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).

Lemma lattice_bounded : forall (A : Set) (x : Map A), bounded_sas_chain bool (ensemble_base A x) lem (S (MapCard A x)).