∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} {X : AlgebraicGeometry.Scheme}
  (𝒰 : AlgebraicGeometry.Scheme.Cover (AlgebraicGeometry.Scheme.precoverage P) X)
  [inst : CategoryTheory.Category.{v_1, u_1} 𝒰.I₀] [inst_1 : 𝒰.LocallyDirected],
  (𝒰.functorOfLocallyDirected.comp AlgebraicGeometry.Scheme.forget).IsLocallyDirected