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_both : forall (A B C D : Set)(P : A -> B -> Prop)(lsa : list A)(lsb : list B)(f1 : A -> C)(f2 : B -> D), list_pred P lsa lsb -> list_pred (fun c d => exists a b, P a b /\ c = (f1 a) /\ d = (f2 b)) (map f1 lsa) (map f2 lsb).