Open Scope R_scope.
(*=========================================================== between in f-ORBITS: ==========================================================*)
(* v IS between z AND t IN AN f-ORBIT: *)
Definition between(m:fmap)(z v t:dart):Prop:=
inv_hmap m -> exd m z ->
exists i:nat, exists j:nat,
Iter (f m) i z = v /\
Iter (f m) j z = t /\
(i <= j < Iter_upb m z)%nat.
(* OK: *)

(* Specifications: *)
Lemma between_expo1:forall(m:fmap)(z v t:dart),
inv_hmap m -> exd m z ->
between m z v t ->
expo1 m z v /\ expo1 m z t.
Lemma between_expo:forall(m:fmap)(z v t:dart),
inv_hmap m -> exd m z ->
between m z v t ->
expo m z v /\ expo m z t.