∀ {α : Type u} {instOrd : Ord α} {β : Type v} {t : Std.DTreeMap.Internal.Impl α fun x => β} [Std.TransOrd α]
  [inst : Inhabited β] (h : t.WF) {k a : α} {v : β},
  Std.DTreeMap.Internal.Impl.Const.get! (Std.DTreeMap.Internal.Impl.insertIfNew k v t ⋯).impl a =
    if compare k a = Ordering.eq ∧ k ∉ t then v else Std.DTreeMap.Internal.Impl.Const.get! t a