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_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.