Proof using.
unfold raft_net_invariant_append_entries, current_term_gt_zero.
simpl. intuition. find_higher_order_rewrite. update_destruct; subst; rewrite_update.
- find_apply_lem_hyp handleAppendEntries_type. intuition.
repeat find_rewrite. auto.
- auto.
Qed.

Lemma current_term_gt_zero_append_entries_reply :
raft_net_invariant_append_entries_reply current_term_gt_zero.