theorem Th17:
  for M be non empty MetrSpace, A be non empty Subset of M for S
  be sequence of (M|A) holds S is sequence of M
proof
  let M be non empty MetrSpace, A be non empty Subset of M;
  let S be sequence of (M|A);
  A c= the carrier of M;
  then the carrier of (M|A) c= the carrier of M by TOPMETR:def 2;
  hence thesis by FUNCT_2:7;
end;
