
theorem
  157 is prime
proof
  now
    157 = 2*78 + 1; hence not 2 divides 157 by NAT_4:9;
    157 = 3*52 + 1; hence not 3 divides 157 by NAT_4:9;
    157 = 5*31 + 2; hence not 5 divides 157 by NAT_4:9;
    157 = 7*22 + 3; hence not 7 divides 157 by NAT_4:9;
    157 = 11*14 + 3; hence not 11 divides 157 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 157 & n is prime
  holds not n divides 157 by XPRIMET1:10;
  hence thesis by NAT_4:14;
end;
