intuition.
eapply NoDup_Permutation.
eapply map_NoDup.
intuition.
eapply getSupport_NoDup.
eapply getSupport_NoDup.
intuition.
apply in_map_iff in H3.
destruct H3.
intuition.
subst.
eapply getSupport_In_evalDist.
intuition.
eapply getSupport_In_evalDist.
eauto.
eapply eqRat_trans.
eapply H1.
trivial.
trivial.
eapply in_map_iff.
econstructor.
split.
eapply H.
trivial.
eapply getSupport_In_evalDist.
intuition.
eapply getSupport_In_evalDist.
eapply H3.
rewrite H2.
trivial.
trivial.
Qed.

Lemma evalDist_getSupport_filter_perm : forall (A: Set)(c1 : Comp A)(c2 : Comp A)(P : A -> bool),
(forall a, P a = true -> eqRat (evalDist c1 a) (evalDist c2 a)) ->
Permutation (filter P (getSupport c1)) (filter P (getSupport c2)).