
theorem LM202:
  for G be finite Group holds
    ex g be Element of G st ord g = upper_bound Ordset G
  proof
    let G be finite Group;
    set A = Ordset G;
    set l = upper_bound A;
    A <> {} & A c= REAL by NUMBERS:19, XBOOLE_1:1;
    then l in A by SEQ_4:133;
    then consider g being Element of G such that
    A3: ord g = l;
    take g;
    thus thesis by A3;
  end;
