∀ {α : Sort u_2} {β : Sort u_1} (p : α → Prop) [inst : DecidablePred p] (x₀ : { a // p a } → β) (x : α → β)
  (hx : x ∘ Subtype.val = x₀) (a : α),
  ↑((fun x => ⟨fun a => if h : p a then x₀ ⟨a, h⟩ else x ⟨a, h⟩, ⋯⟩) ((fun x a => ↑x ↑a) ⟨x, hx⟩)) a = ↑⟨x, hx⟩ a