Lemma 37.64.5. In Situation 37.64.1 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 37.64.3) 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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