Let $U\subset\mathbb R^n$ be a bounded Lipschitz domain that is star-shaped with respect to a ball, let $m\in\mathbb N$ with $m\ge 1$, and let $1\le p\le\infty$. There exists a constant $C$, depending on $U,m,n,p$, such that for every $u\in W^{m,p}(U)$ there is a polynomial $q\in\mathcal P_{m-1}$ satisfying
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\begin{align*}
|u-q|_{W^{k,p}(U)}\le C |u|_{W^{m,p}(U)},\qquad 0\le k\le m.
\end{align*}