
theorem Th6:
  for A being Interval holds 0 ** A is interval
proof
  let A be Interval;
  per cases;
  suppose
    A = {};
    hence thesis;
  end;
  suppose
    A <> {};
    then 0 ** A = {0} by Th3;
    then 0 ** A = [.0,0 .] by XXREAL_1:17;
    hence thesis;
  end;
end;
