Non-violence can be derived from any ethical position that views others as equal to yourself in all ways.
Actually, I don't think I agree with this. If everyone is equal and there are a limited amount of resources, why isn't everyone allowed to compete (or fight if necessary) for those resources? To the victor go the spoils? On the contrary, I think it is only when we have some sense of the dignity of the human person or a sense of self-sacrifice for another "equal" that we could hope for non-violence. Not all ethical positions contain a sense of this dignity. Certainly not all contain a sense of self-sacrifice. Ayn Rand's objectivism is all about self-interest. When the interests of the totally self-interested collide with one another, violence is possible and probable. What ethical systems teach self-sacrificial concern (or might I even proffer the word love) for others?
Evidence: Cats don't ask other cats for evidence of their dignity or debate the nature of it in public discussion forums.