∀ {R : Type u_1} [inst : CommRing R] [inst_1 : ValuativeRel R] [inst_2 : TopologicalSpace R] [IsValuativeTopology R]
  {s : Set R} {x : R}, s ∈ nhds x ↔ ∃ γ, {z | (ValuativeRel.valuation R) (z - x) < ↑γ} ⊆ s