∀ {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp]
  [inst : Std.LawfulEqCmp cmp] [Inhabited α] {k fallback : α} {f : β k → β k},
  (t.modify k f).getKeyD k fallback = if k ∈ t then k else fallback