Definition lattice_bounded_def_1 (p : prechain bool) : Prop :=
lattice_bounded_def_0 p ->
forall m : Map bool, lattice_bounded_def_0 (concat bool p m).

Lemma lattice_bounded_2 :
forall p : prechain bool,
lattice_bounded_def_1 p ->
forall m : Map bool, lattice_bounded_def_1 (concat bool p m).