Proof using rmri.
intros.
eapply lifted_committed_log_allEntries_preserved; eauto;
intros; find_higher_order_rewrite; update_destruct_simplify.
- intros. find_higher_order_rewrite.
erewrite doLeader_same_log; eauto.
- auto.
- repeat find_rewrite. auto.
- auto.
Qed.

Lemma doLeader_message_lci :
forall st h os st' ms m t n pli plt es ci,
doLeader st h = (os, st', ms) ->
In m ms ->
snd m = AppendEntries t n pli plt es ci ->
ci = commitIndex st'.