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)).