_mult.con".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_nth.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_nth.con".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_scal.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_scal.con".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_abs.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_abs.con".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_recip.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_recip.con".
(* UNEXPORTED
End Other_Results.
Section Corollaries.
*)
-inline cic:/CoRN/ftc/MoreFunctions/I.var.
+inline "cic:/CoRN/ftc/MoreFunctions/I.var".
-inline cic:/CoRN/ftc/MoreFunctions/cI.var.
+inline "cic:/CoRN/ftc/MoreFunctions/cI.var".
-inline cic:/CoRN/ftc/MoreFunctions/F.var.
+inline "cic:/CoRN/ftc/MoreFunctions/F.var".
-inline cic:/CoRN/ftc/MoreFunctions/G.var.
+inline "cic:/CoRN/ftc/MoreFunctions/G.var".
-inline cic:/CoRN/ftc/MoreFunctions/contF.var.
+inline "cic:/CoRN/ftc/MoreFunctions/contF.var".
-inline cic:/CoRN/ftc/MoreFunctions/contG.var.
+inline "cic:/CoRN/ftc/MoreFunctions/contG.var".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_div.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_div.con".
-inline cic:/CoRN/ftc/MoreFunctions/FNorm_wd.con.
+inline "cic:/CoRN/ftc/MoreFunctions/FNorm_wd.con".
(* UNEXPORTED
End Corollaries.
Section Sums.
*)
-inline cic:/CoRN/ftc/MoreFunctions/I.var.
+inline "cic:/CoRN/ftc/MoreFunctions/I.var".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_Sumx.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_Sumx.con".
(*#*
%\begin{convention}% Assume [f] is a sequence of continuous functions.
%\end{convention}%
*)
-inline cic:/CoRN/ftc/MoreFunctions/f.var.
+inline "cic:/CoRN/ftc/MoreFunctions/f.var".
-inline cic:/CoRN/ftc/MoreFunctions/contF.var.
+inline "cic:/CoRN/ftc/MoreFunctions/contF.var".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_Sum0.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_Sum0.con".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_Sum.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_Sum.con".
(* UNEXPORTED
End Sums.
%\end{convention}%
*)
-inline cic:/CoRN/ftc/MoreFunctions/I.var.
+inline "cic:/CoRN/ftc/MoreFunctions/I.var".
-inline cic:/CoRN/ftc/MoreFunctions/pI.var.
+inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
-inline cic:/CoRN/ftc/MoreFunctions/F.var.
+inline "cic:/CoRN/ftc/MoreFunctions/F.var".
-inline cic:/CoRN/ftc/MoreFunctions/G.var.
+inline "cic:/CoRN/ftc/MoreFunctions/G.var".
-inline cic:/CoRN/ftc/MoreFunctions/H.var.
+inline "cic:/CoRN/ftc/MoreFunctions/H.var".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_wdl.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_wdl.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_wdr.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_wdr.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_unique.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_unique.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_imp_inc.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_inc.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_imp_inc'.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_inc'.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Continuous.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Continuous.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Continuous'.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Continuous'.con".
(* UNEXPORTED
End Basic_Properties.
Section More_Results.
*)
-inline cic:/CoRN/ftc/MoreFunctions/I.var.
+inline "cic:/CoRN/ftc/MoreFunctions/I.var".
-inline cic:/CoRN/ftc/MoreFunctions/pI.var.
+inline "cic:/CoRN/ftc/MoreFunctions/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.
+inline "cic:/CoRN/ftc/MoreFunctions/F.var".
-inline cic:/CoRN/ftc/MoreFunctions/F'.var.
+inline "cic:/CoRN/ftc/MoreFunctions/F'.var".
-inline cic:/CoRN/ftc/MoreFunctions/G.var.
+inline "cic:/CoRN/ftc/MoreFunctions/G.var".
-inline cic:/CoRN/ftc/MoreFunctions/G'.var.
+inline "cic:/CoRN/ftc/MoreFunctions/G'.var".
-inline cic:/CoRN/ftc/MoreFunctions/derF.var.
+inline "cic:/CoRN/ftc/MoreFunctions/derF.var".
-inline cic:/CoRN/ftc/MoreFunctions/derG.var.
+inline "cic:/CoRN/ftc/MoreFunctions/derG.var".
-inline cic:/CoRN/ftc/MoreFunctions/included_imp_Derivative.con.
+inline "cic:/CoRN/ftc/MoreFunctions/included_imp_Derivative.con".
-inline cic:/CoRN/ftc/MoreFunctions/Included_imp_Derivative.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Included_imp_Derivative.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_const.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_const.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_id.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_id.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_plus.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_plus.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_inv.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_inv.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_minus.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_minus.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_mult.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_mult.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_scal.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_scal.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_nth.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_nth.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_recip.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_recip.con".
