Ltac prog_assoc_r :=
    eapply comp_spec_eq_trans_r; [ idtac | eapply comp_spec_assoc].(* A bounded repeat based on fold. *)
Definition repeatMax(A : Set)(eqd : EqDec A)(c : Comp A)(P : A -> bool) def (n : nat):=
  compFold _ (fun a' i => if (P a') then (ret a') else c) def (allNatsLt n).

Lemma list_pred_map_l_if : forall (A B C : Set) (P : C -> B -> Prop)(lsa : list A)(lsb : list B)(f : A -> C), list_pred P (map f lsa) lsb -> list_pred (fun a b => P (f a) b) lsa lsb.