reserve i,j,k for Nat;
reserve K for non empty addLoopStr,
  a for Element of K,
  p for FinSequence of the carrier of K,
  R for Element of i-tuples_on the carrier of K;
reserve K for left_zeroed right_zeroed add-associative right_complementable
  non empty addLoopStr,
  R,R1,R2 for Element of i-tuples_on the carrier of K;
reserve K for non empty addLoopStr,
  a1,a2 for Element of K,
  p1,p2 for FinSequence of the carrier of K,
  R1,R2 for Element of i-tuples_on the carrier of K;

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;
