induction ls; intuition; simpl in *.
eapply comp_spec_eq_refl.
comp_simp.
eauto.
Qed.

(* Specifications: *)
Theorem prob_fold_add_false_0 :
forall (A B : Set)(c : Comp A)(ls : list B)(P : A -> bool),
Pr[compFold _ (fun b _ => x <-$ c; ret b && (P x)) false ls] == 0.