∀ {ι : Type u_1} {A : Type u_3} {σ : Type u_4} [inst : Semiring A] [inst_1 : DecidableEq ι] [inst_2 : AddCommMonoid ι]
  [inst_3 : PartialOrder ι] [CanonicallyOrderedAdd ι] [inst_5 : SetLike σ A] [inst_6 : AddSubmonoidClass σ A]
  (𝒜 : ι → σ) [inst_7 : GradedRing 𝒜] {a b : A} {n i : ι} [inst_8 : Sub ι] [OrderedSub ι] [AddLeftReflectLE ι],
  a ∈ 𝒜 i → i ≤ n → ↑(((DirectSum.decompose 𝒜) (a * b)) n) = a * ↑(((DirectSum.decompose 𝒜) b) (n - i))