∀ (R : Type u_2) [inst : CommRing R] [inst_1 : IsDedekindDomain R] (K : Type u_1) [inst_2 : Field K]
  [inst_3 : Algebra R K] [inst_4 : IsFractionRing R K] (v : IsDedekindDomain.HeightOneSpectrum R) (x y : R),
  ⟨↑((WithVal.equiv (IsDedekindDomain.HeightOneSpectrum.valuation K v)).symm ((algebraMap R K) (x * y))), ⋯⟩ =
    ⟨↑((WithVal.equiv (IsDedekindDomain.HeightOneSpectrum.valuation K v)).symm ((algebraMap R K) x)), ⋯⟩ *
      ⟨↑((WithVal.equiv (IsDedekindDomain.HeightOneSpectrum.valuation K v)).symm ((algebraMap R K) y)), ⋯⟩