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 lattice_bounded :
forall d : preDTA,
bounded_sas_chain bool (ensemble_base state d) (lemd d)
(S (MapCard state d)).