Lemma 37.59.3. Let $f : X \to S$ be a local complete intersection morphism. Let $P$ be a scheme smooth over $S$. Let $U \subset X$ be an open subscheme and $i : U \to P$ an immersion of schemes over $S$. Then $i$ is a Koszul-regular immersion.

Proof. This is the defining property of a local complete intersection morphism. See discussion above. $\square$

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