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