
theorem
  19 is prime
proof
  now
    let n be Element of NAT;
    19 = 2*9 + 1;
    then
A1: not 2 divides 19 by Th9;
    19 = 3*6 + 1;
    then
A2: not 3 divides 19 by Th9;
    assume 1<n & n*n<=19 & n is prime;
    hence not n divides 19 by A1,A2,Lm3;
  end;
  hence thesis by Th14;
end;
