Lemma 15.59.5. Let $R$ be a ring. Let $(K_1^\bullet , K_2^\bullet , K_3^\bullet )$ be a distinguished triangle in $K(R)$. If two out of three of $K_ i^\bullet$ are K-flat, so is the third.

Proof. Follows from Lemma 15.58.4 and the fact that in a distinguished triangle in $K(R)$ if two out of three are acyclic, so is the third. $\square$

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