(* 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.