∀ {F : Type u_1} {R : Type u_2} {A : Type u_3} {B : Type u_4} [inst : CommSemiring R] [inst_1 : Ring A]
  [inst_2 : Algebra R A] [inst_3 : Ring B] [inst_4 : Algebra R B] [inst_5 : FunLike F A B] [AlgHomClass F R A B] (φ : F)
  (a : A), spectrum R (φ a) ⊆ spectrum R a