theorem
  for k being Nat holds arity TrivialOp(k) = k
proof
  let k be Nat;
  now
    dom TrivialOp(k) = {k |-> {}} by Def7;
    then k |-> {} in dom TrivialOp(k) by TARSKI:def 1;
    hence ex x being FinSequence st x in dom TrivialOp(k);
    let x be FinSequence;
    assume x in dom TrivialOp(k);
    then x in {k |-> {}} by Def7;
    then x = k |-> {} by TARSKI:def 1;
    hence len x = k by CARD_1:def 7;
  end;
  hence thesis by MARGREL1:def 25;
end;
