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.
$\square$

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