(* t IS A ITERATED SUCC OF z IN AN ORBIT IS EQUIVALENT TO: there exists j <= p-1 s.t. zj = t: *)

Lemma expo1_ex_j:
forall(m:fmap)(z t:dart), inv_hmap m -> exd m z ->
let p:= Iter_upb m z in
(ex_j m z t (p - 1)%nat <-> expo1 m z t).