(*======================================================== FACE OPERATIONS IN QHMAPS ========================================================*)
(* The following operations are designed for qhmaps, but are defined on fmap for convenience *)
(* Successor F in a face - direct version, designed for qhmaps: *)
Definition F(m:fmap)(x:dart):=
A_1 m di1 (A_1 m di0 x).
(* To have a successor in a (direct) face for x: *)
Definition succf(m:fmap)(x:dart):Prop:=
pred m di0 x /\ pred m di1 (A_1 m di0 x).
(* Decidability of succf:*)

(* Specifications: *)
Lemma succf_dec :
forall (m:fmap)(x:dart),
{succf m x}+{~succf m x}.