∀ (X : AlgebraicGeometry.Scheme) (R : CommRingCat) [inst : IsLocalRing ↑R]
  (xf : (x : ↥X) × { f // IsLocalHom (CommRingCat.Hom.hom f) }),
  (fun f => ⟨f (IsLocalRing.closedPoint ↑R), ⟨AlgebraicGeometry.Scheme.stalkClosedPointTo f, ⋯⟩⟩)
      ((fun xf => CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Spec.map ↑xf.snd) (X.fromSpecStalk xf.fst))
        xf) =
    xf