∀ {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 : AddRightCancelMonoid ι] [inst_5 : SetLike.GradedMonoid A]
  (r : DirectSum ι fun i => ↥(A i)) {i : ι} (r' : ↥(A i)) (j : ι),
  ↑((r * (DirectSum.of (fun i => ↥(A i)) i) r') (j + i)) = ↑(r j) * ↑r'