∀ {α : Type u} {instOrd : Ord α} {β : Type v} {t : Std.DTreeMap.Internal.Impl α fun x => β} [Std.TransOrd α],
  t.WF →
    ∀ {k a : α} {fallback v : β},
      Std.DTreeMap.Internal.Impl.Const.getD (Std.DTreeMap.Internal.Impl.insert! k v t) a fallback =
        if compare k a = Ordering.eq then v else Std.DTreeMap.Internal.Impl.Const.getD t a fallback