The argument in [Gub98, Lemma 7.6] shows that $L$ admits a formal metric. Hence, tensoring by $L^{-1}$, we can assume that $L=\mathcal{O}_{V}$ and we are reduced to prove that for any continuous function $f\colon V\to{\mathbb{R}}$ there exists a sequence of model functions $(\varphi_{n})_{n\in{\mathbb{N}}}$ which converges uniformly to $f$ which was done in Proposition 2.13. ∎