reserve x, x1, x2, y, z, X9 for set,
  X, Y for finite set,
  n, k, m for Nat,
  f for Function;

theorem
  n!/((n-'k)!) is Element of NAT
proof
n!/((n-'k)!) is integer by IRRAT_1:36,NAT_D:35;
  hence thesis by INT_1:3;
end;
