∀ {A B C P : CommRingCat} (f : A ⟶ B) (g : A ⟶ C) (inl : B ⟶ P) (inr : C ⟶ P),
  CategoryTheory.IsPushout f g inl inr →
    CategoryTheory.IsPullback (AlgebraicGeometry.Spec.map inl) (AlgebraicGeometry.Spec.map inr)
      (AlgebraicGeometry.Spec.map f) (AlgebraicGeometry.Spec.map g)