∀ {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] {S : Set (IsDedekindDomain.HeightOneSpectrum R)} {n : ℕ}
  {a b : Kˣ ⧸ (powMonoidHom n).range},
  a ∈ {x | ∀ v ∉ S, (v.valuationOfNeZeroMod n) x = 1} →
    b ∈ {x | ∀ v ∉ S, (v.valuationOfNeZeroMod n) x = 1} → ∀ v ∉ S, (v.valuationOfNeZeroMod n) (a * b) = 1