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!

---

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: