∀ {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.ExtTreeMap α β cmp} [inst : Std.TransCmp cmp]
  {f : α → β → Bool}, (Std.ExtTreeMap.filter f t).size = t.size ↔ ∀ (k : α) (h : k ∈ t), f (t.getKey k h) t[k] = true