Definition lifted_leaders_have_leaderLogs_strong (net : ghost_log_network) :=
    forall h,
      type (snd (nwState net h)) = Leader ->
      exists ll es,
        In (currentTerm (snd (nwState net h)), ll) (leaderLogs (fst (nwState net h))) /\
        log (snd (nwState net h)) = es ++ ll /\
        (forall e : entry, In e es -> eTerm e = currentTerm (snd (nwState net h))).

Lemma lifted_leaders_have_leaderLogs_strong_invariant : forall net, msg_refined_raft_intermediate_reachable net -> lifted_leaders_have_leaderLogs_strong net.