reserve a, b, r, s for Real;

theorem Th20:
  for X being Subset of REAL st X is bounded_above holds X c=
  left_closed_halfline(upper_bound X)
proof
  let X be Subset of REAL such that
A1: X is bounded_above;
  let x be object;
  assume
A2: x in X;
  then reconsider x as Real;
  x <= upper_bound X by A1,A2,SEQ_4:def 1;
  hence thesis by XXREAL_1:234;
end;
