Proof using.
unfold wonElection. intros. find_apply_lem_hyp leb_true_le. omega.
Qed.

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.