theorem
  for h being PartFunc of W,REAL holds
  h.:Y is real-bounded & upper_bound(h.:Y) = lower_bound(h.:Y) implies
  h|Y is constant
proof
  let h be PartFunc of W,REAL;
  rng (h|Y) = h.:Y by RELAT_1:115;
  hence thesis by Th18;
end;
