The manipulation with tetrad coefficients shows that abstract index formulas can, in principle, be obtained from tensor formulas with respect to a coordinate tetrad by "replacing greek by latin indices". However care must be taken that a coordinate tetrad formula defines a genuine tensor when differentiation is involved. Since the coordinate vector fields have vanishing Lie bracket (i.e. commute: ∂ ∂ μ μ ∂ ∂ ν ν = ∂ ∂ ν ν ∂ ∂ μ μ ), naive substitutions of formulas that correctly compute tensor coefficients with respect to a coordinate tetrad may not correctly define a tensor with respect to a general tetrad because the Lie bracket is non-vanishing: [ e a , e b ] ≠ ≠ 0 . Thus, it is sometimes said that tetrad coordinates provide a non-holonomic basis.