Proof of the LTV

[Questionable]

This is kind of a spin-off of my last thread regarding anarcho-capitalism, but I feel like it's distant enough to warrant starting a new one since the subject of the discussion has completely shifted from concentration/monopolization to the Labor of Theory of Value.

Basically, my opponent has been demanding proof of the LTV for a long time, proof which I am unable to deliver. I can explain the LTV and how it works and how the capitalist needs surplus-labor to expand his empire, but I can't really PROVE it. In my defense, I claimed he couldn't prove how dead capital generates more wealth. Here's what my opponent is saying:

That isn't what I said, but I have offered an explanation: gathering together capital can allow for more efficient production, so both workers and owners get more than if they did otherwise. They pretty much have to get more, otherwise they wouldn't go to work for the owner to begin with. And just because they labor directly on the materials, doesn't mean they "produced" all of the output; the owner had a part as well.

Labor time would clearly have units of time (or people-time). Capital does not have these units; that wouldn't make any sense. So we can't add them. There is nothing to disprove in the equation, because it doesn't say anything.

What's called a use-value? According to wikipedia, the intrinsic value is very different from use-value, which is basically utility and therefore depends entirely on the person using it.

His position seems pretty easy to criticize using the LTV, but it's going around in circles. The argument has been "Capitalists need surplus-labor" "No they don't. Prove it." "Prove that they can't." I know this is bad logic, so I'm looking to give my opponent more concrete evidence of exploitation of labor. If anyone can help me, I'll appreciate it very much.

[Book O'Dead]

This is kind of a spin-off of my last thread regarding anarcho-capitalism, but I feel like it's distant enough to warrant starting a new one since the subject of the discussion has completely shifted from concentration/monopolization to the Labor of Theory of Value.

Basically, my opponent has been demanding proof of the LTV for a long time, proof which I am unable to deliver.

The only answer I could offer is that the capitalist already has a monopoly over the means of production by the time and at the moment in which he purchases the labor power of the worker.