Definition logs_leaderLogs_inductive net :=
    logs_leaderLogs net /\
    logs_leaderLogs_nw net.

(* Specifications: *)
Theorem lift_sorted : forall net, refined_raft_intermediate_reachable net -> logs_sorted (deghost net).
Theorem lift_logs_sorted : forall net h, refined_raft_intermediate_reachable net -> sorted (log (snd (nwState net h))).
Lemma lift_nextIndex_safety : forall net, refined_raft_intermediate_reachable net -> nextIndex_safety (deghost net).
Lemma nextIndex_sanity : forall net h h', refined_raft_intermediate_reachable net -> type (snd (nwState net h)) = Leader -> pred (getNextIndex (snd (nwState net h)) h') <> 0 -> exists e, findAtIndex (log (snd (nwState net h))) (pred (getNextIndex (snd (nwState net h)) h')) = Some e.
Lemma update_elections_data_client_request_leaderLogs : forall h st client id c, leaderLogs (update_elections_data_client_request h st client id c) = leaderLogs (fst st).
Lemma update_elections_data_timeout_leaderLogs : forall h st, leaderLogs (update_elections_data_timeout h st) = leaderLogs (fst st).
Lemma update_elections_data_appendEntries_leaderLogs : forall h st t h' pli plt es ci, leaderLogs (update_elections_data_appendEntries h st t h' pli plt es ci) = leaderLogs (fst st).
Lemma update_elections_data_requestVote_leaderLogs : forall h h' t lli llt st, leaderLogs (update_elections_data_requestVote h h' t h' lli llt st) = leaderLogs (fst st).
Lemma update_elections_data_requestVoteReply_leaderLogs : forall h h' t st t' ll' r, In (t', ll') (leaderLogs (fst st)) -> In (t', ll') (leaderLogs (update_elections_data_requestVoteReply h h' t r st)).