∀ {ι : Type u_2} {β : ι → Type u_1} [inst : (i : ι) → Zero (β i)] [inst_1 : DecidableEq ι] (p : ι → Prop)
  [inst_2 : DecidablePred p] (i : ι) (x : β i) (j : ι),
  ((if p i then fun₀ | i => x else 0) j = if p i then (fun₀ | i => x) j else 0) →
    (DFinsupp.filter p fun₀ | i => x) j = (if p i then fun₀ | i => x else 0) j