Proposition 8

Let K be a field, v a valuation on K, L a finite quasi-Galois extension of K of degree n and $(v'_i)_{1 \leq i \leq g}$ a complete system of extensions of v to L. Then $e(v'_i/v)$ and $f(v'_i/v)$ have values e and $\mathfrak{f}$ independent of i. Then $ef g \leq n$. If the integral closure in L of the ring A of v is a finitely generated A-module, then $ef g = n$.

This follows immediately from Theorems 1 (no. 3) and 2 (no. 5).