no goals
R : Type u
inst✝¹ : Ring R
Γ₀ : Type v
inst✝ : LinearOrderedCommGroupWithZero Γ₀
_i : Valued R Γ₀
s : Set R
x : R
⊢ s ∈ 𝓝 x ↔ ∃ γ, {y | ↑v (y - x) < ↑γ} ⊆ s
simp only [← nhds_translation_add_neg x, ← sub_eq_add_neg, preimage_setOf_eq, true_and,
  ((hasBasis_nhds_zero R Γ₀).comap fun y => y - x).mem_iff]