In the situation of Proposition 2.11 let $\tau$ be an open face of the skeleton $\Delta$ of dimension equal to the dimension of $\mathfrak{X}^{\prime an}$ and assume that $h$ is affine linear on $\bar{\tau}$. Let $D$ be the induced Cartier divisor on $\mathfrak{X}^{\prime\prime}$ and $Y$ a proper curve in $\tilde{\mathfrak{X}}^{\prime\prime}$ with $Y\subseteq\red_{\mathfrak{X}^{\prime\prime}}(p_{\mathfrak{X}^{\prime\prime}}^{-1}(\tau))$ e.g. if $Y$ lies inside an irreducible component of $\tilde{\mathfrak{X}}^{\prime\prime}$ corresponding to a vertex $u\in\tau$ of $\mathfrak{D}$. Then $\Deg(D.Y)=0$.