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
-ContFunctions
-*)
+include "metrics/ContFunctions.ma".
(* UNEXPORTED
-Section Reals.
+Section Reals
*)
(*#* **Real numbers
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/dIR.con".
-inline cic:/CoRN/metrics/IR_CPMSpace/bin_fun_strext_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_as_CSetoid_fun.con".
-inline cic:/CoRN/metrics/IR_CPMSpace/dIR_nneg.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_com.con".
-inline cic:/CoRN/metrics/IR_CPMSpace/dIR_pos_imp_ap.con.
+inline "cic:/CoRN/metrics/IR_CPMSpace/dIR_pos_imp_ap.con".
(* begin hide *)
-inline cic:/CoRN/metrics/IR_CPMSpace/IR_tri_ineq.con.
+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/dIR_tri_ineq.con".
-inline cic:/CoRN/metrics/IR_CPMSpace/IR_dIR_is_CPsMetricSpace.con.
+inline "cic:/CoRN/metrics/IR_CPMSpace/IR_dIR_is_CPsMetricSpace.con".
-inline cic:/CoRN/metrics/IR_CPMSpace/IR_as_CPsMetricSpace.con.
+inline "cic:/CoRN/metrics/IR_CPMSpace/IR_as_CPsMetricSpace.con".
-inline cic:/CoRN/metrics/IR_CPMSpace/X.var.
+alias id "X" = "cic:/CoRN/metrics/IR_CPMSpace/Reals/X.var".
-inline cic:/CoRN/metrics/IR_CPMSpace/rev_tri_ineq'.con.
+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_lipschitz.con".
-inline cic:/CoRN/metrics/IR_CPMSpace/d_is_uni_continuous.con.
+inline "cic:/CoRN/metrics/IR_CPMSpace/d_is_uni_continuous.con".
-inline cic:/CoRN/metrics/IR_CPMSpace/d_is_continuous.con.
+inline "cic:/CoRN/metrics/IR_CPMSpace/d_is_continuous.con".
(* UNEXPORTED
-End Reals.
+End Reals
*)
(* UNEXPORTED
-Section Addition.
+Section Addition
*)
(*#* **Addition of continuous functions
Lipschitz/uniformly continuous/continuous.
*)
-inline cic:/CoRN/metrics/IR_CPMSpace/plus_resp_lipschitz.con.
+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_uni_continuous.con".
-inline cic:/CoRN/metrics/IR_CPMSpace/plus_resp_continuous.con.
+inline "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_continuous.con".
(* UNEXPORTED
-End Addition.
+End Addition
*)