induction ls; simpl in *; intuition.
destruct (P a); simpl.
eapply IHls.
rewrite fold_add_body_eq.
eapply IHls.
symmetry.
eapply ratAdd_0_r.
intuition.
Qed.

(* Specifications: *)
Theorem evalDist_left_ident_eq : forall (B : Set)(eqd : EqDec B)(b : B)(A : Set)(c2 : B -> Comp A)  a,
(evalDist (x <-$ ret b; (c2 x)) a) == (evalDist (c2 b) a).