reserve i,j,k,l for natural Number;
reserve A for set, a,b,x,x1,x2,x3 for object;
reserve D,D9,E for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve d9,d19,d29,d39 for Element of D9;
reserve p,q,r for FinSequence;
reserve s for Element of D*;

theorem
  for z being Tuple of i,D for f being Function of D,D9
  holds f*z is Element of i-tuples_on D9
proof
  let z be Tuple of i,D;
  let f be Function of D,D9;
  reconsider s = f*z as FinSequence of D9 by Th30;
  len z = i by CARD_1:def 7;
  then len s = i by Th31;
  hence thesis by Th90;
end;
