Lemma 15.91.16. In Situation 15.91.15. For $K \in D(A)$ the object $K' = R\mathop{\mathrm{lim}}\nolimits (K \otimes _ A^\mathbf {L} K_ n^\bullet )$ is derived complete with respect to $I$.

Proof. This is a special case of Lemma 15.91.14 because $f_ i^ n$ acts by an endomorphism of $K_ n^\bullet$ which is homotopic to zero by Lemma 15.28.6. $\square$

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