Lemma 29.30.14. Let $f : X \to S$ be a syntomic morphism. The function $x \mapsto \dim _ x(X_{f(x)})$ is locally constant on $X$.

Proof. By Lemma 29.30.10 the morphism $f$ locally looks like a standard syntomic morphism of affines. Hence the result follows from Lemma 29.30.13. $\square$

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