induction ls; intuition; simpl in *.
omega.
destruct n.
econstructor; eauto.
destruct (IHls n).
omega.
econstructor; eauto.
Qed.

Theorem rndListElem_support_None :
forall (A : Set) eqd (ls : list A),
In None (getSupport (rndListElem eqd ls)) <->
ls = nil.