Although this is not the "detailed proof" you seek, still you might find Chaitin's own reasoning interesting, as articulated in his *Scientific American* article "The Limits of Reason" ([PDF download link](http://www.umcs.maine.edu/~chaitin/sciamer3.pdf)): <hr /> ![GCincomp][1]<hr /> [1]: https://i.sstatic.net/yMViB.png