Definition CandidateEntriesLowered net e h :=
      currentTerm (nwState net h) = eTerm e ->
      wonElection (dedup name_eq_dec (votesReceived (nwState net h))) = true ->
      type (nwState net h) <> Candidate.

Lemma candidate_entries_lowered' : forall net, CandidateEntries net -> votes_correct net -> cronies_correct net -> forall h h' e, In e (log (snd (nwState net h'))) -> CandidateEntriesLowered (deghost net) e h.