∀ {Γ₀ : Type u_2} [inst : LinearOrderedCommGroupWithZero Γ₀] {K : Type u_3} [inst_1 : Field K] (v : Valuation K Γ₀)
  (R : Type u_4) [inst_2 : CommRing R] [inst_3 : Algebra R K] [inst_4 : IsIntegralClosure R ℤ K]
  (a : NumberField.RingOfIntegers (WithVal v)),
  (NumberField.RingOfIntegers.withValEquiv v R) a =
    (↑↑(IsIntegralClosure.equiv ℤ R (WithVal v) (NumberField.RingOfIntegers (WithVal v)))).symm a