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)).