[AndrewC]

Thus, the set of hyperbolas and the set of square circles are not one and the same, and it is a false conclusion to consider that a hyperbola must also be a square circle ;)

No need to prove that. Rocks aren't trees.

[general_re]

No need to prove that. Rocks aren't trees.

I read your post as objecting that my definition of trees was broad enough to include rocks, so I added to it in order to explicitly state that rocks are not necessarily trees. Although, I suppose that it is still possible that some rocks are trees, based on what I've got so far - just not all of them ;)