Lemma 69.6.10. Notation and assumptions as in Situation 69.6.1. If

$f$ is a isomorphism,

$f_0$ is locally of finite presentation,

then $f_ i$ is a isomorphism for some $i \geq 0$.

Lemma 69.6.10. Notation and assumptions as in Situation 69.6.1. If

$f$ is a isomorphism,

$f_0$ is locally of finite presentation,

then $f_ i$ is a isomorphism for some $i \geq 0$.

**Proof.**
Being an isomorphism is equivalent to being étale, universally injective, and surjective, see Morphisms of Spaces, Lemma 66.51.2. Thus the lemma follows from Lemmas 69.6.2, 69.6.4, and 69.6.5.
$\square$

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