theorem Th69:
  for G being addGroup, a being Element of G holds (Omega).G * a = (Omega).G
proof
  let G be addGroup, a be Element of G;
  let h be Element of G;
  (h * (-a)) * a = h * ((-a) + a) by Th24
    .= h * 0_G by Def5
    .= h by Th19;
  hence thesis by Th58,STRUCT_0:def 5;
end;
