∀ {ι : Type u_1} {β : ι → Type u_2} [inst : DecidableEq ι] [inst_1 : (i : ι) → Zero (β i)]
  [inst_2 : (i : ι) → (x : β i) → Decidable (x ≠ 0)] {i : ι} {b : β i} (w : ι),
  (w ∈ (fun₀ | i => b).support) = (w ∉ {i}) → w ∉ (fun₀ | i => b).support → i = w