X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fcontribs%2FCoRN-Decl%2Fmetrics%2FIR_CPMSpace.ma;fp=matita%2Fcontribs%2FCoRN-Decl%2Fmetrics%2FIR_CPMSpace.ma;h=fd53f08381cf0bf72f05855c4b0306f36b45b4a3;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/matita/contribs/CoRN-Decl/metrics/IR_CPMSpace.ma b/matita/contribs/CoRN-Decl/metrics/IR_CPMSpace.ma new file mode 100644 index 000000000..fd53f0838 --- /dev/null +++ b/matita/contribs/CoRN-Decl/metrics/IR_CPMSpace.ma @@ -0,0 +1,105 @@ +(**************************************************************************) +(* ___ *) +(* ||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 +*) +