(*=========================================================== expe AND bottom ============================================================*)
(* expo and between in an edge: *)
Definition expe(m:fmap)(z t:dart):=
MA0.expo m z t.
Definition betweene(m:fmap)(z v t:dart):=
MA0.between m z v t.
(* TO HAVE expe_bottom: *)

Lemma bottom_cA: forall(m:fmap)(k:dim)(z:dart),
inv_hmap m -> exd m z ->
bottom m k (cA m k z) = bottom m k z.