theorem
  ord 0_G = 1
proof
A1: for n st n * (0_G) = 0_G & n <> 0 holds 1 <= n by NAT_1:14;
  ( not 0_G is being_of_order_0)& 1 * (0_G) = 0_G by Lm4;
  hence thesis by A1,Def11;
end;
