
theorem Th4:
  for F being Field for V being VectSp of F for W being Subspace of
  V holds (Omega).W is Subspace of V
proof
  let F be Field;
  let V be VectSp of F;
  let W be Subspace of V;
  thus the carrier of (Omega).W c= the carrier of V by VECTSP_4:def 2;
  thus 0.(Omega).W = 0.W .= 0.V by VECTSP_4:def 2;
  thus thesis by VECTSP_4:def 2;
end;
