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

Definition P7(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) -> 
     forall j:nat, n0 < j <= nr - 1 ->
       Iter (f m) n0 z <> Iter (f m) j z)%nat.

(* Specifications: *)
Lemma LP7: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) -> forall j:nat, n0 < j <= nr - 1 -> Iter (f m) n0 z <> Iter (f m) j z)%nat.