intros.
specialize (getSupport_correct c1).
specialize (getSupport_correct c2).
intros.
inversion H0; clear H0.
inversion H1; clear H1.
intuition.
apply H3.
intuition.
eapply H4; eauto.
eapply eqRat_trans.
eapply H.
eauto.
eapply H4.
intuition.
eapply H3; eauto.
eapply eqRat_trans.
eapply eqRat_symm.
eapply H.
eauto.
Qed.

Lemma perm_map_in : forall (A B : Set)(lsa : list A)(lsb : list B)(f : A -> B)(f_inv : B -> A),
(forall b, In b lsb -> f (f_inv b) = b) ->
(forall a, In a lsa <-> In (f a) lsb) ->
NoDup (map f lsa) ->
NoDup lsb ->
Permutation (map f lsa) lsb.