∀ {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp] {k : α},
  (t.erase k).isEmpty = false → ∀ {fallback : α}, (cmp ((t.erase k).maxKeyD fallback) (t.maxKeyD fallback)).isLE = true