theorem Th8:
  for V being Z_Module,
      a being Element of INT.Ring,
      v,w being Vector of V holds
  a * (v - w) = a * v - a * w
  proof
    let V be Z_Module,
        a be Element of INT.Ring,
        v,w be Vector of V;
  thus a * (v - w) = a * v + a * (- w) by VECTSP_1:def 14
    .= a * v - a * w by Th6;
end;
