intuition.
eapply NoDup_Permutation.
eapply filter_NoDup.
eapply support_NoDup.
eapply filter_NoDup.
eapply support_NoDup.
intuition.
eapply filter_In in H0.
eapply filter_In.
intuition.
eapply getSupport_In_evalDist.
apply getSupport_In_evalDist in H1.
intuition.
apply H1.
eapply eqRat_trans.
eapply H.
trivial.
trivial.
intuition.
eapply filter_In in H0.
eapply filter_In.
intuition.
eapply getSupport_In_evalDist.
apply getSupport_In_evalDist in H1.
intuition.
apply H1.
eapply eqRat_trans.
eapply eqRat_symm.
eapply H.
trivial.
trivial.
Qed.

Lemma evalDist_getSupport_perm_id : forall (A : Set)(c1 c2 : Comp A),
(forall a, eqRat (evalDist c1 a) (evalDist c2 a)) ->
Permutation (getSupport c1) (getSupport c2).