reserve k for Nat;
reserve p for Prime;

theorem Ttool17a:
  p < 17 implies
  p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13
  proof
    assume p < 17;
    then 1+1 < p+1 & p < 16+1 by XREAL_1:6,INT_2:def 4;
    then per cases by NAT_1:13;
    suppose 2 <= p < 13;
      hence thesis by Ttool13a;
    end;
    suppose 13 <= p <= 13+1 or 14 <= p <= 14+1 or 15 <= p <= 15+1;
      then p = 13 by XPRIMES0:14,15,16,NAT_1:9;
      hence thesis;
    end;
  end;
