Proof. Combinging Lemma 76.12.3 and Derived Categories of Spaces, Lemma 74.25.7 we see that $R\Gamma (X, K \otimes ^\mathbf {L} E)$ is pseudo-coherent in $D(A)$ for all pseudo-coherent $E$ in $D(\mathcal{O}_ X)$. Thus the lemma follows from More on Morphisms of Spaces, Lemma 75.51.4. $\square$

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