∀ (X : Type u_1) {𝕜 : Type u_4} {A : Type u_3} {B : Type u_2} [inst : TopologicalSpace X] [inst_1 : CommSemiring 𝕜]
  [inst_2 : TopologicalSpace A] [inst_3 : Semiring A] [inst_4 : IsTopologicalSemiring A] [inst_5 : Star A]
  [inst_6 : Algebra 𝕜 A] [inst_7 : TopologicalSpace B] [inst_8 : Semiring B] [inst_9 : IsTopologicalSemiring B]
  [inst_10 : Star B] [inst_11 : Algebra 𝕜 B] (φ : A →⋆ₐ[𝕜] B) (hφ : Continuous ⇑φ) (r : 𝕜),
  { toFun := ⇑φ, continuous_toFun := hφ }.comp ((algebraMap 𝕜 C(X, A)) r) = (algebraMap 𝕜 C(X, B)) r