∀ {R : Type u_4} {S : Type u_1} {M : Type u_2} {N : Type u_6} {P : Type u_3} {Q : Type u_5} [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 : AddCommMonoid Q] [inst_7 : Module R M] [inst_8 : Module R N]
  [inst_9 : Module R P] [inst_10 : Module R Q] [inst_11 : Module S M] [inst_12 : IsScalarTower R S M]
  [inst_13 : Coalgebra S M] [inst_14 : Module S N] [inst_15 : IsScalarTower R S N] [inst_16 : Coalgebra S N]
  [inst_17 : Coalgebra R P] [inst_18 : Coalgebra R Q] (f : M →ₗc[S] N) (g : P →ₗc[R] Q),
  CoalgebraStruct.counit ∘ₗ TensorProduct.AlgebraTensorModule.map f.toLinearMap g.toLinearMap = CoalgebraStruct.counit