∀ {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap α β cmp} [Std.TransCmp cmp] {k : α} {f : β → β},
  (t.modify k f).maxKey? = Option.map (fun km => if cmp km k = Ordering.eq then k else km) t.maxKey?