[Picture index](http://www.azimuthproject.org/azimuth/show/Pete+Morcos)

In writing these proofs, I found it quite convenient to have given names to the 1-hop, 2-hop etc. formulas in my earlier posts.

References to earlier posts: [1-hop constraint](https://forum.azimuthproject.org/discussion/2186/petepics-chapter-1-iterated-galois-maps-the-1-hop-constraint), [2-hop inequality](https://forum.azimuthproject.org/discussion/2187/petepics-chapter-1-iterated-galois-maps-the-2-hop-inequality), [3-hop equivalence](https://forum.azimuthproject.org/discussion/2188/petepics-chapter-1-iterated-galois-maps-the-3-hop-equivalence), [4-hop fixed point](https://forum.azimuthproject.org/discussion/2189/petepics-chapter-1-iterated-galois-maps-the-4-hop-fixed-point).