Lemma 87.20.4. Let $S$ be a scheme. Let $X \to Y$ be a morphism of affine formal algebraic spaces which is representable by algebraic spaces, surjective, and flat. Then $X$ is adic* if and only if $Y$ is adic*.

**Proof.**
The proof is exactly the same as the proof of Lemma 87.20.2 except that at the end we use Lemma 87.8.5.
$\square$

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