induction c; simpl in *; intuition.
subst.
destruct (e a0 a0).
eapply rat1_ne_rat0.
trivial.
congruence.
destruct (e a a0); subst.
intuition.
right.
intuition.
apply in_getUnique_if in H0.
apply in_flatten in H0.
destruct H0.
intuition.
apply in_map_iff in H2.
destruct H2.
intuition.
eapply sumList_0 in H1; eauto.
apply ratMult_0 in H1; intuition.
eapply IHc; eauto.
subst.
eapply H; eauto.
apply (in_getUnique (flatten (map (fun b : B => getSupport (c0 b)) (getSupport c)))).
apply in_flatten.
apply sumList_nz in H0.
destruct H0.
intuition.
apply ratMult_nz in H2.
intuition.
econstructor.
split.
eapply in_map_iff.
econstructor.
split.
eapply eq_refl.
eapply H1.
eapply H.
eauto.
eapply in_getAllBvectors.
apply ratMult_0 in H0.
intuition.
apply ratMult_0 in H1.
intuition.
unfold indicator in *.
case_eq (b a); intuition.
rewrite H1 in H0.
eapply rat1_ne_rat0.
trivial.
eapply filter_not_In.
eauto.
eauto.
eapply ratInverse_nz; eauto.
eapply IHc.
eapply filter_In.
eauto.
trivial.
apply ratMult_nz in H.
intuition.
apply ratMult_nz in H0.
intuition.
unfold indicator in *.
case_eq (b a); intuition;
rewrite H0 in H.
eapply filter_In.
intuition.
eapply IHc.
trivial.
exfalso.
intuition.
Qed.

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