GK rule truth table example

$I(R \wedge) = (I(\Gamma \Rightarrow A, \Delta) \wedge I(\Gamma \Rightarrow B, \Delta)) \rightarrow I(\Gamma \Rightarrow A \wedge B, \Delta) = ((\bigwedge_{C\in\Gamma}C \rightarrow A \vee \bigvee_{D\in\Delta}D) \wedge (\bigwedge_{C\in\Gamma}C \rightarrow B \vee \bigvee_{D\in\Delta}D)) \rightarrow (\bigwedge_{C\in\Gamma}C \rightarrow (A \wedge B) \vee \bigvee_{D\in\Delta}D)$

\scriptsize
\setlength{\tabcolsep}{1pt}
\begin{tabular}{cccc|ccccccccccc}
A & B & $\bigwedge_{C\in\Gamma} C$ & $\bigvee_{D\in\Delta} D$ & (($\bigwedge_{C\in\Gamma} C$ & $\rightarrow$ & $A \vee \bigvee_{D\in\Delta}D$) & $\wedge$ & ($\bigwedge_{C\in\Gamma} C$ & $\rightarrow$ & $B \vee \bigvee_{D\in\Delta}D$)) & {\color{blue}$\rightarrow$} & ($\bigwedge_{C\in\Gamma} C$ & $\rightarrow$ & $(A \wedge B) \vee \bigvee_{D\in\Delta}D$) \\
\hline
0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & {\color{blue}1} & 0 & 1 & 0 \\
0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & {\color{blue}1} & 0 & 1 & 1 \\
0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & {\color{blue}1} & 1 & 0 & 0 \\
0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & {\color{blue}1} & 1 & 1 & 1 \\
0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & {\color{blue}1} & 0 & 1 & 0 \\
0 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & {\color{blue}1} & 0 & 1 & 1 \\
0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & {\color{blue}1} & 1 & 0 & 0 \\
0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & {\color{blue}1} & 1 & 1 & 1 \\
1 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & {\color{blue}1} & 0 & 1 & 0 \\
1 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & {\color{blue}1} & 0 & 1 & 1 \\
1 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & {\color{blue}1} & 1 & 0 & 0 \\
1 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & {\color{blue}1} & 1 & 1 & 1 \\
1 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & {\color{blue}1} & 0 & 1 & 1 \\
1 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & {\color{blue}1} & 0 & 1 & 1 \\
1 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & {\color{blue}1} & 1 & 1 & 1 \\
1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & {\color{blue}1} & 1 & 1 & 1
\end{tabular}