(* 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 expo_eq_eqs_orb:forall(m:fmap)(x y:dart), inv_hmap m -> exd m x -> exd m y -> (expo m x y <-> eqs (Iter_orb m x) (Iter_orb m y)).