∀ {A : Type u_1} {σ : Type u_2} [inst : CommRing A] [inst_1 : SetLike σ A] [inst_2 : AddSubgroupClass σ A] {𝒜 : ℕ → σ}
  [inst_3 : GradedRing 𝒜] (U : (TopologicalSpace.Opens ↑(ProjectiveSpectrum.top 𝒜))ᵒᵖ)
  (a b : (x : ↥(Opposite.unop U)) → HomogeneousLocalization.AtPrime 𝒜 (↑x).asHomogeneousIdeal.toIdeal),
  (AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.isLocallyFraction 𝒜).pred a →
    (AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.isLocallyFraction 𝒜).pred b →
      (AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.isLocallyFraction 𝒜).pred (a * b)