intuition.
rewrite <- map_id.
eapply Permutation_sym.
eapply evalDist_getSupport_perm; intuition.
symmetry.
eauto.
Qed.

Lemma sumList_f_inverse : forall (A B : Set)(ls : list A)(f : A -> B)(f_inv : B -> A)(fa : A -> Rat),
(forall a, In a ls -> f_inv (f a) = a) ->
sumList (map f ls) (fun (b : B) => fa (f_inv b) ) ==
sumList ls fa.