theorem
  for D be non empty set, f be Function of [:D,D:],REAL st f
  is_metric_of D holds SpaceMetr(D,f) is non empty
proof
  let D be non empty set, f be Function of [:D,D:], REAL;
  assume f is_metric_of D;
  then SpaceMetr(D,f) = MetrStruct(#D,f#) by Def7;
  hence thesis;
end;
