
theorem Th32:
  43 is prime
proof
  now
    let n be Element of NAT;
    43 = 2*21 + 1;
    then
A1: not 2 divides 43 by Th9;
    43 = 3*14 + 1;
    then
A2: not 3 divides 43 by Th9;
    43 = 13*3 + 4;
    then
A3: not 13 divides 43 by Th9;
    43 = 11*3 + 10;
    then
A4: not 11 divides 43 by Th9;
    43 = 19*2 + 5;
    then
A5: not 19 divides 43 by Th9;
    43 = 17*2 + 9;
    then
A6: not 17 divides 43 by Th9;
    43 = 23*1 + 20;
    then
A7: not 23 divides 43 by Th9;
    43 = 7*6 + 1;
    then
A8: not 7 divides 43 by Th9;
    43 = 5*8 + 3;
    then
A9: not 5 divides 43 by Th9;
    assume 1<n & n*n<=43 & n is prime;
    hence not n divides 43 by A1,A2,A9,A8,A4,A3,A6,A5,A7,Lm6;
  end;
  hence thesis by Th14;
end;
