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).

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