Lemma 10.104.8. Let R be a Noetherian local Cohen-Macaulay ring of dimension d. Let 0 \to K \to R^{\oplus n} \to M \to 0 be an exact sequence of R-modules. Then either M = 0, or \text{depth}(K) > \text{depth}(M), or \text{depth}(K) = \text{depth}(M) = d.
Proof. This is a special case of Lemma 10.72.6. \square
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