∀ {α : Type u} {cmp : α → α → Ordering} {β : Type v} {t : Std.DTreeMap α (fun x => β) cmp} [Std.TransCmp cmp] {k : α}
  {f : Option β → Option β},
  (Std.DTreeMap.Const.alter t k f).maxKey? = some k ↔
    (f (Std.DTreeMap.Const.get? t k)).isSome = true ∧ ∀ k' ∈ t, (cmp k' k).isLE = true