induction ls; simpl in *; intuition.
subst.
destruct (in_dec _ a0 (getUnique ls _)); simpl; auto.
destruct (in_dec _ a (getUnique ls _)); simpl.
eapply IHls. trivial.
right.
eapply IHls.
trivial.
Qed.

(* Specifications: *)
Lemma getUnique_NoDup : forall (A : Set)(ls : list A)(eqd: eq_dec A),
NoDup (getUnique ls eqd).