∀ {R : Type u_1} [inst : CommRing R] [inst_1 : Algebra R ℚ] [inst_2 : IsIntegralClosure R ℤ ℚ]
  [inst_3 : IsDedekindDomain R] [inst_4 : IsFractionRing R ℚ] (v : IsDedekindDomain.HeightOneSpectrum R) (r : ℚ),
  ((UniformSpace.Completion.mapRingEquiv
              (WithVal.congr (IsDedekindDomain.HeightOneSpectrum.valuation ℚ v)
                (Rat.padicValuation ↑(Rat.HeightOneSpectrum.primesEquiv v)) (RingEquiv.refl ℚ))
              ⋯ ⋯).trans
          Padic.withValRingEquiv).toFun
      ((algebraMap ℚ (IsDedekindDomain.HeightOneSpectrum.adicCompletion ℚ v)) r) =
    (algebraMap ℚ ℚ_[↑(Rat.HeightOneSpectrum.primesEquiv v)]) r