reserve k for Nat;
reserve p for Prime;

theorem Ttool5a:
  p < 5 implies p = 2 or p = 3
  proof
    assume p < 5;
    then 1+1 < p+1 & p < 4+1 by XREAL_1:6,INT_2:def 4;
    then per cases by NAT_1:13;
    suppose 2 <= p < 3;
      hence thesis by Th1;
    end;
    suppose 3 <= p <= 3+1;
      hence thesis by XPRIMES0:4,NAT_1:9;
    end;
  end;
