theorem
  for F being Function of [:D,D9:],E for z1 being Tuple of i,D
   for z2 being Tuple of i,D9 holds F.:(z1,z2) is Element of i
  -tuples_on E
proof
  let F be Function of [:D,D9:],E;
  let z1 be Tuple of i,D;
  let z2 be Tuple of i,D9;
  reconsider r = F.:(z1,z2) as FinSequence of E by Th68;
  len z1 = i & len z2 = i by CARD_1:def 7;
  then len r = i by Th70;
  hence thesis by Th90;
end;
