
theorem
  47 is prime
proof
  now
    47 = 2*23 + 1; hence not 2 divides 47 by NAT_4:9;
    47 = 3*15 + 2; hence not 3 divides 47 by NAT_4:9;
    47 = 5*9 + 2; hence not 5 divides 47 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 47 & n is prime
  holds not n divides 47 by XPRIMET1:6;
  hence thesis by NAT_4:14;
