induction 1; intuition; simpl in *.
apply length_getUnique_nz.
apply length_nz_exists in IHwell_formed_comp.
destruct IHwell_formed_comp.
eapply length_flatten_nz.
eapply in_map_iff.
econstructor; intuition; eauto.
eapply H1.
trivial.
apply getAllBvectors_length_nz.
destruct (filter P (getSupport c)); simpl in *; intuition.
Qed.

Lemma filter_NoDup : forall (A : Set)(ls : list A)(P : A -> bool),
NoDup ls ->
NoDup (filter P ls).