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@@ -417,6 +417,8 @@ Now, let $\BRev_\beta(F)$ denote the revenue of the $\beta$-bundling mechanism i
 
 \begin{lemma}[Theorem 6.1 in \citep{yao}, with a constant of 7 instead of 8.5] Let $F =F_1\times\dots\times F_m$, let $\BRev_\beta(F)$ denote the revenue of the $\beta$-bundling mechanism, and let $\Rev_\beta(F)$ denote the revenue of the optimal $\beta$-exclusive mechanism. Then, $$\Rev_\beta(F) \leq 7\cdot \BRev_\beta(F).$$ \end{lemma}
 
+Now, to summarize the results of these lemmas, we have shown that there is a constant approximation to the r
+
 \section{Conclusion}
 
 \bibliographystyle{abbrvnat}