Lemma 86.20.8. In the situation above. If $X$ is locally Noetherian, $f$ is locally of finite type, and $U' \to U$ is étale, then $f_{/T}$ is rig-étale.
Proof. The proof is exactly the same as the proof of Lemma 86.20.7 except with Lemmas 86.4.3 and 86.15.2 replaced by Lemmas 86.8.4 and 86.17.2 $\square$
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