(*===========================================================
                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 between_bottom_B0_bis: forall(m:fmap)(x' x:dart), inv_hmap m -> exd m x -> exd m x' -> x' <> x -> let x0 := bottom m zero x in let m0 := B m zero x' in ((betweene m x0 x' x -> bottom m0 zero x = A m zero x') /\ (~betweene m x0 x' x -> bottom m0 zero x = bottom m zero x)).