  In this short paper, we prove the following generalization of a result of
Methuku and P\'{a}lv\"{o}lgyi. Let $P$ be a poset, then there exists a constant
$C_{P}$ with the following property. Let $k$ and $n$ be arbitrary positive
integers such that $n$ is at least the dimension of $P$, and let $w$ be the
size of the largest antichain of the grid $[k]^{n}$ endowed with the usual
pointwise ordering. If $S$ is a subset of $[k]^{n}$ not containing an induced
copy of $P$, then $|S|\leq C_{P}w$.
