Proof using.
induction l; simpl in *; auto.
intros.
specialize (IHl y (max z a)).
forward IHl; eauto. concludes.
forward IHl; [eapply le_trans; eauto; eauto using Max.le_max_l|].
concludes. auto.
Qed.

Lemma advanceCommitIndex_commitIndex :
forall st h,
commitIndex st <= commitIndex (advanceCommitIndex st h).