reserve x,y,y1,y2 for object;
reserve GF for add-associative right_zeroed right_complementable Abelian
  associative well-unital distributive non empty doubleLoopStr,
  V,X,Y for Abelian add-associative right_zeroed right_complementable
  vector-distributive scalar-distributive scalar-associative scalar-unital non
  empty ModuleStr over GF;
reserve a for Element of GF;
reserve u,u1,u2,v,v1,v2 for Element of V;
reserve W,W1,W2 for Subspace of V;
reserve V1 for Subset of V;
reserve w,w1,w2 for Element of W;

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;
