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.

(* Specifications: *)
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.
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.
Lemma predta_coacc_contain_coacc_ads_3 :
forall (d : preDTA) (a0 a1 : ad),
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.