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[helm.git] / matita / contribs / CoRN-Decl / metrics / IR_CPMSpace.ma

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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+set "baseuri" "cic:/matita/CoRN-Decl/metrics/IR_CPMSpace".
+
+include "CoRN.ma".
+
+(* $Id: IR_CPMSpace.v,v 1.4 2004/04/23 10:01:02 lcf Exp $ *)
+
+include "metrics/ContFunctions.ma".
+
+(* UNEXPORTED
+Section Reals
+*)
+
+(*#* **Real numbers
+*)
+
+(*#* 
+%\begin{convention}%
+Let [X] be a  pseudo metric space.
+%\end{convention}%
+*)
+
+(*#*
+The real numbers with the usual distance form a pseudo metric space. 
+*)
+
+inline "cic:/CoRN/metrics/IR_CPMSpace/dIR.con".
+
+inline "cic:/CoRN/metrics/IR_CPMSpace/bin_fun_strext_dIR.con".
+
+inline "cic:/CoRN/metrics/IR_CPMSpace/dIR_as_CSetoid_fun.con".
+
+inline "cic:/CoRN/metrics/IR_CPMSpace/dIR_nneg.con".
+
+inline "cic:/CoRN/metrics/IR_CPMSpace/dIR_com.con".
+
+inline "cic:/CoRN/metrics/IR_CPMSpace/dIR_pos_imp_ap.con".
+
+(* begin hide *)
+
+inline "cic:/CoRN/metrics/IR_CPMSpace/IR_tri_ineq.con".
+
+(* end hide *)
+
+inline "cic:/CoRN/metrics/IR_CPMSpace/dIR_tri_ineq.con".
+
+inline "cic:/CoRN/metrics/IR_CPMSpace/IR_dIR_is_CPsMetricSpace.con".
+
+inline "cic:/CoRN/metrics/IR_CPMSpace/IR_as_CPsMetricSpace.con".
+
+alias id "X" = "cic:/CoRN/metrics/IR_CPMSpace/Reals/X.var".
+
+inline "cic:/CoRN/metrics/IR_CPMSpace/rev_tri_ineq'.con".
+
+(*#*
+A pseudo metric is Lipschitz. Hence it is uniformly continuous and continuous.
+*)
+
+inline "cic:/CoRN/metrics/IR_CPMSpace/d_is_lipschitz.con".
+
+inline "cic:/CoRN/metrics/IR_CPMSpace/d_is_uni_continuous.con".
+
+inline "cic:/CoRN/metrics/IR_CPMSpace/d_is_continuous.con".
+
+(* UNEXPORTED
+End Reals
+*)
+
+(* UNEXPORTED
+Section Addition
+*)
+
+(*#* **Addition of continuous functions
+*)
+
+(*#*
+The sum of two Lipschitz/uniformly continous/continuous functions is again 
+Lipschitz/uniformly continuous/continuous.
+*)
+
+inline "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_lipschitz.con".
+
+inline "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_uni_continuous.con".
+
+inline "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_continuous.con".
+
+(* UNEXPORTED
+End Addition
+*)
+