Definition lifted_one_leaderLog_per_term (net : ghost_log_network) : Prop :=
    forall h h' t ll ll',
      In (t, ll) (leaderLogs (fst (nwState net h))) ->
      In (t, ll') (leaderLogs (fst (nwState net h'))) ->
      h = h' /\ ll = ll'.

(* Specifications: *)
Lemma lifted_one_leaderLog_per_term_invariant : forall net, msg_refined_raft_intermediate_reachable net -> lifted_one_leaderLog_per_term net.
Lemma lifted_leaderLog_in_log : forall net leader ll e, msg_refined_raft_intermediate_reachable net -> type (snd (nwState net leader)) = Leader -> In (currentTerm (snd (nwState net leader)), ll) (leaderLogs (fst (nwState net leader))) -> In e ll -> In e (log (snd (nwState net leader))).