X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FCoRN-Decl%2Fmetrics%2FContFunctions.ma;h=504a7d7a064111f114f4d29d9c6a365a65b15969;hb=HEAD;hp=b4fa706898f738223f65cab96de232d6827f79c1;hpb=3199f2a8428b5d19a3a803c1b03d9f90e4120f74;p=helm.git diff --git a/helm/software/matita/contribs/CoRN-Decl/metrics/ContFunctions.ma b/helm/software/matita/contribs/CoRN-Decl/metrics/ContFunctions.ma index b4fa70689..504a7d7a0 100644 --- a/helm/software/matita/contribs/CoRN-Decl/metrics/ContFunctions.ma +++ b/helm/software/matita/contribs/CoRN-Decl/metrics/ContFunctions.ma @@ -16,14 +16,14 @@ set "baseuri" "cic:/matita/CoRN-Decl/metrics/ContFunctions". +include "CoRN.ma". + (* $Id: ContFunctions.v,v 1.3 2004/04/23 10:01:02 lcf Exp $ *) -(* INCLUDE -CPseudoMSpaces -*) +include "metrics/CPseudoMSpaces.ma". (* UNEXPORTED -Section Continuous_functions. +Section Continuous_functions *) (*#* **Continuous functions, uniformly continuous functions and Lipschitz functions @@ -32,30 +32,30 @@ Let [A] and [B] be pseudo metric spaces. %\end{convention}% *) -inline cic:/CoRN/metrics/ContFunctions/A.var. +alias id "A" = "cic:/CoRN/metrics/ContFunctions/Continuous_functions/A.var". -inline cic:/CoRN/metrics/ContFunctions/B.var. +alias id "B" = "cic:/CoRN/metrics/ContFunctions/Continuous_functions/B.var". (*#* We will look at some notions of continuous functions. *) -inline cic:/CoRN/metrics/ContFunctions/continuous.con. +inline "cic:/CoRN/metrics/ContFunctions/continuous.con". -inline cic:/CoRN/metrics/ContFunctions/continuous'.con. +inline "cic:/CoRN/metrics/ContFunctions/continuous'.con". -inline cic:/CoRN/metrics/ContFunctions/uni_continuous.con. +inline "cic:/CoRN/metrics/ContFunctions/uni_continuous.con". -inline cic:/CoRN/metrics/ContFunctions/uni_continuous'.con. +inline "cic:/CoRN/metrics/ContFunctions/uni_continuous'.con". -inline cic:/CoRN/metrics/ContFunctions/uni_continuous''.con. +inline "cic:/CoRN/metrics/ContFunctions/uni_continuous''.con". -inline cic:/CoRN/metrics/ContFunctions/lipschitz.con. +inline "cic:/CoRN/metrics/ContFunctions/lipschitz.con". -inline cic:/CoRN/metrics/ContFunctions/lipschitz'.con. +inline "cic:/CoRN/metrics/ContFunctions/lipschitz'.con". (* UNEXPORTED -End Continuous_functions. +End Continuous_functions *) (* UNEXPORTED @@ -87,44 +87,44 @@ Implicit Arguments lipschitz' [A B]. *) (* UNEXPORTED -Section Lemmas. +Section Lemmas *) (* begin hide *) -inline cic:/CoRN/metrics/ContFunctions/nexp_power.con. +inline "cic:/CoRN/metrics/ContFunctions/nexp_power.con". (* end hide *) -inline cic:/CoRN/metrics/ContFunctions/continuous_imp_continuous'.con. +inline "cic:/CoRN/metrics/ContFunctions/continuous_imp_continuous'.con". -inline cic:/CoRN/metrics/ContFunctions/continuous'_imp_continuous.con. +inline "cic:/CoRN/metrics/ContFunctions/continuous'_imp_continuous.con". -inline cic:/CoRN/metrics/ContFunctions/uni_continuous_imp_uni_continuous'.con. +inline "cic:/CoRN/metrics/ContFunctions/uni_continuous_imp_uni_continuous'.con". -inline cic:/CoRN/metrics/ContFunctions/uni_continuous'_imp_uni_continuous.con. +inline "cic:/CoRN/metrics/ContFunctions/uni_continuous'_imp_uni_continuous.con". -inline cic:/CoRN/metrics/ContFunctions/uni_continuous'_imp_uni_continuous''.con. +inline "cic:/CoRN/metrics/ContFunctions/uni_continuous'_imp_uni_continuous''.con". -inline cic:/CoRN/metrics/ContFunctions/lipschitz_imp_lipschitz'.con. +inline "cic:/CoRN/metrics/ContFunctions/lipschitz_imp_lipschitz'.con". -inline cic:/CoRN/metrics/ContFunctions/lipschitz'_imp_lipschitz.con. +inline "cic:/CoRN/metrics/ContFunctions/lipschitz'_imp_lipschitz.con". (*#* Every uniformly continuous function is continuous and every Lipschitz function is uniformly continuous. *) -inline cic:/CoRN/metrics/ContFunctions/uni_continuous_imp_continuous.con. +inline "cic:/CoRN/metrics/ContFunctions/uni_continuous_imp_continuous.con". -inline cic:/CoRN/metrics/ContFunctions/lipschitz_imp_uni_continuous.con. +inline "cic:/CoRN/metrics/ContFunctions/lipschitz_imp_uni_continuous.con". (* UNEXPORTED -End Lemmas. +End Lemmas *) (* UNEXPORTED -Section Identity. +Section Identity *) (*#* **Identity @@ -135,18 +135,18 @@ The identity function is Lipschitz. Hence it is uniformly continuous and continuous. *) -inline cic:/CoRN/metrics/ContFunctions/id_is_lipschitz.con. +inline "cic:/CoRN/metrics/ContFunctions/id_is_lipschitz.con". -inline cic:/CoRN/metrics/ContFunctions/id_is_uni_continuous.con. +inline "cic:/CoRN/metrics/ContFunctions/id_is_uni_continuous.con". -inline cic:/CoRN/metrics/ContFunctions/id_is_continuous.con. +inline "cic:/CoRN/metrics/ContFunctions/id_is_continuous.con". (* UNEXPORTED -End Identity. +End Identity *) (* UNEXPORTED -Section Constant. +Section Constant *) (*#* **Constant functions @@ -160,22 +160,22 @@ Any constant function is Lipschitz. Hence it is uniformly continuous and continuous. *) -inline cic:/CoRN/metrics/ContFunctions/B.var. +alias id "B" = "cic:/CoRN/metrics/ContFunctions/Constant/B.var". -inline cic:/CoRN/metrics/ContFunctions/X.var. +alias id "X" = "cic:/CoRN/metrics/ContFunctions/Constant/X.var". -inline cic:/CoRN/metrics/ContFunctions/const_fun_is_lipschitz.con. +inline "cic:/CoRN/metrics/ContFunctions/const_fun_is_lipschitz.con". -inline cic:/CoRN/metrics/ContFunctions/const_fun_is_uni_continuous.con. +inline "cic:/CoRN/metrics/ContFunctions/const_fun_is_uni_continuous.con". -inline cic:/CoRN/metrics/ContFunctions/const_fun_is_continuous.con. +inline "cic:/CoRN/metrics/ContFunctions/const_fun_is_continuous.con". (* UNEXPORTED -End Constant. +End Constant *) (* UNEXPORTED -Section Composition. +Section Composition *) (*#* **Composition @@ -191,58 +191,58 @@ The composition of two Lipschitz/uniformly continous/continuous functions is again Lipschitz/uniformly continuous/continuous. *) -inline cic:/CoRN/metrics/ContFunctions/X.var. +alias id "X" = "cic:/CoRN/metrics/ContFunctions/Composition/X.var". -inline cic:/CoRN/metrics/ContFunctions/B.var. +alias id "B" = "cic:/CoRN/metrics/ContFunctions/Composition/B.var". -inline cic:/CoRN/metrics/ContFunctions/f.var. +alias id "f" = "cic:/CoRN/metrics/ContFunctions/Composition/f.var". -inline cic:/CoRN/metrics/ContFunctions/C.var. +alias id "C" = "cic:/CoRN/metrics/ContFunctions/Composition/C.var". -inline cic:/CoRN/metrics/ContFunctions/g.var. +alias id "g" = "cic:/CoRN/metrics/ContFunctions/Composition/g.var". -inline cic:/CoRN/metrics/ContFunctions/comp_resp_lipschitz.con. +inline "cic:/CoRN/metrics/ContFunctions/comp_resp_lipschitz.con". -inline cic:/CoRN/metrics/ContFunctions/comp_resp_uni_continuous.con. +inline "cic:/CoRN/metrics/ContFunctions/comp_resp_uni_continuous.con". -inline cic:/CoRN/metrics/ContFunctions/comp_resp_continuous.con. +inline "cic:/CoRN/metrics/ContFunctions/comp_resp_continuous.con". (* UNEXPORTED -End Composition. +End Composition *) (* UNEXPORTED -Section Limit. +Section Limit *) (*#* **Limit *) -inline cic:/CoRN/metrics/ContFunctions/MSseqLimit.con. +inline "cic:/CoRN/metrics/ContFunctions/MSseqLimit.con". (* UNEXPORTED Implicit Arguments MSseqLimit [X]. *) -inline cic:/CoRN/metrics/ContFunctions/MSseqLimit'.con. +inline "cic:/CoRN/metrics/ContFunctions/MSseqLimit'.con". (* UNEXPORTED Implicit Arguments MSseqLimit' [X]. *) -inline cic:/CoRN/metrics/ContFunctions/MSseqLimit_imp_MSseqLimit'.con. +inline "cic:/CoRN/metrics/ContFunctions/MSseqLimit_imp_MSseqLimit'.con". -inline cic:/CoRN/metrics/ContFunctions/MSseqLimit'_imp_MSseqLimit.con. +inline "cic:/CoRN/metrics/ContFunctions/MSseqLimit'_imp_MSseqLimit.con". -inline cic:/CoRN/metrics/ContFunctions/seqcontinuous'.con. +inline "cic:/CoRN/metrics/ContFunctions/seqcontinuous'.con". (* UNEXPORTED Implicit Arguments seqcontinuous' [A B]. *) -inline cic:/CoRN/metrics/ContFunctions/continuous'_imp_seqcontinuous'.con. +inline "cic:/CoRN/metrics/ContFunctions/continuous'_imp_seqcontinuous'.con". (* UNEXPORTED -End Limit. +End Limit *)