theorem
  for GF being Field, V being VectSp of GF, v being Element of V, W
  being Subspace of V holds v in W iff - v + W = the carrier of W
proof
  let GF be Field, V be VectSp of GF, v be Element of V, W be Subspace of V;
  - 1_GF <> 0.GF by VECTSP_2:3;
  then v in W iff ((- 1_GF) * v) + W = the carrier of W by Th50,Th51;
  hence thesis by VECTSP_1:14;
end;
