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