X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fcontribs%2FCoRN-Decl%2Fmetrics%2FCPMSTheory.ma;h=aef56d5a9ca6c8d9078689cfcfd2f9f25397798e;hb=d92f4fde249a95ae38360b0ce0fcaa0bd265ad8b;hp=fe04f4fb1121618cc6e78c7d8b6344af2e33ba47;hpb=0e0d5c57eb154bf20d101f09e560401434156c1d;p=helm.git diff --git a/matita/contribs/CoRN-Decl/metrics/CPMSTheory.ma b/matita/contribs/CoRN-Decl/metrics/CPMSTheory.ma index fe04f4fb1..aef56d5a9 100644 --- a/matita/contribs/CoRN-Decl/metrics/CPMSTheory.ma +++ b/matita/contribs/CoRN-Decl/metrics/CPMSTheory.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/metrics/CPMSTheory". +include "CoRN.ma". + (* $Id: CPMSTheory.v,v 1.6 2004/04/23 10:01:02 lcf Exp $ *) -(* INCLUDE -Prod_Sub -*) +include "metrics/Prod_Sub.ma". (* UNEXPORTED Section lists. @@ -37,19 +37,19 @@ finite sets of representants, instead of finite subsetoids. This seems to make the proofs a bit easier. *) -inline cic:/CoRN/metrics/CPMSTheory/MSmember.con. +inline "cic:/CoRN/metrics/CPMSTheory/MSmember.con". (* UNEXPORTED Implicit Arguments MSmember [X]. *) -inline cic:/CoRN/metrics/CPMSTheory/to_IR.con. +inline "cic:/CoRN/metrics/CPMSTheory/to_IR.con". -inline cic:/CoRN/metrics/CPMSTheory/from_IR.con. +inline "cic:/CoRN/metrics/CPMSTheory/from_IR.con". -inline cic:/CoRN/metrics/CPMSTheory/list_IR.con. +inline "cic:/CoRN/metrics/CPMSTheory/list_IR.con". -inline cic:/CoRN/metrics/CPMSTheory/is_P.con. +inline "cic:/CoRN/metrics/CPMSTheory/is_P.con". (*#* If a real number is element of a list in the above defined sense, @@ -57,14 +57,14 @@ it is an element of the list in the sense of [member], that uses the setoid equality. *) -inline cic:/CoRN/metrics/CPMSTheory/member1.con. +inline "cic:/CoRN/metrics/CPMSTheory/member1.con". (*#* The image under a certain mapping of an element of a list $l$ #l# is member of the list of images of elements of $l$ #l#. *) -inline cic:/CoRN/metrics/CPMSTheory/map_member.con. +inline "cic:/CoRN/metrics/CPMSTheory/map_member.con". (* UNEXPORTED End lists. @@ -77,13 +77,13 @@ Section loc_and_bound. (*#* **Pseudo Metric Space theory *) -inline cic:/CoRN/metrics/CPMSTheory/Re_co_do.con. +inline "cic:/CoRN/metrics/CPMSTheory/Re_co_do.con". -inline cic:/CoRN/metrics/CPMSTheory/Re_co_do_strext.con. +inline "cic:/CoRN/metrics/CPMSTheory/Re_co_do_strext.con". -inline cic:/CoRN/metrics/CPMSTheory/re_co_do.con. +inline "cic:/CoRN/metrics/CPMSTheory/re_co_do.con". -inline cic:/CoRN/metrics/CPMSTheory/re_co_do_well_def.con. +inline "cic:/CoRN/metrics/CPMSTheory/re_co_do_well_def.con". (* UNEXPORTED Implicit Arguments MSmember [X]. @@ -94,11 +94,11 @@ Again we see that the image under a certain mapping of an element of a list $l$ #l# is member of the list of images of elements of $l$ #l#. *) -inline cic:/CoRN/metrics/CPMSTheory/map_member'.con. +inline "cic:/CoRN/metrics/CPMSTheory/map_member'.con". -inline cic:/CoRN/metrics/CPMSTheory/bounded.con. +inline "cic:/CoRN/metrics/CPMSTheory/bounded.con". -inline cic:/CoRN/metrics/CPMSTheory/MStotally_bounded.con. +inline "cic:/CoRN/metrics/CPMSTheory/MStotally_bounded.con". (*#* Total boundedness is preserved under uniformly continuous mappings. @@ -108,18 +108,18 @@ Total boundedness is preserved under uniformly continuous mappings. Implicit Arguments SubPsMetricSpace [X]. *) -inline cic:/CoRN/metrics/CPMSTheory/unicon_resp_totallybounded.con. +inline "cic:/CoRN/metrics/CPMSTheory/unicon_resp_totallybounded.con". -inline cic:/CoRN/metrics/CPMSTheory/MStotallybounded_totallybounded.con. +inline "cic:/CoRN/metrics/CPMSTheory/MStotallybounded_totallybounded.con". (*#* Every image under an uniformly continuous function of an totally bounded pseudo metric space has an infimum and a supremum. *) -inline cic:/CoRN/metrics/CPMSTheory/infimum_exists.con. +inline "cic:/CoRN/metrics/CPMSTheory/infimum_exists.con". -inline cic:/CoRN/metrics/CPMSTheory/supremum_exists.con. +inline "cic:/CoRN/metrics/CPMSTheory/supremum_exists.con". (*#* A subspace $P$#P# of a pseudo metric space $X$#X# is said to be located if for all @@ -131,25 +131,25 @@ between $x$#x# and the elements of $P$#P#. Implicit Arguments dsub'_as_cs_fun [X]. *) -inline cic:/CoRN/metrics/CPMSTheory/located.con. +inline "cic:/CoRN/metrics/CPMSTheory/located.con". (* UNEXPORTED Implicit Arguments located [X]. *) -inline cic:/CoRN/metrics/CPMSTheory/located'.con. +inline "cic:/CoRN/metrics/CPMSTheory/located'.con". (* UNEXPORTED Implicit Arguments located' [X]. *) -inline cic:/CoRN/metrics/CPMSTheory/located_imp_located'.con. +inline "cic:/CoRN/metrics/CPMSTheory/located_imp_located'.con". (*#* Every totally bounded pseudo metric space is located. *) -inline cic:/CoRN/metrics/CPMSTheory/MStotally_bounded_imp_located.con. +inline "cic:/CoRN/metrics/CPMSTheory/MStotally_bounded_imp_located.con". (*#* For all $x$#x# in a pseudo metric space $X$#X#, for all located subspaces $P$#P# of $X$#X#, @@ -160,9 +160,9 @@ $d(x,y)\leq \mbox{inf}\{d(x,p)|p \in P\}+(n+1)^{-1}$ one to use the latter as an argument of [map]. *) -inline cic:/CoRN/metrics/CPMSTheory/Floc.con. +inline "cic:/CoRN/metrics/CPMSTheory/Floc.con". -inline cic:/CoRN/metrics/CPMSTheory/Flocfun.con. +inline "cic:/CoRN/metrics/CPMSTheory/Flocfun.con". (*#* A located subset $P$#P# of a totally bounded pseudo metric space $X$ @@ -170,33 +170,33 @@ A located subset $P$#P# of a totally bounded pseudo metric space $X$ bounded. *) -inline cic:/CoRN/metrics/CPMSTheory/locatedsub_totallybounded_imp_totallyboundedsub.con. +inline "cic:/CoRN/metrics/CPMSTheory/locatedsub_totallybounded_imp_totallyboundedsub.con". (*#* Here are some definitions that could come in handy: *) -inline cic:/CoRN/metrics/CPMSTheory/MSCauchy_seq.con. +inline "cic:/CoRN/metrics/CPMSTheory/MSCauchy_seq.con". (* UNEXPORTED Implicit Arguments MSseqLimit' [X]. *) -inline cic:/CoRN/metrics/CPMSTheory/MSComplete.con. +inline "cic:/CoRN/metrics/CPMSTheory/MSComplete.con". (*#* A compact pseudo metric space is a pseudo metric space which is complete and totally bounded. *) -inline cic:/CoRN/metrics/CPMSTheory/MSCompact.con. +inline "cic:/CoRN/metrics/CPMSTheory/MSCompact.con". (*#* A subset $P$#P# is %\emph{open}%#open# if for all $x$#x# in $P$#P# there exists an open sphere with centre $x$#x# that is contained in $P$#P#. *) -inline cic:/CoRN/metrics/CPMSTheory/open.con. +inline "cic:/CoRN/metrics/CPMSTheory/open.con". (* UNEXPORTED Implicit Arguments open [X]. @@ -208,7 +208,7 @@ element $x$#x# of a located pseudo metric space $X$#X# and the ele subspace $P$#P# of $X$#X#. *) -inline cic:/CoRN/metrics/CPMSTheory/infima.con. +inline "cic:/CoRN/metrics/CPMSTheory/infima.con". (* UNEXPORTED Implicit Arguments infima [X]. @@ -220,7 +220,7 @@ A non-empty totally bounded sub-pseudo-metric-space $P$#P# is said to be all points that are in some sense close to $P$#P#. *) -inline cic:/CoRN/metrics/CPMSTheory/well_contained.con. +inline "cic:/CoRN/metrics/CPMSTheory/well_contained.con". (* UNEXPORTED End loc_and_bound.