Lemma 29.50.1. Let $S$ be a scheme. Let $f : X \to S$ be a morphism of schemes. Let $x \in X$, and set $s = f(x)$. Assume
$S$ is locally Noetherian,
$f$ is locally of finite type,
$X$ and $S$ integral, and
Moreover, equality holds if $S$ is universally catenary.