∀ {R : Type u} {A : Type v} {B : Type w} {C : Type u₁} {D : Type v₁} [inst : CommSemiring R] [inst_1 : Semiring A]
  [inst_2 : Semiring B] [inst_3 : Semiring C] [inst_4 : Semiring D] [inst_5 : Algebra R A] [inst_6 : Algebra R B]
  [inst_7 : Algebra R C] [inst_8 : Algebra R D] (φ₁ : C →ₐ[R] D) (φ₂ : B →ₐ[R] C) (φ₃ : A →ₐ[R] B),
  (φ₁.comp φ₂).comp φ₃ = φ₁.comp (φ₂.comp φ₃)