(* proof sketch: prove for in_any_log. the only time new entries
  come into the system is on a leader, and leaders have leaderLogs in
  their term.  *)

  Definition in_any_log_term_was_created net :=
    forall e,
      in_any_log net e ->
      term_was_created net (eTerm e).Ltac iae_case :=
    match goal with
      | [ H : in_any_log _ _ |- _ ] => invcs H
    end.

Lemma term_was_created_preserved : forall net net' t, term_was_created net t -> (forall h t ll, In (t, ll) (leaderLogs (fst (nwState net h))) -> In (t, ll) (leaderLogs (fst (nwState net' h)))) -> term_was_created net' t.