
theorem Th3:
  for F being Field for V being VectSp of F for W being Subspace of
  (Omega).V holds W is Subspace of V
proof
  let F be Field;
  let V be VectSp of F;
  let W be Subspace of (Omega).V;
  thus the carrier of W c= the carrier of V by VECTSP_4:def 2;
  thus 0.W = 0.(Omega).V by VECTSP_4:def 2
    .= 0.V;
  thus thesis by VECTSP_4:def 2;
end;
