Ltac start_unchanged :=
    red; intros; eapply one_leaderLog_per_term_unchanged; eauto; subst.(* solve invariant by lemma which shows leader logs do not change *)
  Ltac unchanged lem :=
    start_unchanged; apply lem.

Lemma pigeon_nodes : forall (q1 q2 : list name), NoDup q1 -> NoDup q2 -> length q1 > div2 (length nodes) -> length q2 > div2 (length nodes) -> exists v, In v q1 /\ In v q2.