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.

(* Specifications: *)
Lemma degree_diff_aux:forall(m:fmap)(z:dart),
P_degree_diff m z 1 (degree m z).
Theorem degree_diff: forall (m:fmap)(z:dart),
inv_hmap m -> exd m z ->
forall i:nat, 0 < i < (degree m z) ->
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.