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 Th26:
  n block n = 1
proof
  set F={f where f is Function of Segm n,Segm n:f is onto "increasing};
A1: F c= {id n}
  proof
    let x be object;
    assume x in F;
    then consider f be Function of Segm n,Segm n such that
A2: x=f and
A3: f is onto "increasing;
    f=id n by A3,Th20;
    hence thesis by A2,TARSKI:def 1;
  end;
  n=0 iff n=0;
  then consider f be Function of Segm n,Segm n such that
A4: f is onto "increasing by Th23;
  f in F by A4;
  then F={id n} by A1,ZFMISC_1:33;
  hence thesis by CARD_1:30;
end;
