
theorem
  41 is prime
proof
  now
    41 = 2*20 + 1; hence not 2 divides 41 by NAT_4:9;
    41 = 3*13 + 2; hence not 3 divides 41 by NAT_4:9;
    41 = 5*8 + 1; hence not 5 divides 41 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 41 & n is prime
  holds not n divides 41 by XPRIMET1:6;
  hence thesis by NAT_4:14;
