(*========================================================
 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 exd_Iter_orb_upb : forall(m:fmap)(z:dart), inv_hmap m -> exd m z -> let n:= Iter_upb m z in exds (Iter_orb m z) (Iter (f m) n z).