∀ {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} [H.IsCartanSubalgebra] [LieAlgebra.IsKilling K L] [LieModule.IsTriangularizable K (↥H) L]
  [PerfectField K] {x : L}, x ∈ H → ((LieAlgebra.ad K L) x).IsSemisimple