theorem Th9:
  for W being strict Subspace of M holds (0).M + W = W & W + (0).M = W
proof
  let W be strict Subspace of M;
  (0).M is Subspace of W by VECTSP_4:39;
  then the carrier of (0).M c= the carrier of W by VECTSP_4:def 2;
  hence (0).M + W = W by Lm3;
  hence thesis by Lm1;
end;
