reserve k for Nat;
reserve p for Prime;

theorem Ttool7a:
  p < 7 implies p = 2 or p = 3 or p = 5
  proof
    assume p < 7;
    then 1+1 < p+1 & p < 6+1 by XREAL_1:6,INT_2:def 4;
    then per cases by NAT_1:13;
    suppose 2 <= p < 5;
      hence thesis by Ttool5a;
    end;
    suppose 5 <= p <= 5+1;
      then p = 5 by XPRIMES0:6,NAT_1:9;
      hence thesis;
    end;
  end;
