(* 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 degree_lub: forall(m:fmap)(z:dart), inv_hmap m -> exd m z -> let p:= degree m z in 0 < p /\ Iter (f m) p z = z /\ forall i:nat, 0 < i < p -> Iter (f m) i z <> z.