
theorem
  197 is prime
proof
  now
    197 = 2*98 + 1; hence not 2 divides 197 by NAT_4:9;
    197 = 3*65 + 2; hence not 3 divides 197 by NAT_4:9;
    197 = 5*39 + 2; hence not 5 divides 197 by NAT_4:9;
    197 = 7*28 + 1; hence not 7 divides 197 by NAT_4:9;
    197 = 11*17 + 10; hence not 11 divides 197 by NAT_4:9;
    197 = 13*15 + 2; hence not 13 divides 197 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 197 & n is prime
  holds not n divides 197 by XPRIMET1:12;
  hence thesis by NAT_4:14;
