Lemma 17.15.2. Let $(X, \mathcal{O}_ X)$ be a ringed space. Let $\mathcal{F}'$, $\mathcal{G}'$ be presheaves of $\mathcal{O}_ X$-modules with sheafifications $\mathcal{F}$, $\mathcal{G}$. Then $\mathcal{F} \otimes _{\mathcal{O}_ X} \mathcal{G} = (\mathcal{F}' \otimes _{p, \mathcal{O}_ X} \mathcal{G}')^\# $.

**Proof.**
Omitted.
$\square$

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