(*========================================================== PROPERTIES of A and A_1 CLOSURES in hmap ==========================================================*)
(* Each existing dart has a succ in the k-closure : *)

Lemma succ_pred_clos :
forall (m:fmap)(k:dim)(z:dart),
inv_hmap m -> exd m z ->
(cA m k z <> nil /\ cA_1 m k z <> nil).