∀ (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}
  (eq1 : CategoryTheory.CategoryStruct.comp (CommRingCat.ofHom Algebra.TensorProduct.includeLeftRingHom) h = s.inl),
  (let __src := CommRingCat.Hom.hom h;
      { toRingHom := __src, commutes' := ⋯ }) =
      Algebra.TensorProduct.productMap
        (let __src := CommRingCat.Hom.hom s.inl;
        { toRingHom := __src, commutes' := ⋯ })
        (let __src := CommRingCat.Hom.hom s.inr;
        { toRingHom := __src, commutes' := ⋯ }) →
    h =
      CommRingCat.ofHom
        (Algebra.TensorProduct.productMap
            (let __src := CommRingCat.Hom.hom s.inl;
            { toRingHom := __src, commutes' := ⋯ })
            (let __src := CommRingCat.Hom.hom s.inr;
            { toRingHom := __src, commutes' := ⋯ })).toRingHom