Pre-historic and pre-colonial cultures are all cro-magnon. Neanderthals don't seem to have been numerous enough to have had neighbours to compete with. The neanderthals died out about 40.000 years ago, well before the end of the last ice age,and their population density doesn't seem to have been high.
And you know this because?
Axioms aren't subject to proof. They are initial assertions - the foundations of a particular mathematical construction.
Human society isn't that kind of construction. It does depend on rules of behavior (which get broken from time to time). Lawyers get rich re-formulating those rules in ways that either make more sense or let their employers make larger profits. The rules prevailing in the US seem to be more aimed at large profits than a more sensible society.