
theorem
  11 is prime
proof
  now
    11 = 2*5 + 1; hence not 2 divides 11 by NAT_4:9;
    11 = 3*3 + 2; hence not 3 divides 11 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 11 & n is prime
  holds not n divides 11 by XPRIMET1:4;
  hence thesis by NAT_4:14;
end;
