reserve m,n for Nat;
reserve i,j for Integer;
reserve S for non empty addMagma;
reserve r,r1,r2,s,s1,s2,t,t1,t2 for Element of S;
reserve G for addGroup-like non empty addMagma;
reserve e,h for Element of G;
reserve G for addGroup;
reserve f,g,h for Element of G;
reserve u for UnOp of G;

theorem
  i * (0_G) = 0_G
proof
  i * (0_G) = |.i.| * (0_G) or i * (0_G) = -(|.i.| * (0_G)) & -(0_G)
  = 0_G by Def8,Th8;
  hence thesis by Lm4;
end;
