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_2 : forall p : prechain bool, lattice_lemd_bounded_1_def p -> forall m : Map bool, lattice_lemd_bounded_1_def (concat bool p m).