∀ {R : Type u_3} {A : Type u_2} {B : Type u_4} {C : Type u_1} [inst : CommSemiring R] [inst_1 : Semiring A]
  [inst_2 : Semiring B] [inst_3 : Semiring C] [inst_4 : Algebra R A] [inst_5 : Algebra R B] [inst_6 : Algebra R C]
  [inst_7 : CoalgebraStruct R A] [inst_8 : CoalgebraStruct R B] [inst_9 : CoalgebraStruct R C] (φ₁ : B →ₐc[R] C)
  (φ₂ : A →ₐc[R] B), (↑↑((↑φ₁).comp ↑φ₂).toRingHom).toFun 1 = 1