Proof using.
intros.
induction ns; intros; auto.
simpl in *.
break_if.
- simpl.
intro.
break_or_hyp.
* find_injection.
contradict H.
left.
trivial.
* contradict H1.
apply IHns.
intro.
contradict H.
right.
assumption.
- apply IHns.
intro.
contradict H.
right.
assumption.
Qed.

Lemma NoDup_map2snd :
forall h (m : B) ns,
NoDup ns ->
NoDup (map2snd m (filter_rel R_dec h ns)).