∀ {α : Type u_2} {β : Type u_1} [inst : DecidableEq β] (x : β) (e : α ≃ { y // y ≠ x }) (b : β),
  (fun a => a.casesOn' x (Subtype.val ∘ ⇑e)) ((fun b => if h : b = x then none else some (e.symm ⟨b, h⟩)) b) = b