theorem
  for R being Ring,
      V being LeftMod of R, a being Element of R,
      v, u being Vector of V holds
    a * Sum<* v,u *> = a * v + a * u
  proof
    let R be Ring;
    let V be LeftMod of R, a be Element of R, v, u be Vector of V;
    thus a * Sum<* v,u *> = a * (v + u) by RLVECT_1:45
    .= a * v + a * u by VECTSP_1:def 14;
  end;
