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;

theorem Th26:
  for K being Abelian right_zeroed add-associative
right_complementable non empty addLoopStr, R being Element of i-tuples_on the
  carrier of K holds R + -R = (i|->0.K) & -R + R = (i|->0.K)
proof
  let K be Abelian right_zeroed add-associative right_complementable non
  empty addLoopStr, R be Element of i-tuples_on the carrier of K;
  thus R + -R = (i|->0.K) by Lm3;
  hence thesis by FINSEQOP:33;
end;
