∀ {F : Type u_4} {R : Type u_2} {A : Type u_1} {B : Type u_3} [inst : CommSemiring R] [inst_1 : Semiring A]
  [inst_2 : Algebra R A] [inst_3 : StarRing A] [inst_4 : Semiring B] [inst_5 : Algebra R B] [inst_6 : StarRing B]
  [inst_7 : FunLike F A B] [inst_8 : AlgHomClass F R A B] [StarHomClass F A B] (f g : F) {a : A},
  f a = g a → star a ∈ (AlgHom.equalizer ↑f ↑g).carrier