Definition lifted_prevLog_leader_sublog (net : network) : Prop :=
    forall leader p t leaderId prevLogIndex prevLogTerm entries leaderCommit,
      type (snd (nwState net leader)) = Leader ->
      In p (nwPackets net) ->
      snd (pBody p) = AppendEntries t leaderId prevLogIndex prevLogTerm entries leaderCommit ->
      currentTerm (snd (nwState net leader)) = prevLogTerm ->
      0 < prevLogIndex ->
      0 < prevLogTerm ->
      exists ple, eIndex ple = prevLogIndex /\
             eTerm ple = prevLogTerm /\
             In ple (log (snd (nwState net leader))).

Lemma lifted_committed_monotonic : forall net t t' e, lifted_committed net e t -> t <= t' -> lifted_committed net e t'.