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 pl_coacc_contain_coacc_ads : forall (d : preDTA) (p : prec_list) (a : ad), prec_occur p a -> prec_list_ref_ok p d -> MapGet bool (pl_coacc d p) a = Some true.