∀ (R : Type u_1) (L : Type u_3) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L],
  (LieIdeal.toLieSubalgebra R L (LieIdeal.killingCompl R L ⊤)).toSubmodule = LinearMap.ker (killingForm R L)