
theorem
  113 is prime
proof
  now
    113 = 2*56 + 1; hence not 2 divides 113 by NAT_4:9;
    113 = 3*37 + 2; hence not 3 divides 113 by NAT_4:9;
    113 = 5*22 + 3; hence not 5 divides 113 by NAT_4:9;
    113 = 7*16 + 1; hence not 7 divides 113 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 113 & n is prime
  holds not n divides 113 by XPRIMET1:8;
  hence thesis by NAT_4:14;
