(* 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).

(* Specifications: *)
Lemma exds_int_gt:forall(m:fmap)(z:dart)(a b:nat)(s:set),
(b < a)%nat -> exds_int m z a b s.
Lemma exds_int_dec : forall(m:fmap)(z:dart)(a b:nat)(s:set),
{exds_int m z a b s} + {~exds_int m z a b s}.