∀ (R : Type u_1) (L : Type u_3) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  [LieAlgebra.IsKilling R L] [IsNoetherian R L] [IsArtinian R L] (H : LieSubalgebra R L) [H.IsCartanSubalgebra],
  LinearMap.ker ((killingForm R L).restrict H.toSubmodule) = ⊥