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).