induction ls; intuition; simpl in *.
econstructor.
destruct (in_dec _ a (getUnique ls _)); eauto.
econstructor; eauto.
Qed.

Theorem length_getUnique_nz : forall (A :Set)(eqd : eq_dec A)(ls : list A),
length ls > 0 ->
length (getUnique ls eqd) > 0.