In the situation of Lemma B.3 suppose that the formal completion $\mathfrak{X}$ of $\mathscr{X}$ is strongly nondegenerate strictly polystable and denote by $\Delta$ the associated skeleton. Then $\varphi$ is convex on every face of $\Delta$ and satisfies $\varphi\leq\varphi\circ p_{\mathfrak{X}}$.