(* UNEXPORTED
End More_Results.
Section More_Corollaries.
*)
-inline cic:/CoRN/ftc/MoreFunctions/I.var.
+inline "cic:/CoRN/ftc/MoreFunctions/I.var".
-inline cic:/CoRN/ftc/MoreFunctions/pI.var.
+inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
-inline cic:/CoRN/ftc/MoreFunctions/F.var.
+inline "cic:/CoRN/ftc/MoreFunctions/F.var".
-inline cic:/CoRN/ftc/MoreFunctions/F'.var.
+inline "cic:/CoRN/ftc/MoreFunctions/F'.var".
-inline cic:/CoRN/ftc/MoreFunctions/G.var.
+inline "cic:/CoRN/ftc/MoreFunctions/G.var".
-inline cic:/CoRN/ftc/MoreFunctions/G'.var.
+inline "cic:/CoRN/ftc/MoreFunctions/G'.var".
-inline cic:/CoRN/ftc/MoreFunctions/derF.var.
+inline "cic:/CoRN/ftc/MoreFunctions/derF.var".
-inline cic:/CoRN/ftc/MoreFunctions/derG.var.
+inline "cic:/CoRN/ftc/MoreFunctions/derG.var".
(* begin show *)
-inline cic:/CoRN/ftc/MoreFunctions/Gbnd.var.
+inline "cic:/CoRN/ftc/MoreFunctions/Gbnd.var".
(* end show *)
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_div.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_div.con".
(* UNEXPORTED
End More_Corollaries.
Section More_Sums.
*)
-inline cic:/CoRN/ftc/MoreFunctions/I.var.
+inline "cic:/CoRN/ftc/MoreFunctions/I.var".
-inline cic:/CoRN/ftc/MoreFunctions/pI.var.
+inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_Sumx.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_Sumx.con".
(* begin show *)
-inline cic:/CoRN/ftc/MoreFunctions/f.var.
+inline "cic:/CoRN/ftc/MoreFunctions/f.var".
-inline cic:/CoRN/ftc/MoreFunctions/f'.var.
+inline "cic:/CoRN/ftc/MoreFunctions/f'.var".
-inline cic:/CoRN/ftc/MoreFunctions/derF.var.
+inline "cic:/CoRN/ftc/MoreFunctions/derF.var".
(* end show *)
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_Sum0.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_Sum0.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_Sum.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_Sum.con".
(* UNEXPORTED
End More_Sums.
Mutatis mutandis for differentiability.
*)
-inline cic:/CoRN/ftc/MoreFunctions/I.var.
+inline "cic:/CoRN/ftc/MoreFunctions/I.var".
-inline cic:/CoRN/ftc/MoreFunctions/pI.var.
+inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_imp_inc.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_imp_inc.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Diffble.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Diffble.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_wd.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_wd.con".
-inline cic:/CoRN/ftc/MoreFunctions/F.var.
+inline "cic:/CoRN/ftc/MoreFunctions/F.var".
-inline cic:/CoRN/ftc/MoreFunctions/G.var.
+inline "cic:/CoRN/ftc/MoreFunctions/G.var".
-inline cic:/CoRN/ftc/MoreFunctions/diffF.var.
+inline "cic:/CoRN/ftc/MoreFunctions/diffF.var".
-inline cic:/CoRN/ftc/MoreFunctions/diffG.var.
+inline "cic:/CoRN/ftc/MoreFunctions/diffG.var".
(*#*
%\begin{convention}% Assume [F] and [G] are differentiable in [I].
%\end{convention}%
*)
-inline cic:/CoRN/ftc/MoreFunctions/included_imp_Diffble.con.
+inline "cic:/CoRN/ftc/MoreFunctions/included_imp_Diffble.con".
-inline cic:/CoRN/ftc/MoreFunctions/Included_imp_Diffble.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Included_imp_Diffble.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_const.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_const.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_id.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_id.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_plus.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_plus.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_inv.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_inv.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_minus.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_minus.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_mult.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_mult.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_nth.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_nth.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_scal.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_scal.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_recip.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_recip.con".
(* UNEXPORTED
End Diffble_Basic_Properties.
Section Diffble_Corollaries.
*)
-inline cic:/CoRN/ftc/MoreFunctions/I.var.
+inline "cic:/CoRN/ftc/MoreFunctions/I.var".
-inline cic:/CoRN/ftc/MoreFunctions/pI.var.
+inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
-inline cic:/CoRN/ftc/MoreFunctions/F.var.
+inline "cic:/CoRN/ftc/MoreFunctions/F.var".
-inline cic:/CoRN/ftc/MoreFunctions/G.var.
+inline "cic:/CoRN/ftc/MoreFunctions/G.var".
-inline cic:/CoRN/ftc/MoreFunctions/diffF.var.
+inline "cic:/CoRN/ftc/MoreFunctions/diffF.var".
