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\section*{Lemma 0A}%
\label{sec:lemma-0a}

Assume that $\langle x_1, \ldots, x_m \rangle = \langle y_1, \ldots, y_m, \ldots, y_{m+k} \rangle$.
Then $x_1 = \langle y_1, \ldots, y_{k+1} \rangle$.

\begin{proof}

  \link{lemma_0a}

\end{proof}

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