I’m currently reading the CLRS Linear Programming chapter and there is something i don’t understand.
The goal is to prove that given a basic set of variables, the associated slack form is unique
They first prove a lemma :
And then they prove the result :
My concern is that to prove the second lemma, they apply the first lemma. However equations (29.79) -> (29.82) only holds for feasable solutions, which is not for any x, so why can they apply the first lemma ?
