(* OK: FOR ALL n0 <= i < j <= nr-1, z^i <> z^j: 
LENGHT: SYMPLIFY: TOO MUCH omegas... *)

Definition P8(m:fmap)(z:dart)(s:set):Prop:= 
 inv_hmap m ->
  (card s <= ndN m ->
   let n0:= ndN m - card s in
   let nr:= Iter_upb_aux m z s in
    exds s (Iter (f m) n0 z) -> 
     diff_int m z n0 (nr - 1))%nat.

Lemma LP8:forall(m:fmap)(z:dart)(s:set), inv_hmap m -> (card s <= ndN m -> let n0:= ndN m - card s in let nr:= Iter_upb_aux m z s in exds s (Iter (f m) n0 z) -> diff_int m z n0 (nr - 1))%nat.