From Evans' blog:

Proof of Metric Compatibility #1

This is simple and follows directly from the tetrad postulate and Leibniz Theorem from the definition of the symmetric metric as

g sub mu nu = q sup a sub mu q sup b sub nu eta sub a b

where the q’s are tetrads and where eta is the Minkowski metric diag (-1 , 1, 1, 1). The tetrad postulate is the rather obscure name given to the very fundamental property that the complete vector field is independent of the way in which it is expressed in terms of components and basis elements. So this completes a thorough check of the basics of the ECE engineering model and spin connection resonance. Obviously it is of key importance to check the basics. This is precisely what the now obsolete standard physics failed to do.

Proof of Metric Compatibility #2