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 Th27:
  k<>0 implies 0 block k = 0
proof
  set F={f where f is Function of Segm 0,Segm k:f is onto "increasing};
  assume
A1: k<>0;
  F ={}
  proof
    assume F<>{};
    then consider x be object such that
A2: x in F by XBOOLE_0:def 1;
    ex f be Function of Segm 0,Segm k st x=f & f is onto "increasing by A2;
    hence thesis by A1;
  end;
  hence thesis;
end;
