(*===========================================================
                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_between_B0:forall(m:fmap)(x z:dart), inv_hmap m -> exd m x -> exd m z -> x <> z -> let z0:= bottom m zero z in ~betweene m z0 x z -> (~MA0.expo m z0 x \/ forall(i j:nat), x = Iter (MA0.f m) i z0 -> z = Iter (MA0.f m) j z0 -> (i < MA0.Iter_upb m z0)%nat -> (j < MA0.Iter_upb m z0)%nat -> (j <= i)%nat).