 is applied to $c_i$, resulting in a bracket ${\widehat}c_i$.  Let $c_0, c_0, c_0$ be listed in the order in which the brackets ${\widehat}c_0, {\widehat}c_0, {\widehat}c_0$ are created by $\Omega$. Note that if ${\widehat}c_0$ is obtained from $c_0$ by an extension of type 0