Since the whole theory won't fit in one wikipedia article, I suggest you read the first chapters or either a) Mas-Collel, Whinston and Green or b) Kreps, Microeconomic Foundations I (not the old undergrad book from him)
This would provide you with the theory to understand this result in a more mathematical correct way.
axioms: * given same price, consumer goes for higher grade product. * as relative price difference decreases, some consumers start going for higher grade product. * rules of arithmetic.
in any case, it seems that we have appreciation for different things. you prefer detailed verbosity, i prefer a simple idea that can be easily understood.
great and profound ideas are not necessarily complex, many of them are quite simple. let's keep them that way.
Did you read my comment? That's exactly what I wrote. This is not a "theorem". Theorems live inside theories, they're logically implied by axioms of the theories. That basic arithmetic proves nothing of the sort.