∀ {ι : Type u_3} [inst : DecidableEq ι] {A : ι → Type u_2} {R : Type u_1} [inst_1 : (i : ι) → AddCommMonoid (A i)]
  [inst_2 : Semiring R] (f : (i : ι) → A i →+ R), (↑(DirectSum.toAddMonoid f)).toFun 0 = 0