(*===========================================================
                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 succ_zi: forall(m:fmap)(z:dart)(i:nat), inv_hmap m -> exd m z -> ~pred m zero z -> (i + 1 < MA0.Iter_upb m z)%nat -> let zi:= Iter (MA0.f m) i z in succ m zero zi.