Proof using.
red. unfold log_properties_hold_on_ghost_logs. intros.
simpl in *.
subst.
find_apply_hyp_hyp; intuition; repeat find_rewrite;
try solve [eapply_prop_hyp msg_log_property msg_log_property; eauto].
Qed.

Lemma log_properties_hold_on_ghost_logs_append_entries :
msg_refined_raft_net_invariant_append_entries' log_properties_hold_on_ghost_logs.