theorem Th9:
  e1 is_a_left_unity_wrt o & e2 is_a_right_unity_wrt o implies e1 = e2
proof
  assume that
A1: e1 is_a_left_unity_wrt o and
A2: e2 is_a_right_unity_wrt o;
  thus e1 = o.(e1,e2) by A2
    .= e2 by A1;
end;
