I would subtitle this question "Bourbaki's dream." The dream faltered on the foundations. Bourbaki tried to give a half-baked half-formalized naive set theory resulting in an embarrassment of epic proportions (with regard to their volume *Theory of Sets*; of course other volumes have been extremely successful, like the Lie theory volume) that has been detailed by Adrian Mathias, an expert in the field unlike any of the Bourbaki, in a series of recent detailed critiques (not merely his essay *The ignorance of Bourbaki*). What I am trying to suggest is that checking *all* of the previous results will get you hopelessly bogged down in the foundations.