Lemma 47.14.3. Let $R \to A$ and $R \to R'$ be ring maps and $A' = A \otimes _ R R'$. Assume

$A$ is perfect as an $R$-module,

$A$ and $R'$ are tor independent over $R$.

Then (47.14.0.1) is an isomorphism for all $K \in D(R)$.

Lemma 47.14.3. Let $R \to A$ and $R \to R'$ be ring maps and $A' = A \otimes _ R R'$. Assume

$A$ is perfect as an $R$-module,

$A$ and $R'$ are tor independent over $R$.

Then (47.14.0.1) is an isomorphism for all $K \in D(R)$.

**Proof.**
Follows from Lemma 47.14.1 and More on Algebra, Lemma 15.98.3 part (1).
$\square$

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