reserve r, s, t, g for Real,

          r3, r1, r2, q3, p3 for Real;

theorem Th7:
  for T being non empty 1-sorted, f being bounded RealMap of T
  holds lower_bound f <= upper_bound f
proof
  let T be non empty 1-sorted, f be bounded RealMap of T;
  f.:the carrier of T is bounded_below & f.:the carrier of T is
  bounded_above by MEASURE6:def 10,def 11;
  hence thesis by SEQ_4:11;
end;
