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).

(* Specifications: *)
Lemma lattice_lemd_bounded_1 : forall m : Map bool, lattice_lemd_bounded_1_def (single bool m).
Lemma lattice_lemd_bounded_2 : forall p : prechain bool, lattice_lemd_bounded_1_def p -> forall m : Map bool, lattice_lemd_bounded_1_def (concat bool p m).
Lemma lattice_lemd_bounded_3 : forall (p : prechain bool) (d : preDTA), chain bool (ensemble_base state d) (lemd d) p -> chain bool (ensemble_base state d) lem p.
Lemma lattice_lemd_bounded : forall (p : prechain bool) (d : preDTA), sas_chain bool (ensemble_base state d) (lemd d) p -> sas_chain bool (ensemble_base state d) lem p.
Lemma lattice_bounded : forall d : preDTA, bounded_sas_chain bool (ensemble_base state d) (lemd d) (S (MapCard state d)).
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.
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.
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.
Lemma predta_coacc_contain_coacc_ads_0 : forall (d : preDTA) (a0 a : ad) (s : state) (c : ad) (p : prec_list) (b : ad) (m : Map bool), preDTA_ref_ok 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 d a0 m) b = Some true.