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