Proof using.
red. unfold log_properties_hold_on_leader_logs. intros.
match goal with
| H : nwState ?net ?h = (?gd, ?d) |- _ =>
replace gd with (fst (nwState net h)) in * by (rewrite H; reflexivity);
replace d with (snd (nwState net h)) in * by (rewrite H; reflexivity);
clear H
end.
simpl in *.
subst. repeat find_higher_order_rewrite.
destruct_update; simpl in *; eauto; finish.
Qed.

Lemma log_properties_hold_on_leader_logs_reboot :
refined_raft_net_invariant_reboot log_properties_hold_on_leader_logs.