proposition: Lemma list_power_length (A B:Type)(l:list A) (l':list B): length (list_power l l') = (length l')^(length l).
proof: Proof. induction l as [ | a m IH ]; [reflexivity|]. cbn. rewrite flat_map_constant_length with (c := length l'). - rewrite IH. apply Nat.mul_comm. - intros x H. apply map_length. Qed.
imports: PeanoNat