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@@ -283,7 +283,7 @@ Suppose, for contradiction, that such a mechanism exists. Consider two experimen
 We now present the proof of Theorem~\ref{thm:main}. Truthfulness and individual
 rationality follows from monotonicity and threshold payments.  Monotonicity and
 budget feasibility follow the same steps as the analysis of Chen \emph{et al.} \cite{chen};
- for the sake of completeness, we briefly restate the proofs in the Appendix.
+ for the sake of completeness, we restate their proof in the Appendix.
  Our proof of the approximation ratio uses a bound on our concave relaxation
 $L$ (Lemma~\ref{lemma:relaxation}). This is our main technical
 contribution; the proof of this lemma can be found in Section~\ref{sec:relaxation}.