Proof using.
intros. unfold logs_leaderLogs_nw, logs_leaderLogs_nw_weak, weak_sanity in *.
intros.
eapply_prop_hyp In In; eauto.
break_exists_exists; intuition; subst; try omega.
break_exists; intuition; eauto.
Qed.
Definition logs_leaderLogs_inductive net :=
logs_leaderLogs net /\
logs_leaderLogs_nw net.

Theorem lift_sorted :
forall net,
refined_raft_intermediate_reachable net ->
logs_sorted (deghost net).