This is [Proposition 2.1.4, six-I] with slightly changed hypotheses; it is the analogue of [Proposition 3.13, Spaltenstein] for sites.

Lemma 21.25.2. In Situation 21.25.1 for any $E \in D_\mathcal {A}(\mathcal{O})$ the canonical map $E \to R\mathop{\mathrm{lim}}\nolimits \tau _{\geq -n} E$ is an isomorphism in $D(\mathcal{O})$.

Proof. Follows immediately from Lemma 21.23.8. $\square$

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