Lemma 86.21.3. Let $S$, $f : X' \to X$, $T \subset |X|$, $U \subset X$, $T' \subset |X'|$, and $U' \subset X'$ be as in Section 86.20. If $X$ is locally Noetherian, $f$ is proper, and $U' \to U$ is an isomorphism, then $f_{/T} : X'_{/T'} \to X_{/T}$ is a formal modification.

**Proof.**
By Formal Spaces, Lemmas 85.16.6 the source and target of the arrow are locally Noetherian formal algebraic spaces. The other conditions follow from Lemmas 86.20.3, 86.20.8, 86.20.9, and 86.20.10.
$\square$

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