(* 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 not_exd_F_1_nil : forall (m:fmap)(z:dart), inv_hmap m -> ~exd m z -> F_1 m z = nil.