Definition lattice_bounded_def_2 (A : Set) (m : Map A) : Prop :=
  forall p : prechain bool,
  sas_chain bool (ensemble_base A m) lem p ->
  chain_length bool p <= S (MapCard A m).

(* Specifications: *)
Lemma lattice_bounded_6 : forall A : Set, lattice_bounded_def_2 A (M0 A).
Lemma lattice_bounded_7 : forall (A : Set) (a : ad) (a0 : A), lattice_bounded_def_2 A (M1 A a a0).
Lemma lattice_bounded_8 : forall (A : Set) (m : Map A), lattice_bounded_def_2 A m -> forall m0 : Map A, lattice_bounded_def_2 A m0 -> lattice_bounded_def_2 A (M2 A m m0).
Lemma lattice_bounded_9 : forall (A : Set) (m : Map A), lattice_bounded_def_2 A m.
Lemma lattice_bounded_10 : forall (A : Set) (m : Map A) (p : prechain bool), sas_chain bool (ensemble_base A m) lem p -> chain_length bool p <= S (MapCard A m).
Lemma lattice_bounded : forall (A : Set) (x : Map A), bounded_sas_chain bool (ensemble_base A x) lem (S (MapCard A x)).