Why is this sign, that I highlighted in yellow, changes to the equal sign? Sevens just cancel, why would something else have to happen? Also, we are proving that this expression we started with in our proof is less than $\epsilon$ as we show in the subsequent statement and not equal.
Oh, I think I got it. So they are just explicitly noting that we have this sign <, but the actual quantity after this sign is going to equal to $\epsilon$ hence this equality sign.