theorem
  for R being Ring
  for V being LeftMod of R, a being Element of R, v, u, w being Vector of V
  holds a * Sum<* v,u,w *> = a * v + a * u + a * w
  proof
    let R be Ring;
    let V be LeftMod of R, a be Element of R, v, u, w be Vector of V;
    thus a * Sum<* v,u,w *> = a * (v + u + w) by RLVECT_1:46
    .= a * (v + u) + a * w by VECTSP_1:def 14
    .= a * v + a * u + a * w by VECTSP_1:def 14;
  end;
