(*=========================================================
                 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 inj_cF_1 : forall (m:fmap), inv_hmap m -> inj_dart (exd m) (cF_1 m).