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

(* Specifications: *)
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.