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
  n block 0 = 1 iff n=0
proof
  n block 0 = 1 implies n=0
  proof
    set F={f where f is Function of Segm n,Segm 0:f is onto "increasing};
A1: card {{}}= 1 by CARD_1:30;
    assume n block 0=1;
    then consider x be object such that
A2: F={x} by A1,CARD_1:29;
    x in F by A2,TARSKI:def 1;
    then ex f be Function of Segm n,Segm 0 st x=f & f is onto "increasing;
    hence thesis;
  end;
  hence thesis by Th26;
end;
