Prove the following results used in the proof of the local flatness theorem in 6 2 (a) The number of independent values of 2x x 'x ' 0 is 40 (b) The corresponding number for 3x x ' x ' xv ' 0 is 80 (c) The corresponding number for g, ' ' 0 is 100 ...

Prove the following results used in the proof of the local fatness theorem in 62 a 2 x x x 0 has 40 ...

Prove the following results used in the proof of the local flatness theorem in 6.2: (a)

Question:

Prove the following results used in the proof of the local flatness theorem in § 6.2:
(a) The number of independent values of ∂2xα/∂xγ'∂xμ'|0 is 40.
(b) The corresponding number for ∂3xα/∂xλ' ∂xμ' ∂xv'|0 is 80.
(c) The corresponding number for gαβ,γ'μ'|0 is 100.