
theorem
  for V being RealUnitarySpace, W being Subspace of V, v being VECTOR of
  V holds - v in v + W iff v in W
proof
  let V be RealUnitarySpace;
  let W be Subspace of V;
  let v be VECTOR of V;
  (- jj) * v = - v by RLVECT_1:16;
  hence thesis by Th52,Th53;
end;
