∀ {α : Type u} {β : α → Type v} {instOrd : Ord α} {t : Std.DTreeMap.Internal.Impl α β} [Std.TransOrd α],
  t.WF →
    ∀ {k fallback : α},
      (Std.DTreeMap.Internal.Impl.erase! k t).isEmpty = false →
        ((Std.DTreeMap.Internal.Impl.erase! k t).minKeyD fallback = t.minKeyD fallback ↔
          ¬compare k (t.minKeyD fallback) = Ordering.eq)