Definition P2_bis
 (m:fmap)(z:dart)(s:set):Prop:=
  (card s <= ndN m ->
    card (Iter_rem_aux m z s) <= ndN m)%nat.

Lemma upb_pos_aux:forall(m:fmap)(z:dart), exd m z -> (card (Iter_rem m z) < ndN m)%nat.