(* OK: ALL z^i FOR n0 <=i <= nr-1 EXIST IN s: *)

Definition P6(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) -> 
      exds_int m z n0 (nr - 1) s)%nat.

Lemma LP6: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) -> exds_int m z n0 (nr - 1) s)%nat.