∀ {α : Type u} {β : α → Type v} {instOrd : Ord α} {t : Std.DTreeMap.Internal.Impl α β} [Std.TransOrd α]
  [inst : Inhabited α] (h : t.WF) {k : α} {v : β k},
  (Std.DTreeMap.Internal.Impl.insertIfNew k v t ⋯).impl.minKey! =
    t.minKey?.elim k fun k' => if compare k k' = Ordering.lt then k else k'