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).