Definition lattice_lemd_bounded_1_def (p : prechain bool) : Prop :=
  lattice_lemd_bounded_0_def p ->
  forall m : Map bool, lattice_lemd_bounded_0_def (concat bool p m).

Lemma predta_coacc_0_contain_coacc_ads : forall (d d' : preDTA) (a : ad) (s : state) (c : ad) (p : prec_list) (b : ad) (m : Map bool), preDTA_ref_ok_distinct d' d -> MapGet state d' a = Some s -> MapGet prec_list s c = Some p -> prec_occur p b -> ensemble_base state d' m -> MapGet bool m a = Some true -> MapGet bool (predta_coacc_0 d d' m) b = Some true.