I am looking for a version of [Ehresmann's theorem](https://en.wikipedia.org/wiki/Ehresmann%27s_lemma) for analytic manifolds over the $p$-adic numbers $\mathbb{Q}_p$ or, more generally, local fields. I follow the conventions from Serre's book "Lie algebras and Lie groups" concerning analytic manifolds over local fields.

Recall that Ehresmann's theorem states that a proper submersion between smooth manifolds is a locally trivial fibration.

> Does a version of this hold for analytic manifolds over $\mathbb{Q}_p$? Namely, is a proper submerision between analytic manifolds over $\mathbb{Q}_p$ a locally trivial fibration?