set "baseuri" "cic:/matita/CoRN-Decl/metrics/CPseudoMSpaces".
+include "CoRN.ma".
+
(* $Id: CPseudoMSpaces.v,v 1.3 2004/04/23 10:01:02 lcf Exp $ *)
-(* INCLUDE
-Intervals
-*)
+include "reals/Intervals.ma".
(*#* *Metric Spaces
*)
(* UNEXPORTED
-Section Relations.
+Section Relations
*)
(*#* **Relations necessary for Pseudo Metric Spaces and Metric Spaces
%\end{convention}%
*)
-inline cic:/CoRN/metrics/CPseudoMSpaces/A.var.
+alias id "A" = "cic:/CoRN/metrics/CPseudoMSpaces/Relations/A.var".
-inline cic:/CoRN/metrics/CPseudoMSpaces/d.var.
+alias id "d" = "cic:/CoRN/metrics/CPseudoMSpaces/Relations/d.var".
(* UNEXPORTED
Set Implicit Arguments.
Unset Strict Implicit.
*)
-inline cic:/CoRN/metrics/CPseudoMSpaces/com.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/com.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/nneg.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/nneg.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/pos_imp_ap.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/pos_imp_ap.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/tri_ineq.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/tri_ineq.con".
(* UNEXPORTED
Set Strict Implicit.
Unset Implicit Arguments.
*)
-inline cic:/CoRN/metrics/CPseudoMSpaces/diag_zero.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/diag_zero.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/apdiag_imp_grzero.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/apdiag_imp_grzero.con".
(* UNEXPORTED
-End Relations.
+End Relations
*)
(* UNEXPORTED
-Section Definition_PsMS0.
+Section Definition_PsMS0
*)
(*#* **Definition of Pseudo Metric Space
%''distance''% #"distance"#, a binairy function that fulfils certain properties.
*)
-inline cic:/CoRN/metrics/CPseudoMSpaces/is_CPsMetricSpace.ind.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/is_CPsMetricSpace.ind".
+
+inline "cic:/CoRN/metrics/CPseudoMSpaces/CPsMetricSpace.ind".
-inline cic:/CoRN/metrics/CPseudoMSpaces/CPsMetricSpace.ind.
+coercion cic:/matita/CoRN-Decl/metrics/CPseudoMSpaces/cms_crr.con 0 (* compounds *).
(* UNEXPORTED
-End Definition_PsMS0.
+End Definition_PsMS0
*)
(* UNEXPORTED
Implicit Arguments cms_d [c].
*)
+(* NOTATION
+Infix "[-d]" := cms_d (at level 68, left associativity).
+*)
+
(* UNEXPORTED
-Section PsMS_axioms.
+Section PsMS_axioms
*)
(*#* **Pseudo Metric Space axioms
%\end{convention}%
*)
-inline cic:/CoRN/metrics/CPseudoMSpaces/A.var.
+alias id "A" = "cic:/CoRN/metrics/CPseudoMSpaces/PsMS_axioms/A.var".
-inline cic:/CoRN/metrics/CPseudoMSpaces/CPsMetricSpace_is_CPsMetricSpace.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/CPsMetricSpace_is_CPsMetricSpace.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/d_com.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/d_com.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/d_nneg.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/d_nneg.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/d_pos_imp_ap.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/d_pos_imp_ap.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/d_tri_ineq.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/d_tri_ineq.con".
(* UNEXPORTED
-End PsMS_axioms.
+End PsMS_axioms
*)
(* UNEXPORTED
-Section PsMS_basics.
+Section PsMS_basics
*)
(*#* **Pseudo Metric Space basics
%\end{convention}%
*)
-inline cic:/CoRN/metrics/CPseudoMSpaces/Y.var.
+alias id "Y" = "cic:/CoRN/metrics/CPseudoMSpaces/PsMS_basics/Y.var".
-inline cic:/CoRN/metrics/CPseudoMSpaces/rev_tri_ineq.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/rev_tri_ineq.con".
(*#*
Instead of taking [pos_imp_ap] as axiom,
we could as well have taken [diag_zero].
*)
-inline cic:/CoRN/metrics/CPseudoMSpaces/diag_zero_imp_pos_imp_ap.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/diag_zero_imp_pos_imp_ap.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/pos_imp_ap_imp_diag_zero.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/pos_imp_ap_imp_diag_zero.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/is_CPsMetricSpace_diag_zero.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/is_CPsMetricSpace_diag_zero.con".
(* UNEXPORTED
-End PsMS_basics.
+End PsMS_basics
*)
(* UNEXPORTED
-Section Zerof.
+Section Zerof
*)
(*#* **Zero function
a pseudo metric space.
*)
-inline cic:/CoRN/metrics/CPseudoMSpaces/zero_fun.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_strext.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_strext.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/Zero_fun.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/Zero_fun.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_com.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_com.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_nneg.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_nneg.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_pos_imp_ap.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_pos_imp_ap.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_tri_ineq.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_tri_ineq.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/zf_is_CPsMetricSpace.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/zf_is_CPsMetricSpace.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/zf_as_CPsMetricSpace.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/zf_as_CPsMetricSpace.con".
(* UNEXPORTED
-End Zerof.
+End Zerof
*)