Lemma 15.116.1. Let $A \to B$ be an extension of discrete valuation rings with fraction fields $K \subset L$. If $K_1/K$ is a solution for $A \subset B$, then for any finite extension $K_2/K_1$ the extension $K_2/K$ is a solution for $A \subset B$.

**Proof.**
This follows from Lemma 15.114.3. Details omitted.
$\square$

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