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

Lemma In_map_inv (A B: Set) (e: B) (f: A -> B) (t: T A): In e (map f t) -> exists e', e = f e' /\ In e' t.