Mankiw's Carbon Theorem

On his blog today Greg Mankiw posits the following theorem:

Cap-and-trade = Carbon tax + Corporate welfare

I this theorem just absolutely hits the nail on the head. Politically it looks like some sort of carbon tax or cap-and-trade scheme is coming both for national security and environmental reasons. The real question left is: where will the money from the tax or cap-and-trade scheme go? Will it go to corporations or will it go to the federal government? My favorite suggestion would combine a carbon tax with a reduction on income taxes. Of course I would also favor an increase in federalism in road construction.