∀ (P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme) {Q : AlgebraicGeometry.AffineTargetMorphismProperty}
  [AlgebraicGeometry.HasAffineProperty P Q] {X Y U V : AlgebraicGeometry.Scheme} {f : X ⟶ Y} {g : U ⟶ Y}
  [inst : AlgebraicGeometry.IsAffine U] [AlgebraicGeometry.IsOpenImmersion g] {iV : V ⟶ X} {f' : V ⟶ U},
  CategoryTheory.IsPullback iV f' f g → P.diagonal f → Q.diagonal f'