-inline cic:/CoRN/ftc/MoreFunctions/diffG.var.
+inline "cic:/CoRN/ftc/MoreFunctions/diffG.var".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_div.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_div.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_Sum0.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Sum0.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_Sumx.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Sumx.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_Sum.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Sum.con".
(* UNEXPORTED
End Diffble_Corollaries.
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.
+inline "cic:/CoRN/ftc/MoreFunctions/I.var".
-inline cic:/CoRN/ftc/MoreFunctions/pI.var.
+inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
(* UNEXPORTED
Section Definitions.
%\end{convention}%
*)
-inline cic:/CoRN/ftc/MoreFunctions/n.var.
+inline "cic:/CoRN/ftc/MoreFunctions/n.var".
-inline cic:/CoRN/ftc/MoreFunctions/F.var.
+inline "cic:/CoRN/ftc/MoreFunctions/F.var".
-inline cic:/CoRN/ftc/MoreFunctions/diffF.var.
+inline "cic:/CoRN/ftc/MoreFunctions/diffF.var".
-inline cic:/CoRN/ftc/MoreFunctions/N_Deriv_fun.con.
+inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv_fun.con".
-inline cic:/CoRN/ftc/MoreFunctions/N_Deriv_char
- (* begin hide *).con.
+inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv_char
+ (* begin hide *).con".
(* end hide *)
-inline cic:/CoRN/ftc/MoreFunctions/N_Deriv_strext.con.
+inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv_strext.con".
-inline cic:/CoRN/ftc/MoreFunctions/N_Deriv_wd.con.
+inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv_wd.con".
-inline cic:/CoRN/ftc/MoreFunctions/N_Deriv.con.
+inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv.con".
(* UNEXPORTED
End Definitions.
All the usual results hold.
*)
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_n_wd.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_n_wd.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_wdr.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_wdr.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_wdl.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_wdl.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_unique.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_unique.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_n_imp_Diffble.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_n_imp_Diffble.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Diffble.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Diffble.con".
-inline cic:/CoRN/ftc/MoreFunctions/le_imp_Diffble_n.con.
+inline "cic:/CoRN/ftc/MoreFunctions/le_imp_Diffble_n.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_n_imp_le.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_n_imp_le.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_n_imp_inc.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_n_imp_inc.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Diffble_n.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Diffble_n.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_inc.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_inc.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_inc'.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_inc'.con".
-inline cic:/CoRN/ftc/MoreFunctions/included_imp_Derivative_n.con.
+inline "cic:/CoRN/ftc/MoreFunctions/included_imp_Derivative_n.con".
-inline cic:/CoRN/ftc/MoreFunctions/included_imp_Diffble_n.con.
+inline "cic:/CoRN/ftc/MoreFunctions/included_imp_Diffble_n.con".
-inline cic:/CoRN/ftc/MoreFunctions/Included_imp_Derivative_n.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Included_imp_Derivative_n.con".
-inline cic:/CoRN/ftc/MoreFunctions/Included_imp_Diffble_n.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Included_imp_Diffble_n.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_plus.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_plus.con".
(* UNEXPORTED
End Basic_Results.
Some new results hold, too:
*)
-inline cic:/CoRN/ftc/MoreFunctions/N_Deriv_Feq.con.
+inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv_Feq.con".
-inline cic:/CoRN/ftc/MoreFunctions/N_Deriv_lemma.con.
+inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv_lemma.con".
-inline cic:/CoRN/ftc/MoreFunctions/N_Deriv_S.con.
+inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv_S.con".
-inline cic:/CoRN/ftc/MoreFunctions/N_Deriv_plus.con.
+inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv_plus.con".
(*#*
Some useful characterization results.
*)
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_O.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_O.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_Sn.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_Sn.con".
(* UNEXPORTED
End More_Results.
As a special case we get a differentiation operator%\ldots%#...#
*)
-inline cic:/CoRN/ftc/MoreFunctions/F.var.
+inline "cic:/CoRN/ftc/MoreFunctions/F.var".
(* begin show *)
-inline cic:/CoRN/ftc/MoreFunctions/diffF.var.
+inline "cic:/CoRN/ftc/MoreFunctions/diffF.var".
(* end show *)
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_imp_Diffble_n.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_imp_Diffble_n.con".
-inline cic:/CoRN/ftc/MoreFunctions/Deriv.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Deriv.con".
(* UNEXPORTED
End Derivating_Diffble.
%\ldots%#...# for which the expected property also holds.
*)
-inline cic:/CoRN/ftc/MoreFunctions/Deriv_lemma.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Deriv_lemma.con".
(*#*
Some more interesting properties.
*)
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_1.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_1.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_chain.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_chain.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Continuous.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Continuous.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Continuous'.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Continuous'.con".
(* UNEXPORTED
End Corollaries.