∀ {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.ExtTreeMap α β cmp} [inst : Std.TransCmp cmp]
  {f : α → β → Bool} {k k' : α},
  t.getKey? k = some k' → (Std.ExtTreeMap.filter f t)[k]? = Option.filter (fun x => f k' x) t[k]?