∀ {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]
  (φ₁ : B →ₐ[R] C) (φ₂ : A →ₐ[R] B), ↑(φ₁.comp φ₂) = (↑φ₁).comp ↑φ₂