
theorem Th45:
  for V being RealUnitarySpace, W being Subspace of V, v being
  VECTOR of V holds v in W iff - v + W = the carrier of W
proof
  let V be RealUnitarySpace;
  let W be Subspace of V;
  let v be VECTOR of V;
  v in W iff ((- jj) * v) + W = the carrier of W by Th43,Th44;
  hence thesis by RLVECT_1:16;
end;
