Corollary flat_map_constant_length A B c (f: A -> list B) l:
  (forall x, In x l -> length (f x) = c) -> length (flat_map f l) = (length l) * c.

Lemma length_list_power (A B:Type)(l:list A) (l':list B): length (list_power l l') = (length l')^(length l).