∀ {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] {m : ℕ} (a : A) (i : ℕ), (GradedRing.proj 𝒜 i) a ^ m ∈ 𝒜 (m * i)