(* EXISTENCY Of THE z^i IN AN INTERVAL *)

Definition exds_int(m:fmap)(z:dart)(a b:nat)(s:set):Prop:=
  forall i:nat, (a <= i <= b)%nat ->  
    exds s (Iter (f m) i z).

Lemma exds_int_gt:forall(m:fmap)(z:dart)(a b:nat)(s:set), (b < a)%nat -> exds_int m z a b s.