X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fcontribs%2FCoRN-Decl%2Fftc%2FContinuity.ma;h=6f884860a89430f04a5213043618cb2701204196;hb=0a9ed4329c069d2e06902934b6d1d58d3690959c;hp=113b47653b890d837e3230659ae32cddaaf7b0fb;hpb=f104e234238586ac846881feb30e1b56a509cfd3;p=helm.git diff --git a/matita/contribs/CoRN-Decl/ftc/Continuity.ma b/matita/contribs/CoRN-Decl/ftc/Continuity.ma index 113b47653..6f884860a 100644 --- a/matita/contribs/CoRN-Decl/ftc/Continuity.ma +++ b/matita/contribs/CoRN-Decl/ftc/Continuity.ma @@ -27,7 +27,7 @@ include "reals/NRootIR.ma". include "ftc/FunctSums.ma". (* UNEXPORTED -Section Definitions_and_Basic_Results. +Section Definitions_and_Basic_Results *) (*#* *Continuity @@ -54,23 +54,23 @@ respectively [P, Q] and [R]. Here we define continuity and prove some basic properties of continuous functions. *) -inline "cic:/CoRN/ftc/Continuity/a.var". +alias id "a" = "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/a.var". -inline "cic:/CoRN/ftc/Continuity/b.var". +alias id "b" = "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/b.var". -inline "cic:/CoRN/ftc/Continuity/Hab.var". +alias id "Hab" = "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/Hab.var". (* begin hide *) -inline "cic:/CoRN/ftc/Continuity/I.con". +inline "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/I.con" "Definitions_and_Basic_Results__". (* end hide *) -inline "cic:/CoRN/ftc/Continuity/F.var". +alias id "F" = "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/F.var". (* begin hide *) -inline "cic:/CoRN/ftc/Continuity/P.con". +inline "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/P.con" "Definitions_and_Basic_Results__". (* end hide *) @@ -88,11 +88,11 @@ inline "cic:/CoRN/ftc/Continuity/contin_prop.con". Assume [F] to be continuous in [I]. Then it has a least upper bound and a greater lower bound on [I]. *) -inline "cic:/CoRN/ftc/Continuity/contF.var". +alias id "contF" = "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/contF.var". (* begin hide *) -inline "cic:/CoRN/ftc/Continuity/Hinc'.con". +inline "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/Hinc'.con" "Definitions_and_Basic_Results__". (* end hide *) @@ -153,7 +153,7 @@ inline "cic:/CoRN/ftc/Continuity/leEq_Norm_Funct.con". inline "cic:/CoRN/ftc/Continuity/less_Norm_Funct.con". (* UNEXPORTED -End Definitions_and_Basic_Results. +End Definitions_and_Basic_Results *) (* UNEXPORTED @@ -165,7 +165,7 @@ Implicit Arguments Norm_Funct [a b Hab F]. *) (* UNEXPORTED -Section Local_Results. +Section Local_Results *) (*#* **Algebraic Properties @@ -173,33 +173,33 @@ Section Local_Results. We now state and prove some results about continuous functions. Assume that [I] is included in the domain of both [F] and [G]. *) -inline "cic:/CoRN/ftc/Continuity/a.var". +alias id "a" = "cic:/CoRN/ftc/Continuity/Local_Results/a.var". -inline "cic:/CoRN/ftc/Continuity/b.var". +alias id "b" = "cic:/CoRN/ftc/Continuity/Local_Results/b.var". -inline "cic:/CoRN/ftc/Continuity/Hab.var". +alias id "Hab" = "cic:/CoRN/ftc/Continuity/Local_Results/Hab.var". (* begin hide *) -inline "cic:/CoRN/ftc/Continuity/I.con". +inline "cic:/CoRN/ftc/Continuity/Local_Results/I.con" "Local_Results__". (* end hide *) -inline "cic:/CoRN/ftc/Continuity/F.var". +alias id "F" = "cic:/CoRN/ftc/Continuity/Local_Results/F.var". -inline "cic:/CoRN/ftc/Continuity/G.var". +alias id "G" = "cic:/CoRN/ftc/Continuity/Local_Results/G.var". (* begin hide *) -inline "cic:/CoRN/ftc/Continuity/P.con". +inline "cic:/CoRN/ftc/Continuity/Local_Results/P.con" "Local_Results__". -inline "cic:/CoRN/ftc/Continuity/Q.con". +inline "cic:/CoRN/ftc/Continuity/Local_Results/Q.con" "Local_Results__". (* end hide *) -inline "cic:/CoRN/ftc/Continuity/incF.var". +alias id "incF" = "cic:/CoRN/ftc/Continuity/Local_Results/incF.var". -inline "cic:/CoRN/ftc/Continuity/incG.var". +alias id "incG" = "cic:/CoRN/ftc/Continuity/Local_Results/incG.var". (*#* The first result does not require the function to be continuous; however, its preconditions are easily verified by continuous