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