
theorem
  37 is prime
proof
  now
    37 = 2*18 + 1; hence not 2 divides 37 by NAT_4:9;
    37 = 3*12 + 1; hence not 3 divides 37 by NAT_4:9;
    37 = 5*7 + 2; hence not 5 divides 37 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 37 & n is prime
  holds not n divides 37 by XPRIMET1:6;
  hence thesis by NAT_4:14;
