destruct c; intuition; simpl in *.
econstructor.
apply in_nil.
econstructor.
eapply getUnique_NoDup.
eapply getAllBvectors_NoDup.
eapply filter_NoDup.
eapply getSupport_NoDup.
Qed.

Lemma filter_not_In : forall (A : Set)(ls : list A)(P : A -> bool) a,
(~In a ls) \/ P a = false <->
~In a (filter P ls).