∀ {σ : Type u_1} {A : Type u} [inst : CommRing A] [inst_1 : SetLike σ A] [inst_2 : AddSubgroupClass σ A] (𝒜 : ℕ → σ)
  [inst_3 : GradedRing 𝒜] {f : A} {m' : ℕ} {g : A} (g_deg : g ∈ 𝒜 m') {x : A} (hx : x = f * g),
  CategoryTheory.CategoryStruct.comp (CommRingCat.ofHom (HomogeneousLocalization.awayMap 𝒜 g_deg hx))
      (AlgebraicGeometry.Proj.awayToSection 𝒜 x) =
    CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Proj.awayToSection 𝒜 f)
      ((AlgebraicGeometry.Proj 𝒜).presheaf.map (CategoryTheory.homOfLE ⋯).op)