Proof using.
intros A0 B f l1 l2 H; apply permutation_map_ex_aux with (l1 := map f l1);
auto.
Qed.

(* Permutation is compatible with flat_map *)
Theorem permutation_flat_map :
forall (A B : Type) (f : A -> list B) l1 l2,
permutation l1 l2 -> permutation (flat_map f l1) (flat_map f l2).