Let $n \in \mathbb{N}$, let $X \subset C[a,b]$ be an $n$-dimensional Haar space, let $f \in C[a,b]$, and let $p \in X$. Suppose there are points $a \le x_0 < x_1 < \dots < x_n \le b$ and a sign $\sigma \in \{-1,1\}$ such that $\sigma(-1)^i(f(x_i)-p(x_i)) \ge m > 0$ for every $i \in \{0,\dots,n\}$. If $E^* = \inf_{q \in X}\|f-q\|_\infty$, then $E^* \ge m$.