∀ {X Y S : AlgebraicGeometry.Scheme} {f : X ⟶ S} {g : Y ⟶ S} (t : ↥(CategoryTheory.Limits.pullback f g)),
  CategoryTheory.Limits.HasPushout
    (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.residueFieldCongr ⋯).inv
      (AlgebraicGeometry.Scheme.Hom.residueFieldMap f (AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint t).x))
    (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.residueFieldCongr ⋯).inv
      (AlgebraicGeometry.Scheme.Hom.residueFieldMap g (AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint t).y))