∀ {α : Type u} {cmp : α → α → Ordering} {β : Type v} {t : Std.ExtDTreeMap α (fun x => β) cmp} [inst : Std.TransCmp cmp]
  [inst_1 : Inhabited α] {k : α} {f : Option β → Option β},
  Std.ExtDTreeMap.Const.alter t k f ≠ ∅ →
    ((Std.ExtDTreeMap.Const.alter t k f).maxKey! = k ↔
      (f (Std.ExtDTreeMap.Const.get? t k)).isSome = true ∧ ∀ k' ∈ t, (cmp k' k).isLE = true)