∀ (R : Type u_5) (S : Type u_4) (M : Type u_1) (N : Type u_2) (P : Type u_3) [inst : CommSemiring R]
  [inst_1 : CommSemiring S] [inst_2 : Algebra R S] [inst_3 : AddCommMonoid M] [inst_4 : AddCommMonoid N]
  [inst_5 : AddCommMonoid P] [inst_6 : Module R M] [inst_7 : Module R N] [inst_8 : Module R P] [inst_9 : Module S M]
  [inst_10 : IsScalarTower R S M] [inst_11 : Coalgebra S M] [inst_12 : Module S N] [inst_13 : IsScalarTower R S N]
  [inst_14 : Coalgebra S N] [inst_15 : Coalgebra R P],
  TensorProduct.map ↑(TensorProduct.AlgebraTensorModule.assoc R S S M N P)
        ↑(TensorProduct.AlgebraTensorModule.assoc R S S M N P) ∘ₗ
      CoalgebraStruct.comul =
    CoalgebraStruct.comul ∘ₗ ↑(TensorProduct.AlgebraTensorModule.assoc R S S M N P)