ScalingStacks

Lemma 3.8. Let $\lVert\mathord{\cdot}\rVert_{n}$ be a norm on $V_{n}(L)$, then $\frac{1}{n}\mathrm{FS}(\lVert\mathord{\cdot}\rVert_{n})$ is a continuous metric on $L$. ([CMor18, Proposition 3.1])