(*=========================================================
                 CLOSURES cF, cF_1 OF F, F_1 :
==========================================================*)

(* SUCCESSOR IN A COMPLETED FACE: *)

Definition cF (m:fmap)(z:dart):=
  cA_1 m one (cA_1 m zero z).Definition cF_1 (m:fmap)(z:dart):=
  cA m zero (cA m one z).

Lemma cF_1_cF:forall (m:fmap)(z:dart), inv_hmap m -> exd m z -> cF_1 m (cF m z) = z.