theorem Th129:
  for V being Z_Module holds V is_the_direct_sum_of (0).V, (Omega).V &
    V is_the_direct_sum_of (Omega).V,(0).V
  proof
    let V be Z_Module;
    V is_the_direct_sum_of (0).V, (Omega).V by Th99,Th107;
    hence thesis by VECTSP_5:41;
  end;
