∀ {α : Type u} {cmp : α → α → Ordering} {β : Type v} {t : Std.DTreeMap α (fun x => β) cmp} [inst : Std.TransCmp cmp]
  {k : α} {f : β → β} {he : (Std.DTreeMap.Const.modify t k f).isEmpty = false},
  cmp ((Std.DTreeMap.Const.modify t k f).maxKey he) (t.maxKey ⋯) = Ordering.eq