matita/contribs/CoRN-Decl/metrics/Prod_Sub.ma

   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 set "baseuri" "cic:/matita/CoRN-Decl/metrics/Prod_Sub".
  18
  19 include "CoRN.ma".
  20
  21 (* $Id: Prod_Sub.v,v 1.4 2004/04/23 10:01:02 lcf Exp $ *)
  22
  23 include "metrics/IR_CPMSpace.ma".
  24
  25 (* UNEXPORTED
  26 Section prodpsmetrics
  27 *)
  28
  29 (*#* **Product-Pseudo-Metric-Spaces
  30 *)
  31
  32 (*#*
  33 The product metric here defined is:
  34 $ d_{prod}((a_1,b_1),(a_2,b_2)):= d_A(a_1,a_2)+d_B(b_1,b_2)$
  35 # 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>)#.
  36 This is %\emph{not}% #<I>not</I># the one used to make the metric of
  37 $\RR^{2}$ #IR<SUP>2</SUP># out of the metric of $\RR$ #IR#.
  38 *)
  39
  40 inline "cic:/CoRN/metrics/Prod_Sub/dprod0.con".
  41
  42 inline "cic:/CoRN/metrics/Prod_Sub/dprod0_strext.con".
  43
  44 inline "cic:/CoRN/metrics/Prod_Sub/d_prod0.con".
  45
  46 inline "cic:/CoRN/metrics/Prod_Sub/prod0cpsmetricspace_is_CPsMetricSpace.con".
  47
  48 inline "cic:/CoRN/metrics/Prod_Sub/Prod0CPsMetricSpace.con".
  49
  50 (* UNEXPORTED
  51 End prodpsmetrics
  52 *)
  53
  54 (* UNEXPORTED
  55 Section subpsmetrics
  56 *)
  57
  58 (*#* **Sub-Pseudo-Metric-Spaces
  59 *)
  60
  61 (*#*
  62 The pseudo metric on a subspace $Y$ #Y# of a pseudo metric space $X$ #X# is
  63 the pseudo metric on $X$ #X# restricted to $Y$ #Y#.
  64 *)
  65
  66 inline "cic:/CoRN/metrics/Prod_Sub/restr_bin_fun.con".
  67
  68 (* UNEXPORTED
  69 Implicit Arguments restr_bin_fun [X].
  70 *)
  71
  72 inline "cic:/CoRN/metrics/Prod_Sub/restr_bin_fun'.con".
  73
  74 (* UNEXPORTED
  75 Implicit Arguments restr_bin_fun' [X].
  76 *)
  77
  78 inline "cic:/CoRN/metrics/Prod_Sub/restr_bin_fun_strext.con".
  79
  80 inline "cic:/CoRN/metrics/Prod_Sub/Build_SubCSetoid_bin_fun.con".
  81
  82 inline "cic:/CoRN/metrics/Prod_Sub/dsub.con".
  83
  84 (* UNEXPORTED
  85 Implicit Arguments dsub [X].
  86 *)
  87
  88 inline "cic:/CoRN/metrics/Prod_Sub/dsub_com.con".
  89
  90 inline "cic:/CoRN/metrics/Prod_Sub/dsub_nneg.con".
  91
  92 inline "cic:/CoRN/metrics/Prod_Sub/dsub_pos_imp_ap.con".
  93
  94 inline "cic:/CoRN/metrics/Prod_Sub/dsub_tri_ineq.con".
  95
  96 inline "cic:/CoRN/metrics/Prod_Sub/is_SubPsMetricSpace.con".
  97
  98 inline "cic:/CoRN/metrics/Prod_Sub/SubPsMetricSpace.con".
  99
 100 (* UNEXPORTED
 101 Implicit Arguments SubPsMetricSpace [X].
 102 *)
 103
 104 inline "cic:/CoRN/metrics/Prod_Sub/from_SubPsMetricSpace.con".
 105
 106 (*#*
 107 The function [dsub'] is used in the definition of %''located''% #"located"#.
 108 It enables one to speak about a distance between an element of a
 109 pseudo metric space and a certain subspace.
 110 *)
 111
 112 inline "cic:/CoRN/metrics/Prod_Sub/dsub'.con".
 113
 114 (* UNEXPORTED
 115 Implicit Arguments dsub' [X].
 116 *)
 117
 118 inline "cic:/CoRN/metrics/Prod_Sub/dsub'_strext.con".
 119
 120 inline "cic:/CoRN/metrics/Prod_Sub/dsub'_as_cs_fun.con".
 121
 122 (* UNEXPORTED
 123 Implicit Arguments dsub'_as_cs_fun [X].
 124 *)
 125
 126 inline "cic:/CoRN/metrics/Prod_Sub/dsub'_uni_continuous''.con".
 127
 128 (* UNEXPORTED
 129 End subpsmetrics
 130 *)
 131