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There is no contradiction in this. The choice is determined by R, and libertarian free will is false. Given a particular R, one's choice will be determined and no other choice can possibly be made.

Your line of reasoning also "proves" random events are false (just substitute "random events" for "libertarian free will"). Probably indicates a problem with your reasoning.

Free will only requires that the "will" can act independently of things outside the will. That "will" and "not-will" are both part of reality (R) doesn't change that.
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