∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
  [inst_3 : IsLocalRing R] [inst_4 : IsLocalRing S] [inst_5 : IsLocalHom (algebraMap R S)] [Algebra.EssFiniteType R S]
  [Algebra.FormallyUnramified R S], Algebra.IsSeparable (IsLocalRing.ResidueField R) (IsLocalRing.ResidueField S)