Lemma 87.21.4. Let $S$ be a scheme. Let $f : X \to Y$ and $Z \to Y$ be morphisms of formal algebraic spaces over $S$. Assume $X$, $Y$, $Z$ are locally Noetherian and $f$ and $g$ locally of finite type. If $f$ is rig-surjective, then the base change $Z \times _ Y X \to Z$ is too.

**Proof.**
Follows in a straightforward manner from the definitions (and Formal Spaces, Lemmas 86.24.9 and 86.24.4).
$\square$

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