(* Predecessor in a face - direct version: *)

Definition F_1 (m:fmap)(z:dart):=
  A m zero (A m one z).(* To have a predecessor in a (direct) face for z: *)

Definition predf(m:fmap)(z:dart):Prop:=
  succ m one z /\ succ m zero (A m one z).

Lemma F_1_F : forall (m:fmap)(z:dart), inv_hmap m -> exd m z -> exd m (F m z) -> F_1 m (F m z) = z.