∀ {α : Type u} {cmp : α → α → Ordering} {β : Type v} {t : Std.DTreeMap.Raw α (fun x => β) cmp} [Std.TransCmp cmp],
  t.WF →
    ∀ {k a : α} {fallback v : β},
      Std.DTreeMap.Raw.Const.getD (t.insertIfNew k v) a fallback =
        if cmp k a = Ordering.eq ∧ k ∉ t then v else Std.DTreeMap.Raw.Const.getD t a fallback