reserve i, j, k, c, m, n for Nat,
  a, x, y, z, X, Y for set,
  D, E for non empty set,
  R for Relation,
  f, g for Function,
  p, q for FinSequence;

theorem Th37:
  for t being Element of n-tuples_on NAT holds (n proj i).t = t.i
proof
  let t be Element of n-tuples_on NAT;
  dom (n proj i) = n-tuples_on NAT by Th35;
  hence thesis by CARD_3:def 16;
end;
