reserve a, b, r, s for Real;

theorem Th24:
  for X being Subset of REAL st X is bounded_below holds X c=
  right_closed_halfline(lower_bound X)
proof
  let X be Subset of REAL such that
A1: X is bounded_below;
  let x be object;
  assume
A2: x in X;
  then reconsider x as Real;
  lower_bound X <= x by A1,A2,SEQ_4:def 2;
  hence thesis by XXREAL_1:236;
end;
