theorem
  for V being Abelian add-associative right_zeroed
  right_complementable vector-distributive scalar-distributive
  scalar-associative scalar-unital non empty ModuleStr over GF holds V is
  Subspace of (Omega).V
  proof
    let V be Abelian add-associative right_zeroed
      right_complementable vector-distributive scalar-distributive
      scalar-associative scalar-unital non empty ModuleStr over GF;
    reconsider VS = V as Subspace of V by Th24;
    for v being Vector of V st v in VS holds v in (Omega).V;
    hence thesis by Th28;
  end;
