Lemma 10.137.2. Let $R \to S$ be a ring map of finite presentation. If for some presentation $\alpha $ of $S$ over $R$ the naive cotangent complex $\mathop{N\! L}\nolimits (\alpha )$ is quasi-isomorphic to a finite projective $S$-module placed in degree $0$, then this holds for any presentation.

**Proof.**
Immediate from Lemma 10.134.2.
$\square$

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