reserve n,k,b for Nat, i for Integer;

theorem Th31:
  71 is prime
  proof
    now
      let n be Element of NAT;
      71 = 2*35 + 1;
      then
      A1: not 2 divides 71 by NAT_4:9;
      71 = 3*23 + 2;
      then
      A2: not 3 divides 71 by NAT_4:9;
      71 = 5*14 + 1;
      then
      A3: not 5 divides 71 by NAT_4:9;
      71 = 7*10 + 1;
      then
      A4: not 7 divides 71 by NAT_4:9;
      71 = 11*6 + 5;
      then
      A5: not 11 divides 71 by NAT_4:9;
      71 = 13*5 + 6;
      then
      A6: not 13 divides 71 by NAT_4:9;
      71 = 17*4 + 3;
      then
      A7: not 17 divides 71 by NAT_4:9;
      71 = 19*3 + 14;
      then
      A8: not 19 divides 71 by NAT_4:9;
      71 = 23*3 + 2;
      then
      A9: not 23 divides 71 by NAT_4:9;
      assume 1<n & n*n<=71 & n is prime;
      hence not n divides 71 by A1,A2,A3,A4,A5,A6,A7,A8,A9,NAT_4:62;
    end;
    hence thesis by NAT_4:14;
  end;
