∀ {α : Type u} {β : α → Type v} {instOrd : Ord α} {t : Std.DTreeMap.Internal.Impl α β} [Std.TransOrd α],
  t.WF →
    ∀ {k a : α} {v : β k},
      (Std.DTreeMap.Internal.Impl.insertIfNew! k v t).getKey? a =
        if compare k a = Ordering.eq ∧ k ∉ t then some k else t.getKey? a