theorem ThA16:
  {}(the carrier of G) + A = {} & A + {}(the carrier of G) = {}
proof
A1: now
    set x = the Element of A + {}(the carrier of G);
    assume A + {}(the carrier of G) <> {};
    then ex g1,g2 st x = g1 + g2 & g1 in A & g2 in {}(the carrier of G)
      by ThX8;
    hence contradiction;
  end;
  now
    set x = the Element of {}(the carrier of G) + A;
    assume {}(the carrier of G) + A <> {};
    then ex g1,g2 st x = g1 + g2 & g1 in {}(the carrier of G) & g2 in A
      by ThX8;
    hence contradiction;
  end;
  hence thesis by A1;
end;
