∀ (R : Type u_1) (S : Type u_2) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (p : PrimeSpectrum R)
  (q : ↑(PrimeSpectrum.comap (algebraMap R S) ⁻¹' {p})),
  ((PrimeSpectrum.preimageEquivFiber R S p) q).asIdeal =
    RingHom.ker
      (Algebra.TensorProduct.lift (Ideal.ResidueField.mapₐ p.asIdeal (↑q).asIdeal (Algebra.ofId R S) ⋯)
          (IsScalarTower.toAlgHom R S (↑q).asIdeal.ResidueField) ⋯).toRingHom