1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
17 set "baseuri" "cic:/matita/CoRN-Decl/metrics/IR_CPMSpace".
19 include "CoRN_notation.ma".
21 (* $Id: IR_CPMSpace.v,v 1.4 2004/04/23 10:01:02 lcf Exp $ *)
23 include "metrics/ContFunctions.ma".
34 Let [X] be a pseudo metric space.
39 The real numbers with the usual distance form a pseudo metric space.
42 inline "cic:/CoRN/metrics/IR_CPMSpace/dIR.con".
44 inline "cic:/CoRN/metrics/IR_CPMSpace/bin_fun_strext_dIR.con".
46 inline "cic:/CoRN/metrics/IR_CPMSpace/dIR_as_CSetoid_fun.con".
48 inline "cic:/CoRN/metrics/IR_CPMSpace/dIR_nneg.con".
50 inline "cic:/CoRN/metrics/IR_CPMSpace/dIR_com.con".
52 inline "cic:/CoRN/metrics/IR_CPMSpace/dIR_pos_imp_ap.con".
56 inline "cic:/CoRN/metrics/IR_CPMSpace/IR_tri_ineq.con".
60 inline "cic:/CoRN/metrics/IR_CPMSpace/dIR_tri_ineq.con".
62 inline "cic:/CoRN/metrics/IR_CPMSpace/IR_dIR_is_CPsMetricSpace.con".
64 inline "cic:/CoRN/metrics/IR_CPMSpace/IR_as_CPsMetricSpace.con".
66 inline "cic:/CoRN/metrics/IR_CPMSpace/X.var".
68 inline "cic:/CoRN/metrics/IR_CPMSpace/rev_tri_ineq'.con".
71 A pseudo metric is Lipschitz. Hence it is uniformly continuous and continuous.
74 inline "cic:/CoRN/metrics/IR_CPMSpace/d_is_lipschitz.con".
76 inline "cic:/CoRN/metrics/IR_CPMSpace/d_is_uni_continuous.con".
78 inline "cic:/CoRN/metrics/IR_CPMSpace/d_is_continuous.con".
88 (*#* **Addition of continuous functions
92 The sum of two Lipschitz/uniformly continous/continuous functions is again
93 Lipschitz/uniformly continuous/continuous.
96 inline "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_lipschitz.con".
98 inline "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_uni_continuous.con".
100 inline "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_continuous.con".