∀ {ι : Type u_1} {A : Type u_2} {σ : Type u_3} [inst : CommRing A] [inst_1 : SetLike σ A]
  [inst_2 : AddSubgroupClass σ A] [inst_3 : AddCommMonoid ι] [inst_4 : DecidableEq ι] (𝒜 : ι → σ)
  [inst_5 : GradedRing 𝒜] (x : Submonoid A),
  HomogeneousLocalization.mk { deg := 0, num := 0, den := 1, den_mem := ⋯ } =
    HomogeneousLocalization.mk { deg := 0, num := 0, den := 1, den_mem := ⋯ }