An fpqc morphism is a "quotient" morphism (as a continuous map between topological spaces)

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Let $f: X \to Y$ be a faithfully flat quasi-compact morphism. Then for a subset $V \subseteq Y$, $V$ is open in $Y$ iff $f^{-1}(V)$ is open in $X$?

I know this is EGA IV2 2.3.12. But its proof is very complicated for me. (I'm not familiar with pro-constructibility.) So are there other good proofs of it or its references?

Thank you very much!