External equality and absolute equality are defined model independently by Fu. It is interesting and important to know whether these two equalities coincide or not. There are some results in Fu's paper for this issue. It is relatively easy to prove the coincidence if the summation operator is in the language, otherwise it is harder. In fact Fu proposed it as an open problem whether the two equalities coincide in some languages without summation. In this paper, the proofs of the coincidence in finite CCS and π calculus without summation are given.
