Error insets are placed inside words. See attached file.
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\layout Proof
Therefore, each equivalence class of the adjacency relation corresponds
to an interval in
\begin_inset Formula $\{1,\ldots,k\}$
\end_inset
.
More precisely, let
\begin_inset Formula $1=\bindex{1}<\bindex{2}<\cdots<\bindex{x}<\bindex{x+1}=k+1$
\end_inset
be indices
\the_end
