Proof using.
red. unfold log_properties_hold_on_ghost_logs. intros.
simpl in *.
subst. repeat find_reverse_rewrite.
eapply_prop_hyp msg_log_property msg_log_property; eauto.
Qed.

Theorem log_properties_hold_on_ghost_logs_invariant :
forall net,
msg_refined_raft_intermediate_reachable net ->
log_properties_hold_on_ghost_logs net.