∀ {α : Type u} {β : Type v} (toFun toFun_1 : α → Option β) (e_toFun : toFun = toFun_1) (invFun invFun_1 : β → Option α)
  (e_invFun : invFun = invFun_1) (inv : ∀ (a : α) (b : β), invFun b = some a ↔ toFun a = some b),
  { toFun := toFun, invFun := invFun, inv := inv } = { toFun := toFun_1, invFun := invFun_1, inv := ⋯ }