∀ (K : Type u_2) (L : Type u_3) [inst : LieRing L] [inst_1 : Field K] [inst_2 : LieAlgebra K L] [FiniteDimensional K L]
  (H : LieSubalgebra K L) [inst_4 : H.IsCartanSubalgebra] [LieModule.IsTriangularizable K (↥H) L] {α : ↥H → K} {x : L},
  x ∈ LieAlgebra.rootSpace H α →
    (∀ y ∈ LieAlgebra.rootSpace H (-α), ((killingForm K L) x) y = 0) → x ∈ LinearMap.ker (killingForm K L)