(*===========================================================
                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 nopred_expe_L_i: forall(m:fmap)(i:nat)(k:dim)(x y z:dart), inv_hmap (L m k x y) -> exd m z -> ~pred m zero z -> let t:= Iter (cA m zero) i z in (i < MA0.Iter_upb m z)%nat -> expe (L m k x y) z t.