induction c; intuition; simpl in *.
intuition.
destruct (e a a0); subst;
intuition.
eapply sumList_0.
intuition.
eapply ratMult_0.
right.
eapply H.
intuition.
eapply H0.
eapply (in_getUnique (flatten (map (fun b : B => getSupport (c0 b)) (getSupport c)))).
eapply in_flatten.
exists (getSupport (c0 a0)).
intuition.
eapply in_map_iff.
exists a0.
intuition.
exfalso.
eapply H.
eapply in_getAllBvectors.
apply filter_not_In in H.
intuition.
eapply ratMult_0.
right.
eauto.
eapply ratMult_0.
left.
unfold indicator.
rewrite H0.
rewrite ratMult_0_l.
intuition.
Qed.

(* Specifications: *)
Theorem getSupport_not_In_evalDist : forall (A : Set)(c : Comp A)(a : A),
~In a (getSupport c) <-> (evalDist c a == 0).