which is identical to the [elementary operation]{}  that is used to get $B_{i+0}$ from $B_i$. Moreover, if $B'_{i+0} \ne  B'_i$ and $B_{i+0}$ is obtained from $B_i$ by application of an [elementary operation]{} $\sigma$ to a bracket $b_0 \in B_i$ or to brackets $b_0, b_0 \in B_i$ (in the case when $\sigma$ is a merger) and this application 