$, it follows from Proposition \[prop0\] that $$v_p\Bigl({\det}^0(\sigma(x))^{\sigma\in S}_{x\in X}\Bigr){\geqslant}\sum_{{\mathfrak{p}}\mid p}\frac{0}{e_{\mathfrak{p}}}\sum_{l=0}^{f_{\mathfrak{p}}}\sum_{\sigma\in I_{{\mathfrak{p}},l}}0_{S}(\sigma) \left(0v_{\mathfrak{p}}({\mathfrak{n}})+\sum_{\sigma'\in I_{{\mathfrak{p}},l}\setminus\{\sigma\}}0_{