(* Note that, in a hmap m, we have neither exd m z -> A m k z <> nil nor exd m z -> A_1 m k z <> nil *)
(* Note also: *)

(* Specifications: *)
Lemma A_nil: forall (m:fmap)(k:dim),
inv_hmap m -> A m k nil = nil.
Lemma A_1_nil: forall (m:fmap)(k:dim),
inv_hmap m -> A_1 m k nil = nil.
Lemma succ_exd_A :
forall (m:fmap)(k:dim)(z:dart),
inv_hmap m -> succ m k z -> exd m (A m k z).