Proof using.
induction ns; intros; auto.
simpl in *.
rewrite IHns; auto.
unfold update2.
break_if; auto.
break_and; subst.
intuition.
Qed.

(* Specifications: *)
Lemma collate_ls_NoDup_in :
forall ns (f : A -> A -> list B) h mg from,
NoDup ns ->
In from ns ->
collate_ls A_eq_dec ns f h mg from h = f from h ++ [mg].