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The Stacks project

Lemma 61.12.3. Any étale covering and any Zariski covering is a pro-étale covering.

Proof. This follows from the corresponding result for fpqc coverings (Topologies, Lemma 34.9.7), Lemma 61.12.2, and the fact that an étale morphism is a weakly étale morphism, see More on Morphisms, Lemma 37.64.9. \square

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