Corollary filter_length f (l : list A) : length (filter f l) + length (filter (fun x => negb (f x)) l) = length l.Corollary filter_length_le f (l : list A): length (filter f l) <= length l.

Lemma filter_length_forallb f (l : list A): length (filter f l) = length l -> forallb f l = true.