helm/software/matita/contribs/procedural/CoRN/metrics/Prod_Sub.mma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 (* This file was automatically generated: do not edit *********************)
  16
  17 include "CoRN.ma".
  18
  19 (* $Id: Prod_Sub.v,v 1.4 2004/04/23 10:01:02 lcf Exp $ *)
  20
  21 include "metrics/IR_CPMSpace.ma".
  22
  23 (* UNEXPORTED
  24 Section prodpsmetrics
  25 *)
  26
  27 (*#* **Product-Pseudo-Metric-Spaces
  28 *)
  29
  30 (*#*
  31 The product metric here defined is:
  32 $ d_{prod}((a_1,b_1),(a_2,b_2)):= d_A(a_1,a_2)+d_B(b_1,b_2)$
  33 # d<SUB>prod</SUB>((a<SUB>1</SUB>,b<SUB>1</SUB>),(a<SUB>2</SUB>,b<SUB>2</SUB>)):= d<SUB>A</SUB>(a<SUB>1</SUB>,b<SUB>1</SUB>)+d<SUB>B</SUB>(b<SUB>1</SUB>,b<SUB>2</SUB>)#.
  34 This is %\emph{not}% #<I>not</I># the one used to make the metric of
  35 $\RR^{2}$ #IR<SUP>2</SUP># out of the metric of $\RR$ #IR#.
  36 *)
  37
  38 inline procedural "cic:/CoRN/metrics/Prod_Sub/dprod0.con" as definition.
  39
  40 inline procedural "cic:/CoRN/metrics/Prod_Sub/dprod0_strext.con" as lemma.
  41
  42 inline procedural "cic:/CoRN/metrics/Prod_Sub/d_prod0.con" as definition.
  43
  44 inline procedural "cic:/CoRN/metrics/Prod_Sub/prod0cpsmetricspace_is_CPsMetricSpace.con" as lemma.
  45
  46 inline procedural "cic:/CoRN/metrics/Prod_Sub/Prod0CPsMetricSpace.con" as definition.
  47
  48 (* UNEXPORTED
  49 End prodpsmetrics
  50 *)
  51
  52 (* UNEXPORTED
  53 Section subpsmetrics
  54 *)
  55
  56 (*#* **Sub-Pseudo-Metric-Spaces
  57 *)
  58
  59 (*#*
  60 The pseudo metric on a subspace $Y$ #Y# of a pseudo metric space $X$ #X# is
  61 the pseudo metric on $X$ #X# restricted to $Y$ #Y#.
  62 *)
  63
  64 inline procedural "cic:/CoRN/metrics/Prod_Sub/restr_bin_fun.con" as definition.
  65
  66 (* UNEXPORTED
  67 Implicit Arguments restr_bin_fun [X].
  68 *)
  69
  70 inline procedural "cic:/CoRN/metrics/Prod_Sub/restr_bin_fun'.con" as definition.
  71
  72 (* UNEXPORTED
  73 Implicit Arguments restr_bin_fun' [X].
  74 *)
  75
  76 inline procedural "cic:/CoRN/metrics/Prod_Sub/restr_bin_fun_strext.con" as lemma.
  77
  78 inline procedural "cic:/CoRN/metrics/Prod_Sub/Build_SubCSetoid_bin_fun.con" as definition.
  79
  80 inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub.con" as definition.
  81
  82 (* UNEXPORTED
  83 Implicit Arguments dsub [X].
  84 *)
  85
  86 inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub_com.con" as lemma.
  87
  88 inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub_nneg.con" as lemma.
  89
  90 inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub_pos_imp_ap.con" as lemma.
  91
  92 inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub_tri_ineq.con" as lemma.
  93
  94 inline procedural "cic:/CoRN/metrics/Prod_Sub/is_SubPsMetricSpace.con" as definition.
  95
  96 inline procedural "cic:/CoRN/metrics/Prod_Sub/SubPsMetricSpace.con" as definition.
  97
  98 (* UNEXPORTED
  99 Implicit Arguments SubPsMetricSpace [X].
 100 *)
 101
 102 inline procedural "cic:/CoRN/metrics/Prod_Sub/from_SubPsMetricSpace.con" as definition.
 103
 104 (*#*
 105 The function [dsub'] is used in the definition of %''located''% #"located"#.
 106 It enables one to speak about a distance between an element of a
 107 pseudo metric space and a certain subspace.
 108 *)
 109
 110 inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub'.con" as definition.
 111
 112 (* UNEXPORTED
 113 Implicit Arguments dsub' [X].
 114 *)
 115
 116 inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub'_strext.con" as lemma.
 117
 118 inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub'_as_cs_fun.con" as definition.
 119
 120 (* UNEXPORTED
 121 Implicit Arguments dsub'_as_cs_fun [X].
 122 *)
 123
 124 inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub'_uni_continuous''.con" as lemma.
 125
 126 (* UNEXPORTED
 127 End subpsmetrics
 128 *)
 129