(* 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).
(* Decidability of succf: *)

(* Specifications: *)
Lemma predf_dec :
forall (m:fmap)(z:dart),
{predf m z}+{~predf m z}.
Lemma predf_exd : forall (m:fmap)(z:dart),
inv_hmap m -> predf m z -> exd m z.