1. I stepped away from this for a while. I took a look at your solution in the answer linked previously. I'm going to be honest here but I have little idea what intervals have to do with integration. I do get the intuition. But not the formality.
2. You're picking a point where y is *not* 0. You're proving that IF (subcontext starts here) such a point exists, there must be some at least open neighbourhood centered at that point such that y is not 0 there as well. This is have no idea how to formally prove. I suppose there's a theorem that I forgot that allows me to say this. However I did …