Let $X$ be a scheme over $S$, where $S$ is a scheme of characteristic $p$. I heard that we can prove that the relative Frobenius $\operatorname{Frob}_{X/S}$ is an isomorphism iff $X\to S$ is étale "by dévissage to $\mathbb{A}^n$".
If I understand correctly, this means that we would use the théorème 3.1.2 in EGA III, which I show here for completeness.
However, I have absolutely no idea how we could use it.
Obs: I know that there exists another question here on Math.SE with the same title but mine is explicitly about using this argument of "dévissage to $\mathbb{A}^n$".