∀ {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.ExtDTreeMap α β cmp} [inst : Std.TransCmp cmp] {k : α}
  {v : β k} {fallback : α},
  (t.insertIfNew k v).maxKeyD fallback = t.maxKey?.elim k fun k' => if cmp k' k = Ordering.lt then k else k'