
theorem
  139 is prime
proof
  now
    139 = 2*69 + 1; hence not 2 divides 139 by NAT_4:9;
    139 = 3*46 + 1; hence not 3 divides 139 by NAT_4:9;
    139 = 5*27 + 4; hence not 5 divides 139 by NAT_4:9;
    139 = 7*19 + 6; hence not 7 divides 139 by NAT_4:9;
    139 = 11*12 + 7; hence not 11 divides 139 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 139 & n is prime
  holds not n divides 139 by XPRIMET1:10;
  hence thesis by NAT_4:14;
