(*========================================================= 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 exd_cF_not_nil : forall (m:fmap)(z:dart),
inv_hmap m -> (exd m z <-> cF m z <> nil).