intuition.
destruct (in_dec (EqDec_dec _) a (getSupport c)).
rewrite evalDist_seq_step.
rewrite (@sumList_exactly_one _ a).
dist_compute.
eapply getSupport_NoDup.
trivial.
intuition.
dist_compute.
rewrite evalDist_seq_step.
assert (evalDist c a == 0).
eapply getSupport_not_In_evalDist; trivial.
rewrite H.
symmetry.
eapply sumList_0.
intuition.
dist_compute.
Qed.

(* Specifications: *)
Theorem filter_ext : forall (A : Set)(ls : list A)(f1 f2 : A -> bool),
(forall a, f1 a = f2 a) ->
filter f1 ls = filter f2 ls.