∀ {σ : Type u_1} {A : Type u} [inst : CommRing A] [inst_1 : SetLike σ A] [inst_2 : AddSubgroupClass σ A] (𝒜 : ℕ → σ)
  [inst_3 : GradedRing 𝒜] (f : A),
  AlgebraicGeometry.Proj.basicOpen 𝒜 f = ⨆ i, AlgebraicGeometry.Proj.basicOpen 𝒜 ((GradedRing.proj 𝒜 i) f)