∀ {α : Type u} {β : α → Type v} {instOrd : Ord α} {t : Std.DTreeMap.Internal.Impl α β} [Std.TransOrd α]
  [inst : Std.LawfulEqOrd α],
  t.WF →
    ∀ {k : α} {f : Option (β k) → Option (β k)} {fallback : α},
      (Std.DTreeMap.Internal.Impl.alter! k f t).isEmpty = false →
        ((Std.DTreeMap.Internal.Impl.alter! k f t).maxKeyD fallback = k ↔
          (f (t.get? k)).isSome = true ∧ ∀ k' ∈ t, (compare k' k).isLE = true)