(* OK!! BUT omega IS LONG... *)
Definition R1
(m:fmap)(z:dart)(i:nat)(s:set):Prop:=
let sr := Iter_rem_aux m z s in
let n := Iter_upb_aux m z s in
(ndN m - card s <= i <= n)%nat ->
~ exds sr (Iter (f m) i z).

(* Specifications: *)
Lemma LR1 :
forall(m:fmap)(z:dart)(i:nat)(s:set),
let sr := Iter_rem_aux m z s in
let n := Iter_upb_aux m z s in
(ndN m - card s <= i <= n)%nat ->
~ exds sr (Iter (f m) i z).