X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fcontribs%2FCoRN-Decl%2Fftc%2FMoreFunctions.ma;h=4d7622ba2318fe4ae14baa440efc243b20854a5c;hb=2951babfd31047ac057714130157da2bc36e906e;hp=71333c0bd57b5c54447a4c2aca03940c51895f95;hpb=52206fa1c090fcdc8386ec8d7e88beca089c7e39;p=helm.git diff --git a/matita/contribs/CoRN-Decl/ftc/MoreFunctions.ma b/matita/contribs/CoRN-Decl/ftc/MoreFunctions.ma index 71333c0bd..4d7622ba2 100644 --- a/matita/contribs/CoRN-Decl/ftc/MoreFunctions.ma +++ b/matita/contribs/CoRN-Decl/ftc/MoreFunctions.ma @@ -29,7 +29,7 @@ Opaque Min Max. *) (* UNEXPORTED -Section Basic_Results. +Section Basic_Results *) (*#* *More about Functions @@ -44,7 +44,7 @@ arbitrary intervals. **Continuity *) -inline "cic:/CoRN/ftc/MoreFunctions/I.var". +alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Basic_Results/I.var". (*#* Trivial stuff. @@ -57,17 +57,17 @@ inline "cic:/CoRN/ftc/MoreFunctions/Continuous_imp_inc.con". %\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 *) @@ -78,7 +78,7 @@ inline "cic:/CoRN/ftc/MoreFunctions/FNorm.con". inline "cic:/CoRN/ftc/MoreFunctions/FNorm_bnd_AbsIR.con". (* UNEXPORTED -End Basic_Results. +End Basic_Results *) (* UNEXPORTED @@ -86,26 +86,26 @@ Hint Resolve Continuous_imp_inc: included. *) (* 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 *) @@ -134,7 +134,7 @@ inline "cic:/CoRN/ftc/MoreFunctions/Continuous_abs.con". inline "cic:/CoRN/ftc/MoreFunctions/Continuous_recip.con". (* UNEXPORTED -End Other_Results. +End Other_Results *) (* UNEXPORTED @@ -148,27 +148,27 @@ Hint Immediate included_imp_Continuous Included_imp_Continuous: continuous. *) (* 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 @@ -176,10 +176,10 @@ Hint Resolve Continuous_div: continuous. *) (* 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". @@ -188,16 +188,16 @@ 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 @@ -205,7 +205,7 @@ Hint Resolve Continuous_Sum0 Continuous_Sumx Continuous_Sum: continuous. *) (* UNEXPORTED -Section Basic_Properties. +Section Basic_Properties *) (*#* **Derivative @@ -216,15 +216,15 @@ Derivative is not that much different. %\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". @@ -241,7 +241,7 @@ inline "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Continuous.con". inline "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Continuous'.con". (* UNEXPORTED -End Basic_Properties. +End Basic_Properties *) (* UNEXPORTED @@ -254,29 +254,29 @@ Hint Immediate Derivative_imp_Continuous Derivative_imp_Continuous': *) (* 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". @@ -301,58 +301,58 @@ inline "cic:/CoRN/ftc/MoreFunctions/Derivative_nth.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 *) @@ -361,11 +361,11 @@ inline "cic:/CoRN/ftc/MoreFunctions/Derivative_Sum0.con". 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 @@ -373,9 +373,9 @@ Section Diffble_Basic_Properties. 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". @@ -383,13 +383,13 @@ inline "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Diffble.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]. @@ -419,7 +419,7 @@ inline "cic:/CoRN/ftc/MoreFunctions/Diffble_scal.con". inline "cic:/CoRN/ftc/MoreFunctions/Diffble_recip.con". (* UNEXPORTED -End Diffble_Basic_Properties. +End Diffble_Basic_Properties *) (* UNEXPORTED @@ -427,20 +427,20 @@ Hint Immediate Diffble_imp_inc: included. *) (* 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". @@ -451,11 +451,11 @@ inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Sumx.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 @@ -463,12 +463,12 @@ Section 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 *) (*#* @@ -476,11 +476,11 @@ 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". @@ -496,11 +496,11 @@ inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv_wd.con". inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv.con". (* UNEXPORTED -End Definitions. +End Definitions *) (* UNEXPORTED -Section Basic_Results. +Section Basic_Results *) (*#* @@ -542,11 +542,11 @@ inline "cic:/CoRN/ftc/MoreFunctions/Included_imp_Diffble_n.con". inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_plus.con". (* UNEXPORTED -End Basic_Results. +End Basic_Results *) (* UNEXPORTED -Section More_Results. +Section More_Results *) (*#* @@ -570,22 +570,22 @@ inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_O.con". 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 *) @@ -594,11 +594,11 @@ inline "cic:/CoRN/ftc/MoreFunctions/Diffble_imp_Diffble_n.con". inline "cic:/CoRN/ftc/MoreFunctions/Deriv.con". (* UNEXPORTED -End Derivating_Diffble. +End Derivating_Diffble *) (* UNEXPORTED -Section Corollaries. +Section Corollaries *) (*#* @@ -620,11 +620,11 @@ inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Continuous.con". inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Continuous'.con". (* UNEXPORTED -End Corollaries. +End Corollaries *) (* UNEXPORTED -End Nth_Derivative. +End Nth_Derivative *) (* UNEXPORTED