Lemma 37.29.6. Let $f : X \to Y$ be a proper, flat morphism of schemes of finite presentation. Let $n_{X/Y}$ be the function on $Y$ giving the dimension of fibres of $f$ introduced in Lemma 37.29.2. Then $n_{X/Y}$ is locally constant.

Proof. Immediate consequence of Lemmas 37.29.4 and 37.29.5. $\square$

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