Lemma 86.11.4. Consider the property $P$ on arrows of $\textit{WAdm}^{adic*}$ defined in Lemma 86.11.1. Then $P$ is stable under composition as defined in Formal Spaces, Remark 85.17.13.

Proof. The statement makes sense by Lemma 86.11.1. The easiest way to prove it is true is to show that (a) compositions of adic ring maps between adic topological rings are adic and (b) that compositions of continuous ring maps preserves the property of being topologically of finite type. We omit the details. $\square$

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