& \langle\xi_n,\MAPOPEN{G^O_n}::\DEEPCLOSE{G^C_n,\Gamma},\tau,\kappa\rangle
\\[1ex]
- \multicolumn{3}{l}{\hspace{2em}
+ \multicolumn{3}{l}{\hspace{2em}\mathit{where} ~
\left\{
\begin{array}{rcll}
\langle\xi_0, G^O_0, G^C_0\rangle & = & \langle\xi, [], []\rangle \\
\langle\xi_{i+1}, G^O_{i+1}, G^C_{i+1}\rangle
& =
& \langle\xi_i, G^O_i, G^C_i\rangle
- & g_i\in G^C_i \\
+ & g_{i+1}\in G^C_i \\
\langle\xi_{i+1}, G^O_{i+1}, G^C_{i+1}\rangle
& =
& \langle\xi, (G^O_i\setminus G^C)\cup G^O, G^C_i\cup G^C\rangle
- & g_i\not\in G^C_i \\
+ & g_{i+1}\not\in G^C_i \\
& & \mathit{where} ~ \langle\xi,G^O,G^C\rangle=\TSEM{T}{\xi_i}{g_{i+1}}
\\
\end{array}