induction ls; intuition.
inversion H.
simpl in *.
intuition; subst.
eapply le_trans.
eapply Max.max_lub_r.
eapply le_refl.
eapply fold_left_max_ge_init.
Qed.

Theorem maxList_correct : forall (ls : list nat) n,
In n ls ->
maxList ls >= n.