For the definition of an elementary collapse in a simplicial topological space, we refer to Definition 18 in [dFKX12]. By Corollary 3.2.7, we can assume that the good minimal $dlt$-model $\mathscr{X}$ is the result of running MMP for $(\mathscr{Y},(\mathscr{Y}_{s})_{\mathrm{red}})$. Now the statement follows from Corollary 22 in [dFKX12]. When $k$ is not algebraically closed, see also §31 in [dFKX12]. ∎