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).

(* Specifications: *)
Lemma lattice_bounded_1 :
forall m : Map bool, lattice_bounded_def_1 (single bool 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).
Lemma lattice_bounded_3 :
forall p : prechain bool,
lattice_bounded_def_0 p ->
forall m : Map bool, lattice_bounded_def_0 (concat bool p m).
Lemma lattice_bounded_4 : forall p : prechain bool, lattice_bounded_def_0 p.
Lemma lattice_bounded_5 :
forall (p : prechain bool) (A : Set) (m0 m1 : Map A),
sas_chain bool (ensemble_base A (M2 A m0 m1)) lem p ->
exists p0 : prechain bool,
(exists p1 : prechain bool,
sas_chain bool (ensemble_base A m0) lem p0 /\
sas_chain bool (ensemble_base A m1) lem p1 /\
lem (M2 bool (prechain_last bool p0) (prechain_last bool p1))
(prechain_last bool p) /\
chain_length bool p0 + chain_length bool p1 = S (chain_length bool p)).