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 Th32:
  n<>0 implies n block 1 = 1
proof
  set F={g where g is Function of Segm n,Segm 1:g is onto "increasing};
  assume n<>0;
  then n >=1+0 by NAT_1:13;
  then consider f be Function of Segm n,Segm 1 such that
A1: f is onto "increasing by Th23;
A2: F c= {f}
  proof
    let x be object;
    assume x in F;
    then consider g be Function of Segm n,Segm 1 such that
A3: x=g and
    g is onto "increasing;
    f=g by CARD_1:49,FUNCT_2:51;
    hence thesis by A3,TARSKI:def 1;
  end;
  f in F by A1;
  then F={f} by A2,ZFMISC_1:33;
  hence thesis by CARD_1:30;
end;
