 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;
 reserve u,v,w for Vector of V;
 reserve F,G,H,I for FinSequence of V;
 reserve j,k,n for Nat;
 reserve f,f9,g for sequence of V;

theorem
  for V being Z_Module, a being Element of INT.Ring holds
    a * Sum(<*>(the carrier of V)) = 0.V by Lm1,Th1;
