induction ls; intuition; simpl in *.
inversion H; clear H; subst.
case_eq (P a); intuition.
econstructor; intuition.
eapply H2.
eapply filter_In; eauto.
Qed.

Lemma getSupport_NoDup : forall (A : Set)(c : Comp A),
NoDup (getSupport c).