∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Semiring B]
  [inst_3 : Algebra R A] [inst_4 : Algebra R B] {C : Type u_4} [inst_5 : Semiring C] [inst_6 : Algebra R C]
  (f : B →ₐ[R] C) (g : A →ₐ[R] B), RingHom.ker (f.comp g) = Ideal.comap g (RingHom.ker f)