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
  j in Seg i & a = R.j implies (-R).j = -a
proof
  assume j in Seg i;
  then j in Seg len -R by CARD_1:def 7;
  then j in dom -R by FINSEQ_1:def 3;
  hence thesis by Th22;
end;
