(* 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.

(* Specifications: *)
Lemma degree_per_aux: forall(m:fmap)(z:dart),
P_degree_per m z 1 (degree m z).
Theorem degree_per: forall (m:fmap)(z:dart),
inv_hmap m -> exd m z ->
Iter (f m) (degree m z) z = z.