Lemma 37.67.5. In Situation 37.67.1 assume $S$ is a locally Noetherian scheme and $X$, $Y$, and $Z$ are locally of finite type over $S$. Then the pushout $Y \amalg _ Z X$ (Proposition 37.67.3) is locally of finite type over $S$.

**Proof.**
Looking on affine opens we recover the result of More on Algebra, Lemma 15.5.1.
$\square$

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