
theorem
  89 is prime
proof
  now
    89 = 2*44 + 1; hence not 2 divides 89 by NAT_4:9;
    89 = 3*29 + 2; hence not 3 divides 89 by NAT_4:9;
    89 = 5*17 + 4; hence not 5 divides 89 by NAT_4:9;
    89 = 7*12 + 5; hence not 7 divides 89 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 89 & n is prime
  holds not n divides 89 by XPRIMET1:8;
  hence thesis by NAT_4:14;
