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.