theorem Th18:
  for h being PartFunc of W,REAL holds
  rng h is real-bounded & upper_bound (rng h) = lower_bound (rng h)
  implies h is constant
proof
  let h be PartFunc of W,REAL;
  assume
A1: rng h is real-bounded & upper_bound (rng h) = lower_bound (rng h);
  assume not h is constant;
  then consider x1,x2 being object such that
A2: x1 in dom h & x2 in dom h and
A3: h.x1 <> h.x2;
  h.x1 in rng h & h.x2 in rng h by A2,FUNCT_1:def 3;
  hence contradiction by A1,A3,SEQ_4:12;
end;
