∀ {α : Type u} {β : α → Type v} {γ : α → Type w} {cmp : α → α → Ordering} {t : Std.DTreeMap.Raw α β cmp}
  [Std.TransCmp cmp] [inst : Std.LawfulEqCmp cmp] {f : (a : α) → β a → Option (γ a)},
  t.WF → ((Std.DTreeMap.Raw.filterMap f t).isEmpty = true ↔ ∀ (k : α) (h : k ∈ t), f k (t.get k h) = none)