Proof using.
intros n. functional induction (div2 n); intros; try omega.
specialize (IHn0 (pred a) (pred b)). omega.
Qed.

Lemma wonElection_one_in_common :
forall l l',
wonElection (dedup name_eq_dec l) = true ->
wonElection (dedup name_eq_dec l') = true ->
exists h, In h l /\ In h l'.