Hello,

For any real number we have either or , in particular this is also true if satisfies . Thus instead of showing "If , then or ." one can show these two statements:

- If and , then or .
- If and , then or .

As the first one is obviously true they do not mention it and only prove the last one.

This is true because .

This is a consequence of this inequality: .

We have hence and must have the same sign. Since is non-negative, has to be non-negative too.