Definition predta_coacc_contain_coacc_ads_def_0 (d : preDTA) 
  (a0 a1 : ad) : Prop :=
  coacc d a0 a1 ->
  preDTA_ref_ok d ->
  exists n : nat,
    MapGet bool (power (Map bool) (predta_coacc d a0) (map_mini state d) n)
      a1 = Some true.

Lemma predta_coacc_contain_coacc_ads_1 : forall (d : preDTA) (a : ad) (s : state), MapGet state d a = Some s -> predta_coacc_contain_coacc_ads_def_0 d a a.