In our paper [3], a sequent system for the contraction‐less positive relevant logic with co‐tenability,, is considered. Its sequent system with the rule of cut, which does not involve the truth constant t, is presented, and the proof that it admits the elimination of cut is given. However, in the proof of the cut‐elimination theorem some forms of proofs, which may cause difficulties for the cut‐elimination argument, are not considered. The purpose of this paper is to present them and to (...) re‐prove that admits the elimination of cut. (shrink)