reserve U1,U2,U3 for Universal_Algebra,
  n,m for Nat,
  x,y,z for object,
  A,B for non empty set,
  h1 for FinSequence of [:A,B:];
reserve h1 for homogeneous quasi_total non empty PartFunc of
    (the carrier of U1)*,the carrier of U1,
  h2 for homogeneous quasi_total non empty PartFunc of
    (the carrier of U2)*,the carrier of U2;

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;
