Proof using.
unfold raft_net_invariant_append_entries, prevLog_leader_sublog.
intros. simpl in *.
repeat find_higher_order_rewrite.
find_apply_hyp_hyp. break_or_hyp.
- find_eapply_lem_hyp app_cons_in_rest; [|solve[eauto]].
find_rewrite. break_if; eauto.
find_copy_apply_lem_hyp handleAppendEntries_type_log.
intuition.
+ congruence.
+ repeat find_rewrite.
eapply_prop_hyp In In; eauto.
- find_apply_lem_hyp handleAppendEntries_not_append_entries.
simpl in *. subst. exfalso. eauto 10.
Qed.

Lemma prevLog_leader_sublog_append_entries_reply :
raft_net_invariant_append_entries_reply prevLog_leader_sublog.