theorem Th54:
  G is Subgroup of G
proof
  dom(the multF of G) = [:the carrier of G,the carrier of G:] by FUNCT_2:def 1;
  hence
  the carrier of G c= the carrier of G & the multF of G = (the multF of G
  )||the carrier of G by RELAT_1:68;
end;
