Definition P_degree_diff(m:fmap)(z:dart)(n1 n2:nat):
  Prop:= inv_hmap m -> exd m z -> 0 < n1 ->  
    forall i:nat, n1 <= i < n2 -> Iter (f m) i z <> z.

Lemma degree_bound: forall (m:fmap)(z:dart), inv_hmap m -> exd m z -> degree m z <= ndN m.