Let $n\geq 1$, and let $\pi$ be a noncrossing partition of the linearly ordered set $[n]:=\{1,\dots,n\}$. A block $V$ of $\pi$ is called an interval block if there exist integers $p$ and $q$ with $1\leq p\leq q\leq n$ such that
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\begin{align*}
V=\{p,p+1,\dots,q\}.
\end{align*}
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Then $\pi$ has an interval block. If $\pi\neq 1_n$, where $1_n$ denotes the one-block partition $\{[n]\}$, then $\pi$ has an interval block that is a proper subset of $[n]$.