fixed some typesetting problems
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@ -83,13 +83,10 @@ We do a second proof of \yaref{thm:hindman}:
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\footnote{Note that here we might need to choose
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a bigger $N$ than the $M$ in \yaref{def:unifrec},
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but $2M$ suffices.}%
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\[
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\forall n.~\exists N% \gg n
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.~\forall r.~(y(r), y(r+1), \ldots, y(r+N - 1)
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\text{ contains }
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(y(0), y(1), \ldots, y(n))
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\text{ as a subsequence.}
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\]
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\begin{IEEEeqnarray*}{rl}
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\forall n.~\exists N.~\forall r.~&(y(r), y(r+1), \ldots, y(r+N - 1)\\
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&\text{ contains } (y(0), y(1), \ldots, y(n)) \text{ as a subsequence.}\\
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\end{IEEEeqnarray*}
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\end{itemize}
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Consider $y(0)$.
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