∀ {ι : Type u_1} {σ : Type u_2} {R : Type u_4} [inst : DecidableEq ι] [inst_1 : Semiring R] [inst_2 : SetLike σ R]
  [inst_3 : AddSubmonoidClass σ R] (A : ι → σ) [inst_4 : AddCommMonoid ι] [inst_5 : PartialOrder ι]
  [CanonicallyOrderedAdd ι] [inst_7 : SetLike.GradedMonoid A] {i : ι} (r : ↥(A i)) (r' : DirectSum ι fun i => ↥(A i))
  (n : ι), ¬i ≤ n → ↑(((DirectSum.of (fun i => ↥(A i)) i) r * r') n) = 0