∀ {α : Type u} {cmp : α → α → Ordering} {β : Type v} {t : Std.ExtDTreeMap α (fun x => β) cmp} [inst : Std.TransCmp cmp]
  {k : α} {f : β → β},
  Std.ExtDTreeMap.Const.modify t k f ≠ ∅ →
    ∀ {fallback : α},
      (Std.ExtDTreeMap.Const.modify t k f).minKeyD fallback =
        if cmp (t.minKeyD fallback) k = Ordering.eq then k else t.minKeyD fallback