theorem
  for K being add-associative right_complementable left_zeroed
          right_zeroed non empty addLoopStr,
      R being Element of i-tuples_on the carrier of K holds
    R - (i|->(0.K)) = R
proof
  let K be add-associative right_complementable left_zeroed right_zeroed non
  empty addLoopStr, R be Element of i-tuples_on the carrier of K;
  thus R - (i|->(0.K)) = R + - (i|->(0.K)) by FINSEQOP:84
    .= R + (i|->(-0.K)) by Th25
    .= R + (i|->(0.K)) by RLVECT_1:12
    .= R by Lm2;
end;
