
theorem
  13 is prime
proof
  now
    13 = 2*6 + 1; hence not 2 divides 13 by NAT_4:9;
    13 = 3*4 + 1; hence not 3 divides 13 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 13 & n is prime
  holds not n divides 13 by XPRIMET1:4;
  hence thesis by NAT_4:14;
end;
