theorem
  b! <= b|^b
  proof
    per cases by NAT_1:23;
    suppose b >=2;
      hence thesis by Th24;
    end;
    suppose
      b = 0;
      hence thesis by NEWTON:4,12;
    end;
    suppose
      b = 1;
      hence thesis by NEWTON:13;
    end;
  end;
