(* OK: *)

Definition P_degree_per(m:fmap)(z:dart)(n1 n2:nat):
  Prop:= inv_hmap m -> exd m z -> 0 < n1 -> n2 <= ndN m ->  
   Iter (f m) n2 z = z.

Theorem expo1_eq_exds_orb :forall(m:fmap)(z t:dart), inv_hmap m -> exd m z -> (expo1 m z t <-> exds (Iter_orb m z) t).