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 Th25:
  for n,k holds
    card {f where f is Function of Segm n,Segm k:f is  onto "increasing}
    is Element of NAT
proof
  let n,k;
  set F= {f where f is Function of Segm n,Segm k:f is onto "increasing};
  F is finite by Th24;
  then reconsider m = card F as Nat;
  card F=card m;
  hence thesis;
end;
