Proof using.
unfold msg_refined_raft_net_invariant_timeout, lifted_maxIndex_sanity, maxIndex_lastApplied, maxIndex_commitIndex.
intuition; simpl in *; repeat find_higher_order_rewrite; update_destruct_simplify; auto;
erewrite handleTimeout_log_same by eauto.
- erewrite handleTimeout_lastApplied; eauto.
- erewrite handleTimeout_commitIndex; eauto.
Qed.

Lemma handleAppendEntries_lastApplied :
forall h st t n pli plt es ci st' m,
handleAppendEntries h st t n pli plt es ci = (st', m) ->
lastApplied st' = lastApplied st.