∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [inst : AlgebraicGeometry.IsImmersion f]
  (U : (↑(AlgebraicGeometry.Scheme.Hom.coborderRange f)).Opens),
  AlgebraicGeometry.Scheme.Hom.app (AlgebraicGeometry.Scheme.Hom.liftCoborder f) U =
    CategoryTheory.CategoryStruct.comp
      (AlgebraicGeometry.Scheme.Hom.app f
        ((AlgebraicGeometry.Scheme.Hom.opensFunctor (AlgebraicGeometry.Scheme.Hom.coborderRange f).ι).obj U))
      (X.presheaf.map (CategoryTheory.eqToHom ⋯).op)