reserve k, l, m, n, i, j for Nat,
  K, N for non empty Subset of NAT,
  Ke, Ne, Me for Subset of NAT,
  X,Y for set;
reserve f for Function of Segm n,Segm k;

theorem Th24:
  for n,k holds
  {f where f is Function of Segm  n,Segm k:f is onto "increasing} is finite
proof
  let n,k;
  defpred P[Function of Segm n,Segm k] means $1 is onto "increasing;
  {f where f is Function of Segm n,Segm k:P[f]} is finite from Sch1;
  hence thesis;
end;
