(*===========================================================
                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.

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.