Proof. Apply Lemmas 75.13.2, 75.13.3, 75.13.4 to get a pseudo-coherent object $K$ of $D(\mathcal{O}_ X)$. Choosing affine $U$ in Lemma 75.13.5 it follows immediately that $K$ restricts to $K_ n$ over $X_ n$. $\square$

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