reserve k for Nat;
reserve p for Prime;

theorem Ttool11a:
  p < 11 implies p = 2 or p = 3 or p = 5 or p = 7
  proof
    assume p < 11;
    then 1+1 < p+1 & p < 10+1 by XREAL_1:6,INT_2:def 4;
    then per cases by NAT_1:13;
    suppose 2 <= p < 7;
      hence thesis by Ttool7a;
    end;
    suppose 7 <= p <= 7+1 or 8 <= p <= 8+1 or 9 <= p <= 9+1;
      then p = 7 by XPRIMES0:10,8,9,NAT_1:9;
      hence thesis;
    end;
  end;
