Proof only exists in purely axiomatic systems (e.g., mathematics). Empirical systems have but evidence, since observation must be assumed to be veridical (should one aim to avoid solipsism). Therefore, you have not proven  anything (that genuinely corresponds to the observable universe). Furthermore, your hypothetical is so far abstracted from reality that its meaningful connections to reality, if any, are not at all apparent (which, according to your criticism of my use of language, is entirely the fault of yourself).

Regardless, I have shown that - at least, within the context of your hypotheticals - reality has to be framed around money (perhaps, via a plutocratic hyperreality) for it to be anything but an instrument of augmenting the abuse of scarcity to one's (perhaps, a plutocrat's) advantage.