Let $\mathscr{X}$ be a $dlt$-model of $X$ and let $h:\mathscr{Y}\to\mathscr{X}$ be a log resolution of $(\mathscr{X},\mathscr{X}_{s})$. Denote by $\Delta$ the log pullback of $(\mathscr{X}_{s})_{\mathrm{red}}$ to $\mathscr{Y}$. Let $x$ be a point of $\mathrm{Sk}(\mathscr{Y})$ such that $\mathrm{red}_{\mathscr{X}}(x)$ does not lie in $\mathscr{X}^{\mathrm{snc}}$. Then $\Delta<(\mathscr{Y}_{s})_{\mathrm{red}}$ locally at $\mathrm{red}_{\mathscr{Y}}(x)$.