unfold intersect in *.
intuition.
apply filter_In in H.
intuition.
destruct (in_dec eqd a ls1).
trivial.
discriminate.
apply filter_In in H.
intuition.
eapply filter_In.
intuition.
destruct (in_dec eqd a ls1); intuition.
Qed.

(* Specifications: *)
Lemma intersect_comm : forall (A : Set)(eqd : eq_dec A)(ls1 ls2 : list A),
NoDup ls1 ->
NoDup ls2 ->
Permutation (intersect eqd ls1 ls2) (intersect eqd ls2 ls1).