Remark 85.17.9 (Variant for Noetherian). Let $P$ be a local property of morphisms of $\textit{WAdm}^{Noeth}$, see Remark 85.17.5. We say $P$ is stable under base change if given $B \to A$ and $B \to C$ in $\textit{WAdm}^{Noeth}$ the property $P(B \to A)$ implies both that $A \widehat{\otimes }_ B C$ is adic Noetherian1 and that $P(C \to A \widehat{\otimes }_ B C)$. In exactly the same way we obtain a variant of Lemma 85.17.7 for morphisms between locally Noetherian formal algebraic spaces over $S$.

[1] See Lemma 85.4.16 for a criterion.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).