∀ (R : Type u_1) [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : IsDiscreteValuationRing R] {K : Type u_2}
  [inst_3 : Field K] [inst_4 : Algebra R K] [inst_5 : IsFractionRing R K] (W : WeierstrassCurve K),
  WeierstrassCurve.valuation_Δ_aux R W =
    if h : WeierstrassCurve.IsIntegral R W then
      ⟨(IsDedekindDomain.HeightOneSpectrum.valuation K (IsDiscreteValuationRing.maximalIdeal R)) W.Δ, ⋯⟩
    else ⟨⊥, WeierstrassCurve.valuation_Δ_aux._proof_4⟩