∀ {ι : Type u_1} {σ : Type u_2} {A : Type u_3} [inst : Semiring A] [inst_1 : DecidableEq ι] [inst_2 : AddCommMonoid ι]
  [inst_3 : PartialOrder ι] [inst_4 : CanonicallyOrderedAdd ι] [inst_5 : SetLike σ A] [inst_6 : AddSubmonoidClass σ A]
  (𝒜 : ι → σ) [inst_7 : GradedRing 𝒜] {I : Ideal A},
  (HomogeneousIdeal.irrelevant 𝒜).toIdeal ≤ I ↔ ∀ i > 0, AddSubmonoid.ofClass (𝒜 i) ≤ I.toAddSubmonoid