∀ {R S : CommRingCat} [inst : IsLocalRing ↑R] [inst_1 : IsLocalRing ↑S] {f : R ⟶ S}
  [IsLocalHom (CommRingCat.Hom.hom f)],
  (AlgebraicGeometry.Spec.map f) (IsLocalRing.closedPoint ↑S) = IsLocalRing.closedPoint ↑R