theorem
  for F being Function of [:D,D9:],E for z being Tuple of i,D
    holds F[:](z,d9) is Element of i-tuples_on E
proof
  let F be Function of [:D,D9:],E;
  let z be Tuple of i,D;
  reconsider r = F[:](z,d9) as FinSequence of E by Th81;
  len z = i by CARD_1:def 7;
  then len r = i by Th82;
  hence thesis by Th90;
end;
