
theorem
  439 is prime
proof
  now
    439 = 2*219 + 1; hence not 2 divides 439 by NAT_4:9;
    439 = 3*146 + 1; hence not 3 divides 439 by NAT_4:9;
    439 = 5*87 + 4; hence not 5 divides 439 by NAT_4:9;
    439 = 7*62 + 5; hence not 7 divides 439 by NAT_4:9;
    439 = 11*39 + 10; hence not 11 divides 439 by NAT_4:9;
    439 = 13*33 + 10; hence not 13 divides 439 by NAT_4:9;
    439 = 17*25 + 14; hence not 17 divides 439 by NAT_4:9;
    439 = 19*23 + 2; hence not 19 divides 439 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 439 & n is prime
  holds not n divides 439 by XPRIMET1:16;
  hence thesis by NAT_4:14;
end;
