(*===========================================================
                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_L_B_top_bot: forall(m:fmap)(x z:dart)(H:inv_hmap m), succ m zero x -> exd m z -> x <> z -> let m0:= L (B m zero x) zero (top m zero x) (bottom m zero x) in bottom m0 zero z = if MA0.expo_dec m x z H then (A m zero x) else bottom m zero z.