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