∀ {A : Type u_1} {σ : Type u_2} [inst : CommRing A] [inst_1 : SetLike σ A] [inst_2 : AddSubmonoidClass σ A] {𝒜 : ℕ → σ}
  [inst_3 : GradedRing 𝒜] (t : Set (ProjectiveSpectrum 𝒜)) (f : A),
  f ∈ ProjectiveSpectrum.vanishingIdeal t ↔ ∀ x ∈ t, f ∈ x.asHomogeneousIdeal