X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fcontribs%2FCoRN-Decl%2Fmetrics%2FCMetricSpaces.ma;fp=matita%2Fcontribs%2FCoRN-Decl%2Fmetrics%2FCMetricSpaces.ma;h=45f6ff0c6e98416aba0c5c1878da32aad358db4d;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/matita/contribs/CoRN-Decl/metrics/CMetricSpaces.ma b/matita/contribs/CoRN-Decl/metrics/CMetricSpaces.ma new file mode 100644 index 000000000..45f6ff0c6 --- /dev/null +++ b/matita/contribs/CoRN-Decl/metrics/CMetricSpaces.ma @@ -0,0 +1,205 @@ +(**************************************************************************) +(* ___ *) +(* ||M|| *) +(* ||A|| A project by Andrea Asperti *) +(* ||T|| *) +(* ||I|| Developers: *) +(* ||T|| The HELM team. *) +(* ||A|| http://helm.cs.unibo.it *) +(* \ / *) +(* \ / This file is distributed under the terms of the *) +(* v GNU General Public License Version 2 *) +(* *) +(**************************************************************************) + +(* This file was automatically generated: do not edit *********************) + +set "baseuri" "cic:/matita/CoRN-Decl/metrics/CMetricSpaces". + +include "CoRN.ma". + +(* $Id: CMetricSpaces.v,v 1.4 2004/04/23 10:01:01 lcf Exp $ *) + +include "metrics/Prod_Sub.ma". + +include "metrics/Equiv.ma". + +(* UNEXPORTED +Section Definition_MS +*) + +(*#* **Definition of Metric Space +*) + +inline "cic:/CoRN/metrics/CMetricSpaces/CMetricSpace.ind". + +coercion cic:/matita/CoRN-Decl/metrics/CMetricSpaces/scms_crr.con 0 (* compounds *). + +(* UNEXPORTED +End Definition_MS +*) + +(* UNEXPORTED +Section MS_basics +*) + +(*#* **Metric Space basics +*) + +inline "cic:/CoRN/metrics/CMetricSpaces/d_CMetricSpace_apdiag_imp_grzero.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/d_zero_imp_eq.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/is_CMetricSpace_diag_zero.con". + +(* UNEXPORTED +End MS_basics +*) + +(* UNEXPORTED +Section prodandsub +*) + +(*#* **Product-Metric-Spaces and Sub-Metric-Spaces +*) + +(*#* +The product of two metric spaces is again a metric space. +*) + +inline "cic:/CoRN/metrics/CMetricSpaces/Prod0CMetricSpaces_apdiag_grzero.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/Prod0CMetricSpace.con". + +(*#* +A subspace of a metric space is again a metric space. +*) + +(* UNEXPORTED +Implicit Arguments SubPsMetricSpace [X]. +*) + +inline "cic:/CoRN/metrics/CMetricSpaces/SubMetricSpace_apdiag_grzero.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/SubMetricSpace.con". + +(* UNEXPORTED +Implicit Arguments SubMetricSpace [X]. +*) + +(* UNEXPORTED +End prodandsub +*) + +(* UNEXPORTED +Section Zeroff +*) + +(*#* **Pseudo Metric Spaces vs Metric Spaces +*) + +(*#* +Not all pseudo metric spaces are a metric space: +*) + +inline "cic:/CoRN/metrics/CMetricSpaces/zf_nis_CMetricSpace.con". + +(*#* +But a pseudo metric space induces a metric space: +*) + +inline "cic:/CoRN/metrics/CMetricSpaces/metric_ap.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/metric_eq.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/metric_ap_irreflexive.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/metric_ap_symmetric.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/metric_ap_cotransitive.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/metric_ap_tight.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/Metric_CSet_is_CSetoid.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/Metric_CSetoid.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/metric_d.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/metric_d_strext.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/Metric_d.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/Metric_d_com.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/Metric_d_nneg.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/Metric_d_pos_imp_ap.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/Metric_d_tri_ineq.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/QuotientCSetoid_is_CPsMetricSpace.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/QuotientCPsMetricSpace.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/Metric_d_apdiag_grzero.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/QuotientCMetricSpace.con". + +(*#* +Some pseudo metric spaces already are a metric space: +*) + +inline "cic:/CoRN/metrics/CMetricSpaces/dIR_apdiag_grzero.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/IR_as_CMetricSpace.con". + +(*#* +In that case the induced metric space is equivalent to the original one: +*) + +inline "cic:/CoRN/metrics/CMetricSpaces/emb.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/emb_strext.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/Emb.con". + +inline "cic:/CoRN/metrics/CMetricSpaces/Quotient_pres_CMetricSpace.con". + +(* UNEXPORTED +End Zeroff +*) + +(* UNEXPORTED +Section Limitt +*) + +(*#* **Limit +*) + +(*#* +A sequence in a metric space has at most one limit. +*) + +(* UNEXPORTED +Implicit Arguments MSseqLimit [X]. +*) + +(* begin hide *) + +inline "cic:/CoRN/metrics/CMetricSpaces/nz.con". + +(* end hide *) + +(* begin hide *) + +inline "cic:/CoRN/metrics/CMetricSpaces/d_wd.con". + +(* end hide *) + +inline "cic:/CoRN/metrics/CMetricSpaces/unique_MSseqLim.con". + +(* UNEXPORTED +End Limitt +*) +