Proof using.
intros. unfold doLeader, advanceCommitIndex in *.
break_match; try solve [find_inversion; simpl in *; intuition].
break_if; try solve [find_inversion; simpl in *; intuition].
find_inversion. simpl. do_in_map. subst.
simpl in *. find_inversion. intuition.
match goal with
| |- context [pred ?x] =>
remember (pred x) as index
end. break_match; simpl in *.
- right. eauto.
- destruct index; intuition.
Qed.

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