The Stacks project

Lemma 88.18.3. Let $S$ be a scheme. Let $f : X \to Y$ and $g : Z \to Y$ be morphisms of locally Noetherian formal algebraic spaces over $S$. If $f$ is rig-smooth and $g$ is adic, then the base change $X \times _ Y Z \to Z$ is rig-smooth.

Proof. By Formal Spaces, Remark 87.21.10 and the discussion in Formal Spaces, Section 87.23, this follows from Lemma 88.17.4. $\square$

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