
theorem
  71 is prime
proof
  now
    71 = 2*35 + 1; hence not 2 divides 71 by NAT_4:9;
    71 = 3*23 + 2; hence not 3 divides 71 by NAT_4:9;
    71 = 5*14 + 1; hence not 5 divides 71 by NAT_4:9;
    71 = 7*10 + 1; hence not 7 divides 71 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 71 & n is prime
  holds not n divides 71 by XPRIMET1:8;
  hence thesis by NAT_4:14;
end;
