Lemma 10.94.2. Let $R \to S$ be a faithfully flat ring map. Let $M$ be an $R$-module. If the $S$-module $M \otimes _ R S$ is countably generated and projective, then $M$ is countably generated and projective.

**Proof.**
Follows from Lemma 10.82.2, Lemma 10.94.1, the fact that countable generation descends, and Theorem 10.92.3.
$\square$

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