Lemma 15.112.2. Let $A$ be a discrete valuation ring with fraction field $K$. Let $L/K$ be a finite Galois extension. Then there are $e \geq 1$ and $f \geq 1$ such that $e_ i = e$ and $f_ i = f$ for all $i$ (notation as in Remark 15.111.6). In particular $[L : K] = n e f$.

Proof. Immediate consequence of Lemma 15.112.1 and the definitions. $\square$

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).