∀ {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} (f_deg : f ∈ 𝒜 m) (hm : 0 < m) {m' : ℕ} {g : A} (g_deg : g ∈ 𝒜 m')
  (hm' : 0 < m') {x : A} (hx : x = f * g) {Z : AlgebraicGeometry.Scheme}
  (h :
    AlgebraicGeometry.Spec
        { carrier := HomogeneousLocalization.Away 𝒜 g,
          commRing := HomogeneousLocalization.homogeneousLocalizationCommRing } ⟶
      Z),
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Proj.pullbackAwayιIso 𝒜 f_deg hm g_deg hm' hx).inv
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Limits.pullback.snd (AlgebraicGeometry.Proj.awayι 𝒜 f f_deg hm)
          (AlgebraicGeometry.Proj.awayι 𝒜 g g_deg hm'))
        h) =
    CategoryTheory.CategoryStruct.comp
      (AlgebraicGeometry.Spec.map (CommRingCat.ofHom (HomogeneousLocalization.awayMap 𝒜 f_deg ⋯))) h