
theorem
  for V be RealLinearSpace, W be Subspace of V holds
  for A1,A2 be VECTOR of VectQuot(V,W),
      v1,v2 be VECTOR of V
  st A1 = v1 + W & A2 = v2 + W
  holds A1 - A2 = (v1 - v2) + W
  proof
    let V be RealLinearSpace, W be Subspace of V;
    let A1,A2 be VECTOR of VectQuot(V,W),
        v1,v2 be VECTOR of V;
    assume
    A1: A1 = v1 + W & A2 = v2 + W; then
    -A2 = -v2 + W by LMQ10;
    hence A1 - A2 = (v1 - v2) + W by A1,LMQ11;
  end;
