(*========================================================
          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.