\begin{equation}
A_{-f}=\Psi_{2}\left(\sum_{f^{\prime}\in\{1,\cdots,F\}-\{f\}}\eta_{IJ,F-1}(A_{f^{\prime}})\right)\ \forall A_{-f}\in\mathcal{M}(I,J,F-1;\widetilde{\Omega})\label{eq:A_minus_f-1}
\end{equation}
