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_2 : forall (d : preDTA) (a0 a1 a2 : ad) (s1 s2 : state) (pl : prec_list) (c : ad), MapGet state d a2 = Some s2 -> MapGet state d a1 = Some s1 -> MapGet prec_list s1 c = Some pl -> prec_occur pl a2 -> coacc d a0 a1 -> predta_coacc_contain_coacc_ads_def_0 d a0 a1 -> predta_coacc_contain_coacc_ads_def_0 d a0 a2.