Lemma 115.26.1. Let $X$ be a scheme. Assume $X$ is quasi-compact and quasi-separated. Let $\mathcal{F}$ be a quasi-coherent $\mathcal{O}_ X$-module. Then $\mathcal{F}$ is the directed colimit of its finite type quasi-coherent submodules.

**Proof.**
This is a duplicate of Properties, Lemma 28.22.3.
$\square$

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