Global Instance Permutation_flat_map (g : A -> list B) :
 Proper ((@Permutation A) ==> (@Permutation B)) (flat_map g).

Lemma Permutation_map_same_l {A} (f : A -> A) (l : list A) : List.NoDup (List.map f l) -> List.incl (List.map f l) l -> Permutation (List.map f l) l.