(*#* **Metric Space basics
*)
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/d_CMetricSpace_apdiag_imp_grzero.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/d_CMetricSpace_apdiag_imp_grzero.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/d_zero_imp_eq.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/d_zero_imp_eq.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/is_CMetricSpace_diag_zero.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/is_CMetricSpace_diag_zero.con" as lemma.
(* UNEXPORTED
End MS_basics
The product of two metric spaces is again a metric space.
*)
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/Prod0CMetricSpaces_apdiag_grzero.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/Prod0CMetricSpaces_apdiag_grzero.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/Prod0CMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/Prod0CMetricSpace.con" as definition.
(*#*
A subspace of a metric space is again a metric space.
Implicit Arguments SubPsMetricSpace [X].
*)
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/SubMetricSpace_apdiag_grzero.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/SubMetricSpace_apdiag_grzero.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/SubMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/SubMetricSpace.con" as definition.
(* UNEXPORTED
Implicit Arguments SubMetricSpace [X].
Not all pseudo metric spaces are a metric space:
*)
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/zf_nis_CMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/zf_nis_CMetricSpace.con" as lemma.
(*#*
But a pseudo metric space induces a metric space:
*)
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap.con" as definition.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_eq.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_eq.con" as definition.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap_irreflexive.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap_irreflexive.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap_symmetric.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap_symmetric.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap_cotransitive.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap_cotransitive.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap_tight.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap_tight.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_CSet_is_CSetoid.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_CSet_is_CSetoid.con" as definition.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_CSetoid.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_CSetoid.con" as definition.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_d.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_d.con" as definition.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_d_strext.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_d_strext.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d.con" as definition.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_com.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_com.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_nneg.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_nneg.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_pos_imp_ap.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_pos_imp_ap.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_tri_ineq.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_tri_ineq.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/QuotientCSetoid_is_CPsMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/QuotientCSetoid_is_CPsMetricSpace.con" as definition.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/QuotientCPsMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/QuotientCPsMetricSpace.con" as definition.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_apdiag_grzero.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_apdiag_grzero.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/QuotientCMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/QuotientCMetricSpace.con" as definition.
(*#*
Some pseudo metric spaces already are a metric space:
*)
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/dIR_apdiag_grzero.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/dIR_apdiag_grzero.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/IR_as_CMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/IR_as_CMetricSpace.con" as definition.
(*#*
In that case the induced metric space is equivalent to the original one:
*)
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/emb.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/emb.con" as definition.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/emb_strext.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/emb_strext.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/Emb.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/Emb.con" as definition.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/Quotient_pres_CMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/Quotient_pres_CMetricSpace.con" as lemma.
(* UNEXPORTED
End Zeroff
(* begin hide *)
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/nz.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/nz.con" as lemma.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/d_wd.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/d_wd.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/unique_MSseqLim.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/unique_MSseqLim.con" as lemma.
(* UNEXPORTED
End Limitt