matita/contribs/CoRN-Decl/metrics/IR_CPMSpace.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/IR_CPMSpace".
  18
  19 include "CoRN.ma".
  20
  21 (* $Id: IR_CPMSpace.v,v 1.4 2004/04/23 10:01:02 lcf Exp $ *)
  22
  23 include "metrics/ContFunctions.ma".
  24
  25 (* UNEXPORTED
  26 Section Reals
  27 *)
  28
  29 (*#* **Real numbers
  30 *)
  31
  32 (*#*
  33 %\begin{convention}%
  34 Let [X] be a  pseudo metric space.
  35 %\end{convention}%
  36 *)
  37
  38 (*#*
  39 The real numbers with the usual distance form a pseudo metric space.
  40 *)
  41
  42 inline "cic:/CoRN/metrics/IR_CPMSpace/dIR.con".
  43
  44 inline "cic:/CoRN/metrics/IR_CPMSpace/bin_fun_strext_dIR.con".
  45
  46 inline "cic:/CoRN/metrics/IR_CPMSpace/dIR_as_CSetoid_fun.con".
  47
  48 inline "cic:/CoRN/metrics/IR_CPMSpace/dIR_nneg.con".
  49
  50 inline "cic:/CoRN/metrics/IR_CPMSpace/dIR_com.con".
  51
  52 inline "cic:/CoRN/metrics/IR_CPMSpace/dIR_pos_imp_ap.con".
  53
  54 (* begin hide *)
  55
  56 inline "cic:/CoRN/metrics/IR_CPMSpace/IR_tri_ineq.con".
  57
  58 (* end hide *)
  59
  60 inline "cic:/CoRN/metrics/IR_CPMSpace/dIR_tri_ineq.con".
  61
  62 inline "cic:/CoRN/metrics/IR_CPMSpace/IR_dIR_is_CPsMetricSpace.con".
  63
  64 inline "cic:/CoRN/metrics/IR_CPMSpace/IR_as_CPsMetricSpace.con".
  65
  66 alias id "X" = "cic:/CoRN/metrics/IR_CPMSpace/Reals/X.var".
  67
  68 inline "cic:/CoRN/metrics/IR_CPMSpace/rev_tri_ineq'.con".
  69
  70 (*#*
  71 A pseudo metric is Lipschitz. Hence it is uniformly continuous and continuous.
  72 *)
  73
  74 inline "cic:/CoRN/metrics/IR_CPMSpace/d_is_lipschitz.con".
  75
  76 inline "cic:/CoRN/metrics/IR_CPMSpace/d_is_uni_continuous.con".
  77
  78 inline "cic:/CoRN/metrics/IR_CPMSpace/d_is_continuous.con".
  79
  80 (* UNEXPORTED
  81 End Reals
  82 *)
  83
  84 (* UNEXPORTED
  85 Section Addition
  86 *)
  87
  88 (*#* **Addition of continuous functions
  89 *)
  90
  91 (*#*
  92 The sum of two Lipschitz/uniformly continous/continuous functions is again
  93 Lipschitz/uniformly continuous/continuous.
  94 *)
  95
  96 inline "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_lipschitz.con".
  97
  98 inline "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_uni_continuous.con".
  99
 100 inline "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_continuous.con".
 101
 102 (* UNEXPORTED
 103 End Addition
 104 *)
 105