(*======================================================== card PROPERTIES OF ORBITS: WITH NOETHERIAN INDUCTION =======================================================*)
(* card OF THE REMAINING / ndN IN THE fmap: *)
Definition P2
(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:forall(m:fmap)(z:dart)(s:set),
(card s < ndN m ->
card (Iter_rem_aux m z s) < ndN m)%nat.