
theorem LMQ10:
  for V be RealLinearSpace, W be Subspace of V holds
  for A be VECTOR of VectQuot(V,W), v be VECTOR of V, a be Real st A = v + W
  holds -A = -v + W
  proof
    let V be RealLinearSpace, W be Subspace of V;
    let A be VECTOR of VectQuot(V,W), v be VECTOR of V, a be Real;
    assume
    A1: A = v + W;
    thus -A = (-1) * A by RLVECT_1:16
           .= (-1) * v + W by A1,LMQ09
           .= -v + W by RLVECT_1:16;
  end;
