Lemma 61.3.6. Let $A \to B$ be a local isomorphism. Then there exist $n \geq 0$, $g_1, \ldots , g_ n \in B$, $f_1, \ldots , f_ n \in A$ such that $(g_1, \ldots , g_ n) = B$ and $A_{f_ i} \cong B_{g_ i}$.

**Proof.**
Omitted.
$\square$

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