∀ {K : Type u_2} {L : Type u_3} [inst : LieRing L] [inst_1 : Field K] [inst_2 : LieAlgebra K L]
  [inst_3 : FiniteDimensional K L] {H : LieSubalgebra K L} [inst_4 : H.IsCartanSubalgebra]
  [inst_5 : LieAlgebra.IsKilling K L] (α : LieModule.Weight K (↥H) L),
  LieAlgebra.IsKilling.coroot α =
    2 •
      (α ((LieAlgebra.IsKilling.cartanEquivDual H).symm (LieModule.Weight.toLinear K (↥H) L α)))⁻¹ •
        (LieAlgebra.IsKilling.cartanEquivDual H).symm (LieModule.Weight.toLinear K (↥H) L α)