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 card_rem_aux_bis:forall(m:fmap)(z:dart)(s:set), (card s <= ndN m -> card (Iter_rem_aux m z s) <= ndN m)%nat.