
theorem
  173 is prime
proof
  now
    173 = 2*86 + 1; hence not 2 divides 173 by NAT_4:9;
    173 = 3*57 + 2; hence not 3 divides 173 by NAT_4:9;
    173 = 5*34 + 3; hence not 5 divides 173 by NAT_4:9;
    173 = 7*24 + 5; hence not 7 divides 173 by NAT_4:9;
    173 = 11*15 + 8; hence not 11 divides 173 by NAT_4:9;
    173 = 13*13 + 4; hence not 13 divides 173 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 173 & n is prime
  holds not n divides 173 by XPRIMET1:12;
  hence thesis by NAT_4:14;
