∀ (R A B : Type u_1) [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : CommRing B] [inst_3 : Algebra R A]
  [inst_4 : Algebra R B]
  (s : CategoryTheory.Limits.PushoutCocone (CommRingCat.ofHom (algebraMap R A)) (CommRingCat.ofHom (algebraMap R B)))
  {h : (CommRingCat.pushoutCocone R A B).pt ⟶ s.pt},
  CategoryTheory.CategoryStruct.comp (CommRingCat.ofHom Algebra.TensorProduct.includeLeftRingHom) h = s.inl →
    ∀ (r : R), (↑↑(CommRingCat.Hom.hom h)).toFun ((algebraMap R (TensorProduct R A B)) r) = (algebraMap R ↑s.pt) r