∀ {R : Type u_2} {L : Type u_3} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (M : Type u_1)
  [_i1 : AddCommGroup M] [_i2 : Module R M] [_i3 : LieRingModule L M] [_i4 : LieModule R L M],
  (∀ K ∈ {K | LieAlgebra.IsEngelian R ↥K}, K ≠ ⊤ → ∃ K' ∈ {K | LieAlgebra.IsEngelian R ↥K}, K < K') →
    ∀ K ∈ {K | LieAlgebra.IsEngelian R ↥K}, (∀ x ∈ {K | LieAlgebra.IsEngelian R ↥K}, ¬K < x) → K = ⊤