∀ {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.Proj 𝒜 ⟶ Z),
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Proj.pullbackAwayιIso 𝒜 f_deg hm g_deg hm' hx).hom
      (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Proj.awayι 𝒜 x ⋯ ⋯) h) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Limits.pullback.fst (AlgebraicGeometry.Proj.awayι 𝒜 f f_deg hm)
        (AlgebraicGeometry.Proj.awayι 𝒜 g g_deg hm'))
      (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Proj.awayι 𝒜 f f_deg hm) h)