Definition lowDistApprox_repeat (A : Set)(c : Comp A)(P : A -> bool) a n : Rat -> Prop := 
  let approx := lowDistApprox c a n in
    let empty := sumList_rel (fun a => lowDistApprox c a n) (filter (fun a => negb (P a)) (getSupport c)) in
  ratMult_rel (ratMult_rel (indicator_rel P a)
    (sumList_rel (fun i => (expRat_rel empty i)) (getNats O (S n)))) (* used to be 0 to n *)
  approx.

Lemma lowDistApprox_repeat_sqrt_div2_left_total : forall (A : Set)(c : Comp A)(P : A -> bool) a, well_formed_comp c -> left_total (fun n => (lowDistApprox_repeat c P a (Nat.sqrt (div2 n)))).