Lemma 20.26.8. Let $(X, \mathcal{O}_ X)$ be a ringed space. A bounded above complex of flat $\mathcal{O}_ X$-modules is K-flat.

**Proof.**
We can check this on stalks, see Lemma 20.26.4. Thus this lemma follows from Modules, Lemma 17.16.2 and More on Algebra, Lemma 15.57.9.
$\square$

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