theorem
  for K being non empty addLoopStr
  for R being Element of 0-tuples_on the carrier of K holds Sum R = 0.K
proof
  let K be non empty addLoopStr,
      R be Element of 0-tuples_on (the carrier of K);
  R=<*>(the carrier of K);
  hence thesis by RLVECT_1:43;
end;
