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_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).