Let $[a,b]$ be a nondegenerate compact interval, let $V \subset C[a,b]$ be an $n$-dimensional Haar space, and let $f \in C[a,b]$. If $h \in V$ is a best uniform approximant to $f$ and $f-h$ is not identically zero, then the residual $r=f-h$ attains its uniform norm at points
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\begin{align*}
a \le t_0 < t_1 < \cdots < t_n \le b
\end{align*}