With notation as above, we say that $\sigma^{\prime}$ is active for $r_{{\mathcal{X}}{\mathcal{X}}^{\prime}}$ if the restriction $\rho|_{Y^{\prime}}\colon Y^{\prime}\to Y$ is a bimeromorphic morphism and the ${\mathbb{Q}}$-linear map defining $r_{{\mathcal{X}}{\mathcal{X}}^{\prime}}|_{\sigma^{\prime}}$ is an isomorphism. In this case, $\sigma^{\prime}$ and $\sigma$ have the same dimension, and $r_{{\mathcal{X}}{\mathcal{X}}^{\prime}}$ maps $\sigma^{\prime}$ homeomorphically onto a ${\mathbb{Z}}$-subsimplex of $\sigma$ of the same dimension.