
theorem
  for A being Interval, x being Real holds x ++ A is Interval
proof
  let A be Interval, x be Real;
  per cases by MEASURE5:1;
  suppose
    A is open_interval;
    then x ++ A is open_interval by Th26;
    hence thesis;
  end;
  suppose
    A is closed_interval;
    then x ++ A is closed_interval by Th27;
    hence thesis;
  end;
  suppose
    A is right_open_interval;
    then x ++ A is right_open_interval by Th28;
    hence thesis;
  end;
  suppose
    A is left_open_interval;
    then x ++ A is left_open_interval by Th29;
    hence thesis;
  end;
end;
