(* 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 inj_F_succf : forall m:fmap, inv_hmap m -> inj_dart (succf m) (F m).