theorem Th110:
  (1).G * a = {a} & a * (1).G = {a}
proof
A1: the carrier of (1).G = {1_G} by Def7;
  hence (1).G * a = {1_G * a} by Th18
    .= {a} by GROUP_1:def 4;
  thus a * (1).G = {a * 1_G} by A1,Th18
    .= {a} by GROUP_1:def 4;
end;
