Lemma 38.8.2. Let $R$ be a ring. Let $I \subset R$ be an ideal. Let $M$ be an $R$-module. Assume

$R$ is Noetherian and $I$-adically complete,

$M$ is flat over $R$, and

$M/IM$ is a projective $R/I$-module.

Then the $I$-adic completion $M^\wedge $ is a flat Mittag-Leffler $R$-module.

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