induction ls; intuition; simpl in *.
intuition.
intuition.
subst.
destruct (eqd a0 a0); subst; intuition.
destruct (eqd a0 a); subst; intuition.
Qed.

(* Specifications: *)
Lemma rndListElem_support:
forall (A : Set)(eqd : EqDec A)(ls : list A) a,
In a ls <->
In (Some a) (getSupport (rndListElem eqd ls)).