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## Homework Statement

I've been reading a textbook on tensor analysis for a while. The book uses the conclusion of "covariant differentiation commutes with contraction" directly and I searched around and found most people just use the conclusion without proof.

## Homework Equations

For example, [tex]\nabla_{i}T^{jk}_{kl}[/tex].

## The Attempt at a Solution

I believe it can be interpreted in two ways. First, form the variant [tex]T^{jk}_{kl}[/tex] with two free indices j, l and apply [tex]\nabla_{i}[/tex] to that tensor; Or, apply [tex]\nabla_{i}[/tex] to the tensor [tex]T^{jk}_{ml}[/tex] and contract m and k. If the two interpretations lead to the same result, it should then be proved.

Any help is appreciated!

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