∀ {α : Type u_3} {β : α → Type u_4} (p : α → Prop) [inst : DecidablePred p] (s : (i : α) → Set (β i)),
  ⇑(Equiv.piEquivPiSubtypeProd p β).symm ⁻¹' Set.univ.pi s = (Set.univ.pi fun i => s ↑i) ×ˢ Set.univ.pi fun i => s ↑i