Definition lifted_leader_completeness_directly_committed (net : ghost_log_network) : Prop :=
    forall t e log h,
      lifted_directly_committed net e ->
      t > eTerm e -> In (t, log) (leaderLogs (fst (nwState net h))) -> In e log.Definition lifted_leader_completeness_committed (net : ghost_log_network) : Prop :=
    forall t t' e log h,
      lifted_committed net e t ->
      t' > t -> In (t', log) (leaderLogs (fst (nwState net h))) -> In e log.Definition lifted_leader_completeness (net : ghost_log_network) : Prop :=
    lifted_leader_completeness_directly_committed net /\
    lifted_leader_completeness_committed net.

Lemma lifted_leader_completeness_invariant : forall net, msg_refined_raft_intermediate_reachable net -> lifted_leader_completeness net.