Well... sure, but I think you're still almost purposely missing the point. Take this example - can we prove that a system of differential equations emerges in a meaningful way from discrete systems? Yes, obviously. That's a far cry from the OP's "if you think about it, all things are quantum", which is where this thread started and what I'm talking about.

It also illustrates the actual point pretty well - when you have a good set of differential equations that describe observed phenomena, that higher level of abstraction gives MORE insight into the processes at play, even when we know that it emerges from something more fundamental. Only when that model is a poor approximation do we need to appeal to the more fundamental regime (or when that fundamental regime is what we're studying).