Lemma 76.31.5. Let $S$ be a scheme. Let $f : X \to Y$ be a proper, flat, finitely presented morphism of algebraic spaces over $S$. Let $n_{X/Y}$ be the function on $Y$ giving the dimension of fibres of $f$ introduced in Lemma 76.31.2. Then $n_{X/Y}$ is locally constant.

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