∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : OrderBot α] [inst_2 : DecidablePred fun x => x = ⊥]
  (a : WithBot { a // a ≠ ⊥ }),
  { toFun := fun a => WithBot.unbotD ⊥ (WithBot.map Subtype.val a), invFun := fun a => if h : a = ⊥ then ⊥ else ↑⟨a, h⟩,
          left_inv := ⋯, right_inv := ⋯ }
        ⊥ ≤
      { toFun := fun a => WithBot.unbotD ⊥ (WithBot.map Subtype.val a),
          invFun := fun a => if h : a = ⊥ then ⊥ else ↑⟨a, h⟩, left_inv := ⋯, right_inv := ⋯ }
        a ↔
    ⊥ ≤ a