General Relativity tensor proof

[regretfuljones]

How would one go about proving this for all coordinate systems?

[Fredrik]

This is very easy. Just use the tensor transformation law, and then the equation given in the question. Then just compare the result to the equation you started with (the tensor transformation law).

\tau'\ ^i_{\ jkl}=[something]\tau^a_{\ bcd}=[something]3\tau^a_{\ dbc}=3\tau'\ ^i_{\ ljk}