Linear Programming: Degeneracy in Simplex Method

Hello everyone,

I am having trouble understanding one line of the proof for a claim that involves degeneracy in the simplex method, all of which are posted below. Idicated by the red arrow is the step that troubles me: "also ".

I have also written my thoughts below.

Thank you very much!

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**Thoughts:**

I know the following from the given fact that the objective value doesn't change after one application of the simplex method:

, since . However, how does the step in red follow from this?

**Actual Question and Proof:**

http://img219.imageshack.us/img219/1047/linprogis.jpg