∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} {C : Type u_4} [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) (a : A), (φ₁.comp φ₂) a = φ₁ (φ₂ a)