theorem
  for V being Abelian add-associative right_zeroed right_complementable
  non empty addLoopStr holds - Sum(<*>(the carrier of V)) = 0.V
proof
  let V be Abelian add-associative right_zeroed right_complementable non
  empty addLoopStr;
  thus - Sum(<*>(the carrier of V)) = - 0.V by Lm4
    .= 0.V;
end;
