Suppose ${\mathcal{X}}$, ${\mathcal{X}}^{\prime}$ and ${\mathcal{X}}^{\prime\prime}$ are snc models, with ${\mathcal{X}}^{\prime}$ dominating ${\mathcal{X}}$ and ${\mathcal{X}}^{\prime\prime}$ dominating ${\mathcal{X}}^{\prime}$. Let $\sigma^{\prime\prime}$ be a simplex of $\Delta({\mathcal{X}}^{\prime\prime})$, and let $\sigma^{\prime}$ be the smallest simplex of $\Delta({\mathcal{X}}^{\prime})$ containing $r_{{\mathcal{X}}^{\prime}{\mathcal{X}}^{\prime\prime}}(\sigma^{\prime\prime})$. Then $\sigma^{\prime\prime}$ is active for $r_{{\mathcal{X}}{\mathcal{X}}^{\prime\prime}}$ iff $\sigma^{\prime\prime}$ is active for $r_{{\mathcal{X}}^{\prime}{\mathcal{X}}^{\prime\prime}}$ and $\sigma^{\prime}$ is active for $r_{{\mathcal{X}}{\mathcal{X}}^{\prime}}$. As a consequence, $A_{{\mathcal{X}}{\mathcal{X}}^{\prime\prime}}=A_{{\mathcal{X}}^{\prime}{\mathcal{X}}^{\prime\prime}}\cap r_{{\mathcal{X}}^{\prime}{\mathcal{X}}^{\prime\prime}}^{-1}(A_{{\mathcal{X}}{\mathcal{X}}^{\prime}})$.