Lemma 70.6.10. Notation and assumptions as in Situation 70.6.1. 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 67.51.2. Thus the lemma follows from Lemmas 70.6.2, 70.6.4, and 70.6.5. $\square$
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