∀ {R : Type u_3} {A : Type u_1} {B : Type u_4} {C : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid A]
  [inst_2 : Module R A] [inst_3 : AddCommMonoid B] [inst_4 : Module R B] [inst_5 : AddCommMonoid C]
  [inst_6 : Module R C] [inst_7 : CoalgebraStruct R A] [inst_8 : CoalgebraStruct R B] [inst_9 : CoalgebraStruct R C]
  (φ₁ : B →ₗc[R] C) (φ₂ : A →ₗc[R] B),
  TensorProduct.map (↑φ₁ ∘ₗ ↑φ₂) (↑φ₁ ∘ₗ ↑φ₂) ∘ₗ CoalgebraStruct.comul = CoalgebraStruct.comul ∘ₗ ↑φ₁ ∘ₗ ↑φ₂