theorem Th44:
  0_H = 0_G
proof
  set h = the Element of H;
  reconsider g = h, g9 = 0_H as Element of G by Th41,STRUCT_0:def 5;
  h + 0_H = h by Def4;
  then g + g9 = g by Th43;
  hence thesis by Th7;
end;
