It's entirely possible that my understanding is incomplete, but that was my interpretation of an explanation Eliezer gave me once. Two comments: first, this toy model is ignoring the question of how to go about searching for useful things to prove; you can think of the AI and its descendants as trying to determine whether or not any action leads to goal G. Second, it's true that the AI can't reflectively trust itself and that this is a problem, but the AI's action criterion doesn't require that it reflectively trust itself to perform actions. However, it does require that it trust its descendants to construct its descendants.