Lemma 65.37.10. Let $X$ and $Y$ be locally Noetherian algebraic spaces over a scheme $S$, and let $f : X \to Y$ be a smooth morphism. For every point $x \in |X|$ with image $y \in |Y|$,

where $\dim _ x(X_ y)$ is the relative dimension of $f$ at $x$ as in Definition 65.33.1.

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