induction ls; intuition; simpl in *.
econstructor.
inversion H0; clear H0; subst.
econstructor; eauto.
intuition.
apply in_map_iff in H0.
destruct H0.
intuition.
assert (x = a).
rewrite <- (H x); intuition.
rewrite <- (H a); intuition.
f_equal.
trivial.
subst.
intuition.
Qed.

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