intuition.
eapply maxList_correct_h.
trivial.
Qed.
(* relational folds and other llist operations *)
Inductive pred_count(A : Type)(p : A -> Prop) : list A -> nat -> Prop :=
| pc_nil :
pred_count p nil 0
| pc_yes :
forall ls n a,
pred_count p ls n ->
p a ->
pred_count p (a :: ls) (S n)
| pc_no : forall ls n a,
pred_count p ls n ->
~p a ->
pred_count p (a :: ls) n.

Lemma pred_count_le_length : forall (A : Type)(P : A -> Prop) ls c,
pred_count P ls c ->
(c <= length ls)%nat.