∀ {R : Type u} {A : Type v} {B : Type w} {C : Type u₁} [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] {e₁₂ : A ≃ₐc[R] B}
  {e₂₃ : B ≃ₐc[R] C}, ↑(e₁₂.trans e₂₃) = (↑e₂₃).comp ↑e₁₂