∀ {I : Type u} [inst : CategoryTheory.Category.{u, u} I] {S X : AlgebraicGeometry.Scheme}
  (D : CategoryTheory.Functor I AlgebraicGeometry.Scheme) (t : D ⟶ (CategoryTheory.Functor.const I).obj S) (f : X ⟶ S)
  (c : CategoryTheory.Limits.Cone D) (hc : CategoryTheory.Limits.IsLimit c) [∀ (i : I), CompactSpace ↥(D.obj i)]
  [AlgebraicGeometry.LocallyOfFiniteType f] [CategoryTheory.IsCofiltered I]
  [∀ {i j : I} (f : i ⟶ j), AlgebraicGeometry.IsAffineHom (D.map f)] {i : I} (a : D.obj i ⟶ X),
  t.app i = CategoryTheory.CategoryStruct.comp a f →
    ∀ {j : I} (b : D.obj j ⟶ X),
      t.app j = CategoryTheory.CategoryStruct.comp b f →
        CategoryTheory.CategoryStruct.comp (c.π.app i) a = CategoryTheory.CategoryStruct.comp (c.π.app j) b →
          ∃ k hik hjk,
            CategoryTheory.CategoryStruct.comp (D.map hik) a = CategoryTheory.CategoryStruct.comp (D.map hjk) b