functions, which justifies its inclusion in this section. @@ -235,9 +235,9 @@ inline "cic:/CoRN/ftc/Continuity/Continuous_I_id.con". Assume [F] and [G] are continuous in [I]. Then functions derived from these through algebraic operations are also continuous, provided (in the case of reciprocal and division) some extra conditions are met. *) -inline "cic:/CoRN/ftc/Continuity/contF.var". +alias id "contF" = "cic:/CoRN/ftc/Continuity/Local_Results/contF.var". -inline "cic:/CoRN/ftc/Continuity/contG.var". +alias id "contG" = "cic:/CoRN/ftc/Continuity/Local_Results/contG.var". inline "cic:/CoRN/ftc/Continuity/Continuous_I_plus.con". @@ -257,16 +257,16 @@ inline "cic:/CoRN/ftc/Continuity/Continuous_I_max.con". (* begin show *) -inline "cic:/CoRN/ftc/Continuity/Hg'.var". +alias id "Hg'" = "cic:/CoRN/ftc/Continuity/Local_Results/Hg'.var". -inline "cic:/CoRN/ftc/Continuity/Hg''.var". +alias id "Hg''" = "cic:/CoRN/ftc/Continuity/Local_Results/Hg''.var". (* end show *) inline "cic:/CoRN/ftc/Continuity/Continuous_I_recip.con". (* UNEXPORTED -End Local_Results. +End Local_Results *) (* UNEXPORTED @@ -274,36 +274,36 @@ Hint Resolve contin_imp_inc: included. *) (* UNEXPORTED -Section Corolaries. +Section Corolaries *) -inline "cic:/CoRN/ftc/Continuity/a.var". +alias id "a" = "cic:/CoRN/ftc/Continuity/Corolaries/a.var". -inline "cic:/CoRN/ftc/Continuity/b.var". +alias id "b" = "cic:/CoRN/ftc/Continuity/Corolaries/b.var". -inline "cic:/CoRN/ftc/Continuity/Hab.var". +alias id "Hab" = "cic:/CoRN/ftc/Continuity/Corolaries/Hab.var". (* begin hide *) -inline "cic:/CoRN/ftc/Continuity/I.con". +inline "cic:/CoRN/ftc/Continuity/Corolaries/I.con" "Corolaries__". (* end hide *) -inline "cic:/CoRN/ftc/Continuity/F.var". +alias id "F" = "cic:/CoRN/ftc/Continuity/Corolaries/F.var". -inline "cic:/CoRN/ftc/Continuity/G.var". +alias id "G" = "cic:/CoRN/ftc/Continuity/Corolaries/G.var". (* begin hide *) -inline "cic:/CoRN/ftc/Continuity/P.con". +inline "cic:/CoRN/ftc/Continuity/Corolaries/P.con" "Corolaries__". -inline "cic:/CoRN/ftc/Continuity/Q.con". +inline "cic:/CoRN/ftc/Continuity/Corolaries/Q.con" "Corolaries__". (* end hide *) -inline "cic:/CoRN/ftc/Continuity/contF.var". +alias id "contF" = "cic:/CoRN/ftc/Continuity/Corolaries/contF.var". -inline "cic:/CoRN/ftc/Continuity/contG.var". +alias id "contG" = "cic:/CoRN/ftc/Continuity/Corolaries/contG.var". (*#* The corresponding properties for subtraction, division and @@ -322,39 +322,39 @@ inline "cic:/CoRN/ftc/Continuity/Continuous_I_min.con". inline "cic:/CoRN/ftc/Continuity/Continuous_I_abs.con". -inline "cic:/CoRN/ftc/Continuity/Hg'.var". +alias id "Hg'" = "cic:/CoRN/ftc/Continuity/Corolaries/Hg'.var". -inline "cic:/CoRN/ftc/Continuity/Hg''.var". +alias id "Hg''" = "cic:/CoRN/ftc/Continuity/Corolaries/Hg''.var". inline "cic:/CoRN/ftc/Continuity/Continuous_I_div.con". (* UNEXPORTED -End Corolaries. +End Corolaries *) (* UNEXPORTED -Section Other. +Section Other *) (* UNEXPORTED -Section Sums. +Section Sums *) (*#* We finally prove that the sum of an arbitrary family of continuous functions is still a continuous function. *) -inline "cic:/CoRN/ftc/Continuity/a.var". +alias id "a" = "cic:/CoRN/ftc/Continuity/Other/Sums/a.var". -inline "cic:/CoRN/ftc/Continuity/b.var". +alias id "b" = "cic:/CoRN/ftc/Continuity/Other/Sums/b.var". -inline "cic:/CoRN/ftc/Continuity/Hab.var". +alias id "Hab" = "cic:/CoRN/ftc/Continuity/Other/Sums/Hab.var". -inline "cic:/CoRN/ftc/Continuity/Hab'.var". +alias id "Hab'" = "cic:/CoRN/ftc/Continuity/Other/Sums/Hab'.var". (* begin hide *) -inline "cic:/CoRN/ftc/Continuity/I.con". +inline "cic:/CoRN/ftc/Continuity/Other/Sums/I.con" "Other__Sums__". (* end hide *) @@ -365,7 +365,7 @@ inline "cic:/CoRN/ftc/Continuity/Continuous_I_Sumx.con". inline "cic:/CoRN/ftc/Continuity/Continuous_I_Sum.con". (* UNEXPORTED -End Sums. +End Sums *) (*#* @@ -395,7 +395,7 @@ The value of the norm is covariant with the length of the interval. inline "cic:/CoRN/ftc/Continuity/included_imp_norm_leEq.con". (* UNEXPORTED -End Other. +End Other *) (* UNEXPORTED