∀ {α : Type u_2} {β : Type u_1} [inst : DecidableEq α] [inst_1 : DecidableEq β] (x x_1 : α ≃. β) (x_2 : α),
  ∀
    x_3 ∈
      { toFun := fun a => if x a = x_1 a then x a else none,
          invFun := fun b => if x.symm b = x_1.symm b then x.symm b else none, inv := ⋯ }
        x_2,
    x_3 ∈ x x_2