(*===========================================================
                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 not_expe_bottom_B0: forall(m:fmap)(x' x:dart), inv_hmap m -> exd m x -> exd m x' -> let m0 := B m zero x' in ~ expe m x' x -> bottom m0 zero x = bottom m zero x.