∀ {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [inst : Std.TransCmp cmp] {k : α}
  {he : (t.erase k).isEmpty = false}, ¬cmp k (t.maxKey ⋯) = Ordering.eq → (t.erase k).maxKey he = t.maxKey ⋯