Add Parametric Morphism (A B: Set): (@map A B)
  with signature (@ext_eq A B) ==> (@ext_eq (L A) (L B))
  as ne_list_map_ext_eq_morph.

Lemma In_map_inv (T U: Set) (f: T -> U) (l: L T) (y: U): List.In y (map f l) -> exists x, f x = y /\ List.In x l.