This has been in my head for a while, and I think I finally have the answer. I was wondering what was so special about the Carnot cycle so it was used to demonstrate the Carnot theorem; the demonstrations I had read didn't used any property specific to the Carnot cycle, but used a reversible engine. Why couldn't it use the Rankine cycle, for example?
And now I've realized that the Carnot theorem hasn't anything to do with the Carnot cycle, does it? It just states that the efficiency of ALL reversible cycles will be the same, but the demonstration talks about an hypothetical reversible cycle, not necessarily the Carnot. Am I right?