∀ {L : Type u_2} [inst : LieRing L] {K : Type u_4} [inst_1 : Field K] [CharZero K] [inst_3 : LieAlgebra K L]
  (H : LieSubalgebra K L) [inst_4 : LieRing.IsNilpotent ↥H] [LieModule.IsTriangularizable K (↥H) L]
  [FiniteDimensional K L] {x : L} {χ : ↥H → K},
  χ ≠ 0 → x ∈ LieAlgebra.rootSpace H χ → IsNilpotent ((LieAlgebra.ad K L) x)