(* Idem: *)

(* Specifications: *)
Lemma pred_exd :
forall (m:fmap)(k:dim)(z:dart),
inv_hmap m -> pred m k z -> exd m z.
Lemma not_exd_A_nil:
forall (m:fmap)(k:dim)(z:dart),
inv_hmap m -> ~exd m z -> A m k z = nil.
Lemma pred_exd_A_1 :
forall (m:fmap)(k:dim)(z:dart),
inv_hmap m -> pred m k z -> exd m (A_1 m k z).
Lemma exd_A_exd :
forall (m : fmap) (k : dim) (z : dart),
inv_hmap m -> exd m (A m k z) -> exd m z.
Lemma exd_cA_1_exd :
forall (m:fmap)(k:dim)(z:dart),
inv_hmap m ->
exd m (cA_1 m k z) -> exd m z.
Lemma exd_cF_1_not_nil : forall (m:fmap)(z:dart),
inv_hmap m -> (exd m z <-> cF_1 m z <> nil).
Lemma exd_cF : forall (m:fmap)(z:dart),
inv_hmap m -> (exd m z <-> exd m (cF m z)).