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 nth_zip : forall (A B : Set)(lsa : list A)(lsb : list B) n a b defa defb, length lsa = length lsb -> nth n (zip lsa lsb) (defa, defb) = (a, b) -> nth n lsa defa = a /\ nth n lsb defb = b.