∀ {R : Type u_1} (A : Type u_1) [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A]
  (U : TopologicalSpace.Opens ↑(AlgebraicGeometry.PrimeSpectrum.Top R)) (r : R) (x : ↥U),
  ∃ V,
    ∃ (_ : ↑x ∈ V),
      ∃ i,
        (AlgebraicGeometry.StructureSheaf.isFractionPrelocal R A).pred fun x =>
          (algebraMap R ((x : ↥U) → AlgebraicGeometry.StructureSheaf.Localizations A ↑x)) r (i x)