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;
