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 st_coacc_contain_coacc_ads : forall (d : preDTA) (s : state) (c : ad) (p : prec_list) (a : ad), state_ref_ok s d -> MapGet prec_list s c = Some p -> prec_occur p a -> MapGet bool (st_coacc d s) a = Some true.