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We prove distality of quantifier-free relations on valued fields with finiteresidue field. By a result of Chernikov-Galvin-Starchenko, this yieldsSzemer\'edi-Trotter-like incidence bounds for function fields over finitefields. We deduce a version of the Elekes-Szab\'o theorem for such fields.

Incidence bounds in positive characteristic via valuations and distality