∀ {A : Type u_1} {σ : Type u_2} [inst : CommRing A] [inst_1 : SetLike σ A] [inst_2 : AddSubgroupClass σ A] {𝒜 : ℕ → σ}
  [inst_3 : GradedRing 𝒜] (f : A) (z : HomogeneousLocalization.NumDenSameDeg 𝒜 (Submonoid.powers f)),
  AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.toFun f ⁻¹'
      ↑(PrimeSpectrum.basicOpen (HomogeneousLocalization.mk z)) =
    Subtype.val ⁻¹' ↑(ProjectiveSpectrum.basicOpen 𝒜 ↑z.num)