induction ls; intuition; simpl in *.
inversion H; clear H; subst.
destruct (in_dec eqd a (getUnique ls eqd)).
exfalso.
apply H2.
eapply in_getUnique_if.
eauto.
f_equal.
eauto.
Qed.

(* Specifications: *)
Lemma getUnique_Permutation : forall (A : Set)(eqd1 eqd2 : eq_dec A)(ls1 ls2 : list A),
Permutation ls1 ls2 ->
Permutation (getUnique ls1 eqd1) (getUnique ls2 eqd2).