
theorem Th9:
  for V being RealUnitarySpace, W being strict Subspace of V holds
  (0).V + W = W & W + (0).V = W
proof
  let V be RealUnitarySpace;
  let W be strict Subspace of V;
  (0).V is Subspace of W by RUSUB_1:33;
  then the carrier of (0).V c= the carrier of W by RUSUB_1:def 1;
  hence (0).V + W = W by Lm3;
  hence thesis by Lm1;
end;
