induction 1; intuition; simpl in *.
rewrite fold_add_init_nat.
symmetry.
rewrite fold_add_init_nat.
symmetry.
f_equal.
eauto.
rewrite plus_comm.
trivial.
Qed.

Lemma intersect_NoDup :
forall (A : Set)(eqd : eq_dec A)(ls1 ls2 : list A),
NoDup ls2 ->
NoDup (intersect eqd ls1 ls2).