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