It seems like I missed something in pumping lemma. Please, help me out
Let's take the simple example from Sipser's book
Prove that language $L = \{0^n1^n | n>=0 \}$ is nonregular. Following the pumping lemma, we choose $s$ to be the string $0^p1^p$, split $s$ into three pieces $s=xyz$ and consider three cases
1) $y$ consists of 0s. (contradiction is understood). OK!
2) $y$ consists of 1s. (contadiction is understood). OK!
3) $y$ consist of both 0s and 1s. "In this case the string xyyz may have the same number of 0s and 1s, but they will be out of order with some 1s before 0s" (but wait a second, we can restrict the order only to allowed one, not understood). not OK!
The same proof can be taken from wikipedia with different explanation
"By the pumping lemma, there must be some decomposition w = xyz with |xy| ≤ p and |y| ≥ 1 such that $xy^iz$ in L for every i ≥ 0. Using |xy| ≤ p, we know y only consists of instances of a"
(but why only a, completely not understood ). not OK!
Please, all I need is just a hist, what I've missed
Thanks!