Lemma 51.4.4. Let $I, J \subset A$ be finitely generated ideals of a ring $A$. Then $\text{cd}(A, I + J) \leq \text{cd}(A, I) + \text{cd}(A, J)$.

**Proof.**
Use the definition and Dualizing Complexes, Lemma 47.9.6.
$\square$

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