--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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/Prod_Sub".
+
+include "CoRN.ma".
+
+(* $Id: Prod_Sub.v,v 1.4 2004/04/23 10:01:02 lcf Exp $ *)
+
+include "metrics/IR_CPMSpace.ma".
+
+(* UNEXPORTED
+Section prodpsmetrics
+*)
+
+(*#* **Product-Pseudo-Metric-Spaces
+*)
+
+(*#*
+The product metric here defined is:
+$ d_{prod}((a_1,b_1),(a_2,b_2)):= d_A(a_1,a_2)+d_B(b_1,b_2)$
+# d<SUB>prod</SUB>((a<SUB>1</SUB>,b<SUB>1</SUB>),(a<SUB>2</SUB>,b<SUB>2</SUB>)):= d<SUB>A</SUB>(a<SUB>1</SUB>,b<SUB>1</SUB>)+d<SUB>B</SUB>(b<SUB>1</SUB>,b<SUB>2</SUB>)#.
+This is %\emph{not}% #<I>not</I># the one used to make the metric of
+$\RR^{2}$ #IR<SUP>2</SUP># out of the metric of $\RR$ #IR#.
+*)
+
+inline "cic:/CoRN/metrics/Prod_Sub/dprod0.con".
+
+inline "cic:/CoRN/metrics/Prod_Sub/dprod0_strext.con".
+
+inline "cic:/CoRN/metrics/Prod_Sub/d_prod0.con".
+
+inline "cic:/CoRN/metrics/Prod_Sub/prod0cpsmetricspace_is_CPsMetricSpace.con".
+
+inline "cic:/CoRN/metrics/Prod_Sub/Prod0CPsMetricSpace.con".
+
+(* UNEXPORTED
+End prodpsmetrics
+*)
+
+(* UNEXPORTED
+Section subpsmetrics
+*)
+
+(*#* **Sub-Pseudo-Metric-Spaces
+*)
+
+(*#*
+The pseudo metric on a subspace $Y$ #Y# of a pseudo metric space $X$ #X# is
+the pseudo metric on $X$ #X# restricted to $Y$ #Y#.
+*)
+
+inline "cic:/CoRN/metrics/Prod_Sub/restr_bin_fun.con".
+
+(* UNEXPORTED
+Implicit Arguments restr_bin_fun [X].
+*)
+
+inline "cic:/CoRN/metrics/Prod_Sub/restr_bin_fun'.con".
+
+(* UNEXPORTED
+Implicit Arguments restr_bin_fun' [X].
+*)
+
+inline "cic:/CoRN/metrics/Prod_Sub/restr_bin_fun_strext.con".
+
+inline "cic:/CoRN/metrics/Prod_Sub/Build_SubCSetoid_bin_fun.con".
+
+inline "cic:/CoRN/metrics/Prod_Sub/dsub.con".
+
+(* UNEXPORTED
+Implicit Arguments dsub [X].
+*)
+
+inline "cic:/CoRN/metrics/Prod_Sub/dsub_com.con".
+
+inline "cic:/CoRN/metrics/Prod_Sub/dsub_nneg.con".
+
+inline "cic:/CoRN/metrics/Prod_Sub/dsub_pos_imp_ap.con".
+
+inline "cic:/CoRN/metrics/Prod_Sub/dsub_tri_ineq.con".
+
+inline "cic:/CoRN/metrics/Prod_Sub/is_SubPsMetricSpace.con".
+
+inline "cic:/CoRN/metrics/Prod_Sub/SubPsMetricSpace.con".
+
+(* UNEXPORTED
+Implicit Arguments SubPsMetricSpace [X].
+*)
+
+inline "cic:/CoRN/metrics/Prod_Sub/from_SubPsMetricSpace.con".
+
+(*#*
+The function [dsub'] is used in the definition of %''located''% #"located"#.
+It enables one to speak about a distance between an element of a
+pseudo metric space and a certain subspace.
+*)
+
+inline "cic:/CoRN/metrics/Prod_Sub/dsub'.con".
+
+(* UNEXPORTED
+Implicit Arguments dsub' [X].
+*)
+
+inline "cic:/CoRN/metrics/Prod_Sub/dsub'_strext.con".
+
+inline "cic:/CoRN/metrics/Prod_Sub/dsub'_as_cs_fun.con".
+
+(* UNEXPORTED
+Implicit Arguments dsub'_as_cs_fun [X].
+*)
+
+inline "cic:/CoRN/metrics/Prod_Sub/dsub'_uni_continuous''.con".
+
+(* UNEXPORTED
+End subpsmetrics
+*)
+