 reserve R for Ring;
 reserve x, y, y1 for set;
 reserve a, b for Element of R;
 reserve V for LeftMod of R;
 reserve v, w for Vector of V;

theorem
  for V being Z_Module,
      a being Element of INT.Ring,
      v being Vector of V holds
  (- a) * (- v) = a * v
  proof
    let V be Z_Module,
        a be Element of INT.Ring,
        v be Vector of V;
    thus (- a) * (- v) = (--a) * v by Th5
    .= a * v;
  end;
