intuition.
eapply dat_exists_h.
trivial.
Qed.
Fixpoint lowDistApproxFromTree(A : Set)(eqd : eq_dec A)(t : DistApproxTree A)(a : A) :=
match t with
| dat_leaf o =>
match o with
| None => 0
| Some a' => if (eqd a a') then 1 else 0
end
| dat_internal t1 t2 =>
(lowDistApproxFromTree eqd t1 a) * (1 / 2) + (lowDistApproxFromTree eqd t2 a) * (1 / 2)
end.
Definition lowDistApprox_ls (A : Set)(c : Comp A) a n (ls : Blist) r :=
exists vals count,
rel_map (fun s v => (evalDet c (ls ++ s) v)) (getAllBlists n) vals /\
pred_count (eq (ca_done a)) vals count /\
count /expnat 2 n == r.

Lemma lowDistApprox_ls_impl : forall n (A : Set)(c : Comp A) a r,
lowDistApprox c a n r ->
lowDistApprox_ls c a n nil r.