(*========================================================
 EXISTENCY PROPERTIES OF ITERATED DARTS, upb IN ORBITS...:
	       WITH NOETHERIAN IND. 
=======================================================*)

(* FOR THE FOLLOWING LEMMA: *)

Definition P1
 (m:fmap)(z:dart)(s:set):Prop:=
    let sr := Iter_rem_aux m z s in
    let n := Iter_upb_aux m z s in
    ~ exds sr (Iter (f m) n z).

Lemma not_exds_Iter_rem_upb : forall(m:fmap)(z:dart), let n:= Iter_upb m z in ~ exds (Iter_rem m z) (Iter (f m) n z).