reserve k for Nat;
reserve p for Prime;

theorem Ttool13a:
  p < 13 implies p = 2 or p = 3 or p = 5 or p = 7 or p = 11
  proof
    assume p < 13;
    then 1+1 < p+1 & p < 12+1 by XREAL_1:6,INT_2:def 4;
    then per cases by NAT_1:13;
    suppose 2 <= p < 11;
      hence thesis by Ttool11a;
    end;
    suppose 11 <= p <= 11+1;
      hence thesis by XPRIMES0:12,NAT_1:9;
    end;
  end;
