∀ {I : Type u} [inst : CategoryTheory.Category.{u, u} I] (D : CategoryTheory.Functor I AlgebraicGeometry.Scheme)
  (c : CategoryTheory.Limits.Cone D) (hc : CategoryTheory.Limits.IsLimit c) [CategoryTheory.IsCofiltered I]
  [∀ {i j : I} (f : i ⟶ j), AlgebraicGeometry.IsAffineHom (D.map f)] [∀ (i : I), CompactSpace ↥(D.obj i)] {i : I}
  (U : (D.obj i).Opens),
  (TopologicalSpace.Opens.map (c.π.app i).base).obj U = ⊤ →
    ∃ j fji, (TopologicalSpace.Opens.map (D.map fji).base).obj U = ⊤