(* 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 exds_orb_eq_ex :forall(m:fmap)(z t:dart), inv_hmap m -> exd m z -> let s:= Iter_orb m z in let p:= Iter_upb m z in (exds s t <-> exists i:nat,(i < p)%nat /\ Iter (f m) i z = t).