∀ {R : Type u_3} {A : Type u_1} {B : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Semiring B]
  [inst_3 : Bialgebra R A] [inst_4 : Bialgebra R B] (f : A ≃ₐ[R] B),
  (Algebra.TensorProduct.map ↑f ↑f).comp (Bialgebra.comulAlgHom R A) = (Bialgebra.comulAlgHom R B).comp ↑f →
    TensorProduct.map { toFun := f.toFun, map_add' := ⋯, map_smul' := ⋯ }
          { toFun := f.toFun, map_add' := ⋯, map_smul' := ⋯ } ∘ₗ
        CoalgebraStruct.comul =
      CoalgebraStruct.comul ∘ₗ { toFun := f.toFun, map_add' := ⋯, map_smul' := ⋯ }