(*===========================================================
                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 betweene_bottom_x_top: forall(m:fmap)(x:dart), inv_hmap m -> succ m zero x -> betweene m (bottom m zero x) x (top m zero x).