∀ {R S : CommRingCat} [inst : Algebra ↑R ↑S] (A : CategoryTheory.Under R),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pushout.inr A.hom (CommRingCat.ofHom (algebraMap ↑R ↑S)))
      (CommRingCat.tensorProdObjIsoPushoutObj S A).inv.right =
    CommRingCat.ofHom Algebra.TensorProduct.includeLeftRingHom