∀ {R : Type u_3} [inst : CommRing R] {A : Type u_1} [inst_1 : CommRing A] [inst_2 : Algebra R A] (L : Type u_2)
  [inst_3 : LieRing L] [inst_4 : LieAlgebra R L] (d : Derivation R A A) (x y : TensorProduct R A L),
  { toFun := ⇑(LinearMap.rTensor L ↑d), map_add' := ⋯, map_smul' := ⋯ } ⁅x, y⁆ =
    ⁅x, { toFun := ⇑(LinearMap.rTensor L ↑d), map_add' := ⋯, map_smul' := ⋯ } y⁆ -
      ⁅y, { toFun := ⇑(LinearMap.rTensor L ↑d), map_add' := ⋯, map_smul' := ⋯ } x⁆